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toAntisymmetrization hfor HasSeparating Subadditive Subperm ##Inacc objD ##izingMap AddQuotient hsnd hscomp hxe hxK comp✝¹ ##FinalModel ofStep ofSigmaCofork ##entIdeal RingSubgroup hadj FiniteInter ##OfD ##OfCof ##OfComplemented invLHom hgx IsCHS IsLawson hnodup hnontriv ##inals algebraMapCLM id✝ id✝¹ ##oundaries succNth hc1 hchain finv ##abell natSize ##DiffBounded evalHom ↑↑l ↑↑u ↑↑D ModSum selfBasis comapOn aestabilizer addU addIndex sumFinsupp sumPi ##Pregroupoid subcover this✝⁶ ##WithZeroMap ##HomologySelfIso i₁✝ trNat ##vexOn hu2 Monadic getLeft hkf starClosure unitOfC hzy hz1 hS₃ equivTo equivTuple hμn h2x hqd hqW ##LimitElement ↑kl negRev contSupp ##inaryPart minpolyGen 1322 hj0 reverseOp hφg pbar dualProd fromFinalModel ##OpColimit ##PosNum LiftP totalVar totalFlipIso hN₂ basisUnique ts✝ IsWellOrderLimitElement SeqRight hG✝ divMonomial takeD hins rs₁ bitraverse ##Coequalizers CommRingCatᵒᵖ stepSet sigmaMk colLen conjExponent G₂ᶜ toAddHom findMin aux₁ toContinuousMultilinearMap embeddingsMatrix hEF ##Injectives SuccDiffBounded nhdsWithin ##EquivOfSurjective fixedField nz✝¹ IsKleinFour measurableEmbedding essInf hH₁ hH₂ ReflectsFinite ##WeightSpace noncommFold MulPosReflectLT finsetBasisIndex reduced✝¹ sectionsMap h𝒜₁ isoOfEquivalence HcJ mapDomainAlgHom rbar hxU₁ ⇑Laurent AssocQuotient ReflGen uliftMap binaryCoproductIso prM toNonUnitalAlgHom toNonUnitalSubring fundamentalInterior fundSystem toΓSpecBase singleObjHomologySelfIso AddEquivClass ##ImInfty Blank removeZero guard nodupKeys ##EquivProdPi essImageInclusion ιMapBifunctorBifunctor₂₃MapObj hrsz contDiffPregroupoid cotangentSpaceBasis ##TensorHomMap CharacterSpace kernelSubobjectIso liftOn₂ locallyRingedSpaceAdjunction localTrivAt eps toLieModuleHom periodicOrbit IsCancelAdd directSum Factorisation mvPolynomialX IsLocalAtSource hmaps EnoughInjectives 512 Mᵈᵃᵃ RankCondition ##Coboundaries infLERight InvariantBasisNumber ↿fun ιInvApp ⇑DomMulAct ⇑DomAddAct DirSupInacc Γ₂N₂ToKaroubiIso rootOfSplitsXPowSubC functorCategoryMonoidal iU₁U QuasiconvexOn IsFiniteAdele rtakeWhile differentIdeal shiftShortComplexFunctorIso ##AssociatedPrime ConstructProducts LazyList Gmodule ##Postcomp instIsEmptyEmpty HasSeparatingCover AddQuotientMeasureEqMeasurePreimage RingSubgroupsBasis ##OfCofinals IsCHSHTuple ##abelling ModSumCongr sumPiEquivProdPi unitOfCoprime totalVariation ⇑LaurentPolynomial 232 38 Colimit Creates GL Geometry Hσ Hgcd IA Prom QFactors R0Space S⁰ S3 ay and bz cx hΨ hℱ hil hNN ima l₁₂ npow ngn torus u5 zα ¬⊥ ¬∫⁻ Γg ⅟x ##low ##Reduced ##sProd ##a₂ ##ause ##Lm ##Mop ##ginaryPart ##PDeriv ##bl ##b0 ##Bet ##ε0 ##996 ##insert ##onential ##ingLemma IsAssociatedPrime toCommRing toOplax toUnitHom ##iftr ##ilinear hfng ##EqTop HasColimitsOfSize ##MulLin Precomp ##AtInfinite read MulLECancellable hxv mkDerivation ##ionBet ofZlattice hpX RingFilterBasis ##TopOrder M₁₂ ##itiveAddChar clPrehaar prodPrime ⇑f✝ ##ityReduced htU ht₃ ##RightResolution hml finOrthonormalBasis toFunAlgHom natPred liftQ hix hyo ↑↑m leftDual leftZigzag comb comapSubmodule ##SupQuotient asEmpty rightZigzag impl l₂₃ sumAssoc ##Presieve Clause x₂✝ shiftEquiv hu1 i₂✝ hl2 kerSquare imagePresheaf exponential ↑rq ↑r₁ hPG partDen ##AuxSeq ↑e₃ h2b0 isoApp PrimitiveAddChar nonUniform G₀ˣ ##BoundedFormula hB✝ hBX transnum subtypeEmb ↑π₀ absorbs VectorAll hwt ##Generate ihxy OneOne hjl hj₂₃ hφ₁ fromRel fromOpposite fromRightResolution ↑u₀ I₂₃ iteratedPDeriv LEComap fslope hR0 GammaAux openness hJ0 onBoundedFormula ##GenTopology ##KanLift IsMulHom d₁0 OverArrows ##EquivalenceFunctor hδε ##Sylow ↑ULift ↑C⁻¹ diagonalSucc ringBasis elim0 step2 OfAr hQε0 QuasiCompact QuasiErgodic rTensorOne lTensorOne pushoutCocone Computability reindexRange SuccChain hfmE linHom linMulLin countableBasis Semiconj₂ hπp gaugeSeminormFamily homMk₃ ##OfIsIso ##MonoidalFunctorPUnit cdf hdivp ##lySupported regularityReduced Hcf IsAdjMatrix ¬↑n toOrderIso IsPrenex binaryBiproduct sieve₀ hχ₂ ##Repr toFiniteAux HdJ wideSpan fundamentalSequence ShrinkingLemma RestrictGenTopology removeNone convergent cpt hunion toBCF shortComplexH ιMapBifunctor₁₂BifunctorMapObj BoundaryGE ##OfCones ##010 CommMonFunctorCategoryEquivalence IsUnramifiedAtInfinite cotangentComplex ##BraidedFunctorPUnit NonarchimedeanRing curr ExponentialIdeal ##CosetEquivalence transferSylow mkPiAlgebraFin toPermHom hdnf ##SpeedOn IsQuasiregular cantorFunctionAux ##ThroughHomotopy quotQuotEquivComm hanti projectiveSeminormAux conjugatesOf DirSupClosed optimalGHInjl optimalGHInjr DiagramOfCones toSheafedSpaceGlueData plusPlusAdjunction coreflectorAdjunction ihyx irreducibleComponents HasUnitSpeedOn boolIndicator IsStableUnderComposition regionBet node4L ##OfCardEq EstimatorData UnivLE presieveOfCoveringAux toLaxMonoidalFunctor toPullbackDiag ColimitCocone QFactorsThroughHomotopy imaginaryPart torusMap Γgerm ##sProdEqOne toCommRingCatIso ofZlatticeBasis prodPrimeFactors kerSquareLift nonUniforms transnumAuxSeq OfArity IsUnramifiedAtInfinitePlaces regionBetween 61 78 88 A⁄R B₁₂ Counit GSMul Hu HN IΨ IΦ J⁻¹ Kᵐᵒᵖ L⁰ Mg M⁰ NNN Pal Piv Se Us Zag average b₁₂ cts d⁻¹ dOne fall grothendieck hIn jx kn lW light linf metricSpace nh ortho qmp rle si uᶜ vᶜ wh wDest yY zw zZ ¬w ¬lt η₁ η₂ νs σa σb τ✝ φm ↥J ↥m ⇑u ⇑𝒰 ⇑Topology ##eSubfamily ##rite ##rome ##Ret ##Rule ##sing ##sInver ##code ##ader ##AB ##hin ##Mellin ##EEqFun ##δ₀ ##εNFA ##97 ##leisli ##ingLeft IsKan function funLeft Finsubgraph FineSubfamily ##imp mapGraph mapNatTrans inst✝³⁸ toMonoid toSheaf toComposition toεNFA HasMellin Subseq ##Init ##Insert ##Clopen rees Property homDiagram FilterBasis hxDh ##tyOp ofComon ofFreeMonoid ##IsLocal hgr ##AlgebraHom ##UnitCounit ##EquivDFinsupp ##ssImage hnn SeminormedCommRing CofiniteTopology h₁₂₃ ##RightIso ↑s₄ ##₁₂IndexData LocalPredicate FunctorsInver sndFrom ##ormalize liftMonoidWithZeroHom a₁₁ hi0 evalOrderHom ↑↑V ↑↑∅ a₂₁ a₂₂ a₂J₂ ↑fun S₁✝ asAlgebraHom hdb addWellApproximable 108 subst subLeft subRight b₂₁ b₂₂ QuotientAction b₁₁ he2 piScalarRight hvt hvz ##indrome M₃✝ neZero hlH hUt hPg hPf MulActionHomClass TensorSign ##DualEquivalence hzr hS₀ 1279 LeftCommutative equivCongr equivEss WithLower orderDualEquivalence ##Hahn ##PropertyFixed hBc ##AdjoinRoot infPrepartition T25Space hAn ##TypeToCat ¬p₁ setSeq ##IndexEquiv hφx dualNumber hKd hKf incr fromEnd IsThin ##sToCycles head₁ ##ImageOfReflective B₁₁ hαβ eval₂RingHom TriangleOpEquivalence total✝ total✝¹ hNx LinearOrderedAddCommGroupWithTop basisOfFraction cmpEq ys₂ ##₂₃IndexData onFinset ##MkCore SeqLeft ##Bundled hGG PrimrecRel cfcAux IsMulOne x⁻¹⁻¹ B₂₁ B₂₂ generatePi toPushforward EvenHom ↑↑f✝ stepNormal UniformContinuous₂ sigmaLift diagramPullback recDiag fourierLp InfHomClass ↥↑↑ Transp TransOrd auxEquiv 1728 hp₁c₁ hp₁c₂ bernoulliFourier Reader rotateR realPart partialGamma hp₂c₁ hp₂c₂ J₂✝ tprodL hfinj Contravariant toEssImage ##VarsEquiv OrientedOrd toContinuousMapHom algHom nonZeroDivisorsRight scott ¬∃ᶠ coyonedaEquiv IsClopenable decomposeAlgEquiv hιcard simpleGraph circumcenterWeightsWithCircumcenter IsLeftDescent PolyCnstr ProjRestrict ProjRestricts codom hscard finsuppLeft uXZ uXY ##CurryCompLim ToType CliqueFreeOn FactorsThru runK ##LindelofSpace CoreUnitCounit equivOfEq injectiveSeminorm ##429 EnrichedFunctor ##UnopOp ##Encode ##ProbaEquiv ShiftMkCore iZW ##266 HiJ ##365 IsCondKernel uniqueUpToIso uniqueElim ##IsoLimitCurryCompLim ⇑ofFun skewAdjointPart ##OfCocones inftyValuationDef ⇑sxy ιTensorObj₄ imageSubobjectIso terminalComparison ##572 ##Conjugate linearEquivFun accept hpc₁ hpc₂ ##BinaryBiproduct skolem₁ ¬eval hsx₁ hsx₂ ⇑dirac ceilRoot hchar✝ mapRightIso mapLeftIso totalShift₁Iso totalShift₂Iso UpgradedStandardBorel hp₃p₄ HasExplicitPullback πSβ ##UniversalPropertyFixed toBlocks₂ IsStrongLimit FundamentalGroupoidFunctor DiagramOfCocones BifunctorComp₁₂IndexData BifunctorComp₂₃IndexData ofTypeFunctor ofTypeMonad vecAlt ⇑normalize constantsVarsEquiv CompleteSemilatticeInf idealFactorsEquivOfQuotEquiv composePath NonarchAddGroupSeminorm hm2n2 OfLocalizationSpan HS₁ toAEEqFun inrNonUnitalStarAlgHom FloatCfg ##enom✝ finSuccAboveEquiv Fsur equivToUnitHom functorCategoryMonoidalEquivalence Promises VectorAllP NNNorm Palindrome Pivot falling grothendieckTypeToCat linftyOp FineSubfamilyOn Subsequent reesAlgebra PropertyIsLocal FunctorsInverting TensorSigns equivEssImageOfReflective ##HahnSeries dualNumberEquiv basisOfFractionalIdeal generatePiSystem bernoulliFourierCoeff ReaderT ⇑diracProbaEquiv ##UniversalPropertyFixedTarget 2ᶜ 241 4✝ 46 Cus Fre Ia K⁻¹ Push Rᵃᵒᵖ S⁻¹ Spanning Vec aS bg bf bme beck b✝¹ cmem epi h₇ hmm hppos hhd il jᶜ jnn mi meq nemp partition pmonic rlt so sV wt xNext xPrev yeq ¬MeasurableSet ¬Nonempty Δ✝ αi μB ω₁ ⇑x ##qForm ##runc ##RTensor ##Tree ##pForm ##pStrip ##Coprime ##Cps ##gEquiv ##ZNum ##bdd ##Urysohn ##05 ##YX input inTangent ##edNatTrans ##erator ##archimedean ##idual ##idental map₁ mapAction ##irth ##ableBy toZero toHamming HasReflexive ##OnFintype ##ortsGrothendieckTopology AddCancelMonoid ##AtImInfty hsg ##ZeroLE compSL compAddChar compHahnSeries ofLinear ofBool ofBraided ofZNum hprim hau ##OfList ##OfZeroLE opow invInter ##EquivGen IsCartesian atEnd hnμ hneq ##LeftRegular hm4 ##Coimage hbg finj ##ToPartialHomeomorph h₂s liftCochain liftIco hi₁₂ hi₂₃ hyv hy2 Constant leftFun SMulAntidiagonal ##esqForm abelian rightDerivedToHomotopyCategory hrr implicit addMonoid addUnit addOpposite addEquivOf sumElim ZeroAtFilter ##SumPUnit he✝¹ LocallyDiscrete shifted x₁✝ shiftComm logGamma hlast L₁✝ ↑m₀ NoAcc ↑rp Relabelling unitVec numerator toLowerSet hq₁ WithUpper WithScott isoRestrict supExtension ##PredLimit eLpNormLESNormFDeriv transDiffeomorph BoundedAtFilter r₂₁ ih₁ normalCore hj₁₂ ltBy updateFinset hopen squash IsTrunc fsum fsymm ##Forget ##eflective TriangleIndexData hNU ¬IsBounded basisOf foldMap ↑A⁻¹ hJK AddCommMonCat Lake inclusionObj toPresheafedSpaceGlueData ##QuotientEquivQuotient output ##ucingCoprod ##QuotKer UniformContinuousConst J₁J ↑T0 coconeAt coconeApp hE₀ ##LocallyRingedSpace residueField residual coords hp1p2 freeGroup ##NhdsClass idealizer dirichle ##algEquiv CofixA hπ₁ algHomEquiv raise g₀⁻¹ circleEquivGen ##CyclesSelfIso ##SingleObj ##OfIsSplit IsMinBadSeq hW₁ zipWithAll RootableBy valuationSubring PolyEquivTensor IsNonarchimedean ##LieHom hxU₂ quotEquivOfEq alternatingWord degtm SMulPosReflectLE sα✝ ##FixedPoints toMulEquiv singleObjCyclesSelfIso killingCompl ClosureAntitone toMeasureOfZeroLE SemiNormedGrp₁ localizationAway ##358 Elementarily balance2 toRelHom hi₁₃ DoubleCentralizer RightFractionRel ##OfMaxSingleton hmsum coinducingCoprod galRestrict FilteredColimit hj₁₃ ##Representable zsmul FGModuleCatDual sheafPushforwardCocontinuous equivRealProdCLM completeTheory Coreflective ¬AE compPartialSumTarget toZNumNeg hp₃p₂ CircularOrder ##OfSep HopfAlgebraCat wPathCasesOn ##SemiHomClass nonUnitalStarAlgHom monadLift vecAppend toSquareBlockProp bipartiteAbove bipartiteBelow heLpNorm₁ IsCodetector fdiv MeasurableSup₂ finSumFinEquiv ##chetUrysohn liftOfRightInverse IsAdicComplete hfz₀ derivationQuotKer restrictedYonedaObj ##trongEpiMonoFactorisation doublingGamma asEmptyCocone OneOneEquiv ↥↑↑I TransportsGrothendieckTopology 241337 CuspForm FrechetUrysohn SpanningTree bmex hmmem meqOfSep xNextIso xPrevIso ##CpsT inTangentCoordinates HasReflexiveCoequalizers invInterpStrip Constants implicitToPartialHomeomorph addOppositeEquiv shiftedWeightSpace logGammaSeq NoAccidental supExtensionOfMaxSingleton ltByCases dirichlet ElementarilyEquivalent derivationQuotKerTotal FrechetUrysohnSpace 23 231 318 724 84 BR Biprod Ed Hy Iₚ Iᵛ Lˣ M✝¹ PD P⁻¹ ST Skeleton br cech em fz fmod gos gmon ic iot ipos ldiff m✝¹ n√ pull sd s₄ tV vC xp y₄ zg zoom ¬X ¬volume βi δl ιX ιₘ ρW φint ⅟r ↑8 ↑4 ⇑π ⇑AddMonoid ⇑prod ∂0 ≤₁ ##eag ##df ##dMin ##cycle ##Sieves ##aDeg ##pad ##Lists ##LCongr ##CHaar ##CApp ##1572 ##fun ##Ec ##Euclidean ##ZSMul ##Zeckendorf ##Bipointed ##74 ##08 ##μν ##464 inerti IsInd IsZeckendorf ##geDisjoint FindMin ##atomic toH toAddGroup toType toOver toBoolRing toAlternatingMap toToΓSpec ##HomIsoLimit ##HomOfDegreewiseSplit ##WithShift AddAut ##MulAux LinearRecurrence hso hs0 hxx hxg compHaus ofSuppBddBelow hpzero ##OfVertex x✝⁵ symmL symmetr opOp opcycle ##IsPullback ##UnitBall GroupNorm valid ##MeasurableEquiv algebraMap₀ prod⁻¹ prodIsoProd fstPiMap universally ##LeftEquiv Covariant htmem ↑sd hcU ##OpenSets ##Coatomic PrimePair equal fints ##ToQuotient ##ToPi R₂✝ FunctorExtension₁ natGenerating Hom₂ spanCompIso hia ##Catalan ↑↑e ##perCatalan leftpad selfProd right₀ rightFun right✝¹ hdng ##ShapeOp addPrehaar addCHaar ##izeRel FreeNonUnital ##Homologyι ##ching insertAt ##AssocAlgebra hea ↑IF piLp closedSieves c₂✝ L₂✝ NoTopOrder ##NonZeroDivisors ##NonAssocAlgebra hP✝ MulActionHom MulActionSemiHomClass starAlgHom partNum partOfVertex ##ArrowIso hz0 hSM hSN StrictUniversalPropertyFixedTarget h23 hq₂ isoZero hε₂ detAux ordered ##SheafOfTypes presheafIso hfga hfgne hBI ##Valid ↥S₁ hFG hF₁ smulTower smulAux hCf hCmax colimitMulAux hA₀ descCochain counitForward hφ₀ hφ₂ extendSubtype limitIsoLimitCurryCompLim multiset ↑X✝ h₃₃ coeLinearMap coeAddMonoidHom 1621 HasFiniteLimits GradedObjectWithShift ys✝ ##Black toNatMultiset divOf ##ConvexOpenSets ##InterClosure ncs rs₂ ##QuotientStabilizer ##empotentOp AsBoolAlg splitMul d₂0 hlead SupHomClass conePointsIsoOfNatIso cocardinal IdempotentOp ↥sp ##twop InfIrred HasLeftKanLift domLCongr OfNatIso IsAsymm finiteInterClosure AbsConvexOpenSets mappingConeHomOfDegreewiseSplit approxChain ofHoms IsMeag toAffineLift ##EquivOfFintype haarProduct ##TotalOrder J₂J initSeg hστ SubsemiringClass hyzD plusLift 18996 1904 191572 ReflectsColimitsOfShape hπb finsetBasis finsetCongr ##Single₀ homMkSucc ppow IsNormalAddSubgroup hWo snd✝² IsLeftAdjoint ⇑i✝ sheafifyCompIso ##WhiskerLeft MinSqFac mulLeftRight mulLeftEmbedding powersetCardAux cauchyPowerSeries c1✝ StoneCech induceHom ##OpcyclesSelfIso ##CurryCompColim ##184 degt0 ##HomEquivHom toNonUnitalRingHom bdA hgsurj c2✝ fibers wideEqualizer singleObjOpcyclesSelfIso listEncode isColimitOfPreserves CondIndepSet htcard ⇑Cardinal ##Matching ofIsEmpty huiE homogeneousHull rowLens continuousMultilinearCurryLeftEquiv ##393 hunit huniv balanceR IsUnramifiedIn ##OfMemRange IsStronglyCoatomic IsStrictTotalOrder ##304 eulerMascheroniConstant endPos endEquivAut gradeBy toIntSubmodule ##keletal ##IsoColimitCompColim ##IsoColimitCurryCompColim continuousLinearMapAt 2620 fullSubcategoryInclusion BoundarylessManifold ##WeakOrder StrongEpiMonoFactorisation ⇑D1 ⇑D2 associatesEquivIsPrincipal ppredConts coverings mapHomotopyCategoryFactors binaryProductIso htris prodMkRight hconn liftedCocone iter₁ CoversTop monoidal coreflection ↑num✝¹ functorObjLeft 25151 5128 e₄₃ hnc₀ ##Coboundary zpowersEquivZPowers wPathDestRight ContextFreeRule IsDetector mappingConeCompHomotopyEquiv IsOrderRightAdjoint isNoetherianRing constantsOn IsCancelMulZero heLpNorm₂ completedRiemannZeta₀ bpowtwop pullbackIsoPullback sigmaFinsuppEquivDFinsupp node3L MeasurableDiv₂ sheafEquivSheafOfTypes primeSpectrumEquiv coconeOfRepresentable neZeroV opowAux numeratorHom EdgeDisjoint gosperCatalan iota n√a δlast inertiaDeg IsIndObject IsZeckendorfRep toToΓSpecMapBasicOpen symmetrizeRel opcyclesToCycles fintsupport natGeneratingSequence FreeNonUnitalNonAssocAlgebra IsMeagre 189967 190432 MinSqFacProp endEquivAutGalois EdgeDisjointTriangles 218 68 71828 89 BC Eras Heq Hstar PProd S1 Ssep Ui U₅ U₆ aem cst fₐ fFold gU gdiff hₗ hde iC iD jn kr l₀ lucasLehmer nv n⁻¹ nab pop plift qn qdf ri room sur simplicial sorted uy v₇ v₈ v₉ zt zn ¬Affine ¬False Γ₁ αW αˢ εc εClosure μu σR ##iOut ##quotient ##Refl ##Rpow ##side ##Some ##Append ##ported ##psub ##fus ##fold ##Hil ##bable ##kmann ##₄₃ ##ISup ##351 ##58 ##νκ ##ʸᵐ independent ##ons ##led ##SpaceUniversal ##ingSpaceUniversal ##icTrivial IsHomeomorph ##GroupBasis ##itSeg funCongrLeft mapₗ mapConst mapSucc toComp toOpens hfk hfμ Initi HasUpper LinearIsometry PreEnvel 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nthRemainder π₁✝ ChainClosure ExistsSeqTendstoAe hinf toSmooth InvImage ↑C₂ ##Residue toPartition ##fectMatching toDualMap toDualLeft toDualRight toLinearMapRight smaller Adual defaultRatCDF coprodMonad hasNext ##ltrahomogeneous J₁S KaroubiKaroubi toTopGlueData pushoutAssoc hYdisj ↑12 pushforwardFamily pushforwardPullbackAdjunction ##EquivOfIso attachBound notBelow boxProd OrientedCmp FermatLastTheoremWith IsSubring IsSubterminal hπS HasRightKanExtension IsInitSeg property✝¹ hDl finsetOrderIso hc₁s fxy hκs rcons fixF cospanCompIso getLastD hffx CircleDeg1Liftˣ semilattice semiOut surjInv ##321 hγt primitiveChar hc₂s h𝒜₂ ##CoprodI ita SuperChain ##FiberBundle toKaroubiEquivalence toKaroubiCompN₂ hxzD SpecializingMap gaussianPDF hgm₀ hr₁1 hr₁0 equivalence₂ nmem degbm Hdg Hdf ofMulDistribMulAction wideCospan ##ToLpNonneg centroidWeightsWithCircumcenter dblY ##509 hXYdisj ##PathConnectedSpace kroneckerMapBilinear hr₂1 hr₂0 BasedNatTrans ##Decode ##SummandHom σ₄₁ perf AddConstEquiv 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¬AffineIndependent αˢʸᵐ ##Hilton ##icTrivialFiberBundle IsHomeomorphicTrivialFiberBundle InitiallySmall HasUpperLowerClosure PreEnvelGroup ProbablePrime mkSelfProdFib prodComonad lengthParity Quandle Γ₀NondegComplexIso coeSimpleFuncNonnegToLpNonneg toSmoothPartitionOfUnity finsetOrderIsoSet semilatticeSup semiOutParam toKaroubiCompN₂IsoN₁ noConfusion bpowpsubone openCoverOfISupEqTop EckmannHilton classifyingSpaceUniversalCover 37 43 437 6779 937 Ahl Bar Cₛ Coin Corners DList E₄ Hv HD Iᶜ Ite Iff Ji Jf J₃ Morph Npos Nfg Uo U₄ U₇ Uᴴ am ane0 dXY eE eP eη familyOfElements fullyFaithful gpos hic hct hbj hOf hgen hyper mE nle tE tDist ule wι xm yc zy zaris ¬Δ ¬⨅ ¬cs αᵒᵖ εε μv ↾fun ⇑MeasurableEquiv √↑d ##uff ##e₂ ##sw ##Sphere ##String ##Operation ##hV ##hang ##mo ##mE ##fl ##Zhang ##₁Y ##Back ##ki ##kleisli ##869 ##45 ##orefle ##alOperation ##rocal ##asing ##reasing ##easure IsQuotient FinEn mapBaseChange toNorm toProperty toUniform toUnits toLatticeHom toQuaternion toFormalMultilinearSeries 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presheafToTypes hfgk hBf IsAddHom IsAddLeftRegular ↥S₂ BoundedLatticeHomClass ⇑g₂₃ subtypeUniv FractionalOperation csZ ##coding ##escence smulAddMonoidHom smulAddHom RightDistribClass RightDerivMeasurableAux hC₂ colimitUncurry colimitIsoColimitCurryCompColim Arbor hA₃ inverseObj ##Generator ##PresheafMap dualPairing hKs hKco sInfGen decreasing iteratedSlice ##edeZhang ##StarSubalgebra IsBoundedAtImInfty h₃✝ ↑z₁ ↑z₂ hRμ ##uares coeSubgraph ¬IsPredLimit basisOneI ##OfLEZero flipEquivalence cmpLE IH2 defin toSingle splitAt ↑C₁ toPseudo SupConvergenceClass map₂Iso LiftRelAux ε₁0 π₂✝ Admissible quotientPi reciprocal OfScientific findim k₁✝ ##ativ iSupLift cokernelComparison k₂✝ coconePoint ULiftHom ↑↑↑γ ##EquivOfRightInverse weightedSumSq realContinuousMap modMonomial J₂S toEquivRange powQuotSucc HasFPowerSeriesWithinAt Cofinal notin measurableAtom idealOfLE ofAddEquivOfLocalizations ##ExactFunctor ReflectsColimit ReflectsEpimorphisms OpenNhdsOf ↑G₁ ↑G₂ hDhV iV₁Y hΦ₁ triangleRotate triangleIndices ↥E1 coyonedaOpColimit IsRightDerivability hWU fixInduction fst✝² sectionsTR powerBasisOfFinite ↥Va ↥Vb WeaklyConnectedComponent ##WhiskerEquiv compactlyGenerated mulLeftMap IsSemisimpleRing gluedIso seminormFamily ##ExtendScalars hpm2 IsPreorder pathDestRight pathDestLeft degb0 sheafComposeNatTrans hZ₁ hZ₁₂ ofMulEquivOfLocalizations ##ChainComplexEquivalence fundamentalFrontier nulldiff toΓSpecCApp InitialMonoClass listDecode hkmn toMeasureOfLEZero dgo ofIsCompl ##Identity ffmE homogeneousSubmodule iZY toModuleIso IsSetAlgebra awayTo convexBodySumFactor elementary ##IsoLimitCoyoneda takeWhile₂ nilpotencyLength he₁e₂ openCoverOfLeft openCoverOfIsIso boundedContinuousFunction toAddMonoidAlgebra cycleRange⁻¹ NrRealPlaces linearEquivAt ##544 2656 toSpecΓ karoubiChainComplexEquivalence pnat hcpd ##richotomy AddRightCancelMonoid zmodRepr ##ZPowOfEquiv ↑fs2 hOg hapb xbar matrixDecomposition ##relled isEmptyElim iter₂ ⇑dg isLocallyGerm functorObjTop 9610 XIsoBiprod 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IsRightDerivabilityStructure powerBasisOfFiniteOfSeparable 26563 fintypeQuotientOfFreeOfNeBot AhlswedeZhang BarrelledSpace 236 230 377 41 448 62 696 Aᶜ B₃ Biproduct Bᵐᵒᵖ CS Eₘ ENat FS Fth FDerivMeasurableAux Gc Hst HSMul HPow Jc L⁻¹ U⁻¹ WPath a4 amalg bt bb bim dX ey e✝¹ f3 fle gV hype hhea hval hSMul hux hInner ie j₀ kᶜ leq land lcoeff phi qp rmap slash thd xmem zorn ¬Polynomial ¬Mem ¬Same ¬gcd ¬Fintype Δ₂ ΦΦ γᵒᵈ δle μt τ⁻¹ ᵃᵒᵖ ᶜᶜ ↑6 ↑ξ ∂⁺ ∂∑ ∂haar ⊗⋙ ￢b 𝒜ᶜ ##ura ##s2 ##write ##T5 ##LTensor ##Cle ##Cod ##Cut ##Nhd ##PadicInt ##25 ##Dbl ##400 ##roperation ##asilinear ##erase ##arrier Isδ₀ ##itute ##ograph ##RingIso ##RingCatIso mapTerm toAdjoin ##EqToHom HasMax ##MapIdIso ##Internal objX objEqToHom ##MulOpposite ##MulPow Pregroupoid hsz hsV homotop ##ZeroMonoid ##ZeroZeroIso compAddMonoidHom cardFactors ##FinFinset ##FinSucc ##Setoid ofGroup ofEmbedding ofMagma ofObjects ofLawson ##OfBasis ##OfBdd symmega atoms hnl hni ##CategoryTheory ##IsoPi SubmodulesBasis connected ⇑f₁₂ ⇑f₂₃ 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mapTermRel HasMaxCutProperty homotopies HasFilteredColimitsOfSize QuasilinearOn negDblY associativity ordT5Nhd hasSmallLocalizedHom Transcendental Rewrites quotDualCoannihilatorToDual DenomsClearable HasUnitMulPowIrreducibleFactorization 2✝ 220 2113 3✝ 35 306 626 779 82 851 8737 Ag A₄ BM BN C2 Categorical Fold Gˣ GNonUnital Hl Hle Hsq IN I4 MX Pfg Qfg RTendsto Sc S4 Shelf Simp U₃ WW Wall Ys Z₀ bn cv cβ coproduct cne0 d1 d2 dYZ geom h7 hen ible iam iseq jy kt lub lax lne mX mz mY ntop ou ok qₗ sid tx tun temperate ¬Complex ¬order ¬to ¬NumberField Φ₁ Φ₂ ΨΨ θ✝ ιY ρpos χ₃ ω₂ ⅟c ↑ad ↑One ↥w √3 ##uential ##xes ##nel ##Repa ##sRing ##scend ##canonical ##Scale ##Shelf ##SimplicialEquiv ##Trichotomy ##oi ##oxes ##pn ##hc ##hIso ##mono ##1Iso ##Nim ##Neigh ##Nndist ##₁₁ ##XXIso ##b₀ ##Bind ##759 ##₄ObjExt ##QhIso ##zech ##Y₂ incre instAddCommGroup ##alShelf ##edAt ##rais ##arse ##repr ##CommMon IsTensorProduct IsFibAux ##bration mapTo mapBiproduct mapEdgeSet toComplete toTwo toAdjunction toCommSemiring toUpperSet toMatroid toRestrictScalars toKerIs ##MonoidAlgebra HasGen Subcanonical ##lyMeasurable ##HomMap ##igrp ##FunOf hsk hs3 hswap homQuotient hxA composableArrows compatibility compFormalMultilinearSeries mkAux ofFinset ofLe ofRe ofMultiset ofQuaternion ofLists hpri hav FiniteDiagram ##reeEqualizer IsSmooth LieCharacter ##OfMap ##OfZeros invUnits ↑ncs hg₃ ##endingCentralSeries ##UnitTheorem ##UnitSphere ##EquivIso ##FiniteIntegral ∂μα GroupTopology hng hn₃ ##IsoSelf SubmodulesRing f₁✝ ##LeftTo ##RightTransversals ↑sm ##Cost ##Covol hbo hbelow finish ##ToLax sndPiMap hiI ##DiffSubset hyr Concyclic evalAddMonoidHom stmts ↑↑H ##onglyMeasurable abToCycles minDegree ##CompQhIso isLift aestr preA preLift preserving ↑p⁻¹ sumComm sumDiffSubset 1027 ##Preord pullbackFst subterminal FreeCoequalizer hev hvb tru PreservesBiproduct PreservesColimits ##ramAux g₂₁ Diffeomorph ##omeo hl1 someExistsOneDivLT tensorDistrib expUnitary derivSeries ↑boxes ##aryComponent starL partBind hIN MemRightTransversals ##DualAnnihilator 121 StrictOrder equivPullback equivReindex hμb₀ autCongr h1✝ OptionT h2p hqf isoC commMap nonZ G₀⁰ hfgx hBg IsAddRightRegular contr IsDesc BoundedMul hFF infNndist InfiniteDimensional M₀ˣ smulg hxy0 ##tendScalars indexes ##PullbackCone ##terate hCA hCuv 1369 h0K ihk hjn ltTrichotomy carrierᶜ pbo dualQuotEquiv ##Isomorphic limitEquivSections topIso ##Inductive IsWellFounded hMp hMf hMN sequential ##Minimum ##Distinguished 1497 ##RangePow ##AffineMap ##TriangleMorphism ¬IsEmpty ¬IsOrtho hJmono UnitalShelf sheafAdjunction cmp✝ cmpα ys₁ Rₘ✝ Hausdorff hGpn typeToCat associatorBimod biUnionIndex Explicit ##QuotientEquiv AsBoolRing ##QuotHom ↑C₀ iUnionNot SupPrime ε₂0 kernelIsoOfEq DifferentiableWithinAtProp pairFunction quotientToQuotient quotientCompQhIso coprodAssoc s1✝ conjNormal hasFiniteIntegral fourierChar hQ0 relNorm IsAscend cokernelIsoOfEq tensorRightHomEquiv finiteCovol ↑MT mapBifunctorAssociator approxBounded ↑B✝ ##Eigenvalue PartialEquivBEq LeftFraction₃ ⇑homeo zipLeft zipRight ##EquivOfFinset ##EquivOfRingEquiv modn partialInv freeHomEquiv J₂F Resp CofreeEqualizer ##IsometryClass ##borSet toEven denom✝ nonZeroDivisorsLeft sconn ↥E2 ##OfIsLimitKernelFork IsComplemented vectorsProdEqOne ##RowLens HasTensor₄ObjExt GrpWithZero polynomialZ ##325 ##sOfInclusions finsuppRight finsuppUnique corecF both gluedLift smallHomMap ##LieSubalgebra congrRight ¬↑a ¬↑f groupoid ##208 homotopyEquiv toHomUnits unitsFst nonzeroMinimum ##RotateIso toNonUnitalNonAssocSemiring mconv isScalarTower isSeparable isSl2 ##CochainComplexEquivalence ##275 sheafificationHomEquiv primaryComponent ##465 t0s Egorov 259 lflip postcomp₁ ##EquivProdFinsupp Elementary AlexDisc sparse ⇑toLex balance1 PreservesFiniteEffectiveEpiFamilies skewAdjointSubmodule thinkN ⇑self toFiberBundleCore hus✝ terminalIsTerminal ##OfMaxAdjoin gammaPDFReal pderivCLM natIsoSc newtonMap 2664 karoubiCochainComplexEquivalence ##295 ↑fs1 IsSeqClosed hI0✝ Fibration 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rightHom hright imp hd✝ addDysonETransform sumg sumCoord 101 109 substructure this✝⁸ insertRec inductive forM c₁F c₁J₁ piIcc piOption forgetMonoidal trPosNum PreservesProduct SigmaHom ↑ia huX hln limSeq zeroCochainsLequiv expOrderIso ##izedBern ↑r⁻¹ functorMap functorExtension₁ hP₀ hI✝ hIP hIoo hIjac ##AuxAux constVSub unitOf unitBall unitLattice hzx hT✝ equivOp equivIoc hμv C₁C h1L₂ h2c h2✝ h2L₂ h2Q0 isoAdd isoLimitCone ##Transported oneCoboundaries Bicategorical presheafEquivOfIso adjoinRoot NormalEpi ↥Sx cs1 w₁✝ RightCommutative hwx ##InvOfBasis AdditiveFunctor 136 ¬p₃ ¬padicNorm ##PresheafOfModules ho₂ h₀ε ##lyGeneratedSpace ##StarAlgEquiv SplitMono signBi seqClosure ↑zb hRL tailing 160 ¬IsCyclic β₁✝ hJE hJ₁ hJle hJmax hX✝ BiUnique HasStrictTerminal typeTo move₂ divLeft divRight IsMulTwo castSuccEmb bsize toSelfAdjoint ↑Pᶜ SpecΓIdentity IsGluing diagonalization toPMF Nullhom ringOfIntegers psigma hle₁ coneLeftOpOfCocone toDualEquiv pairMap sigmaι InfPrime InfConvergenceClass toAddSubsemigroup key✝ rTensorHom tan⁻¹ NegZeroClass ##MonoidalStar ##BlockDiagonal coconeLeftOpOfCone hE₁ gpint gpcont coordinate ##EquivOfFiniteNoetherian rotateLeft rotateRight modNat partialSections revFind PreservesLimitPair hfsurj ##SequenceProp idealOfCofinals decodeList hHG hπU HasRightDerivedFunctor hρx prevn isLimitWhiskerEquiv ##MapObjFun Predicate IsRightInversion hW₃ snd✝³ CofanMapObjFun ⇑↑v fst✝³ ##IsoOfIso Nonnegg hf01 hf0✝ compactOpen toPrenex nd₁ inclLift equalizerSubobject adjointDomain HasLines hψ₁ hψ₂ h𝒜s ##697 Hcos congrHom disjointSum extFunctorObj homotopyTo hft1 ##OptionEquivPolynomial ##276 wideCoequalizer dfma toDilation equivOfIsometry SemiRingCat HasWidePullbacks Hsin contractLeftAux factorThruImageSubobject balLeft balRight glb loopOfHom domDomCongrEquiv ghostMap hyp1 hg0✝ ##366 hrsU HolorIndex iWU principalSeg HasStrongEpiMonoFactorisation cotangentEquivIdeal hξ₀ ##ensedSet periodizedBern ##oneCechExtend IsGenerating endMonoidalStar stereographic toIntAlgHom usucc hsnemp HeytAlg ##BinaryBiproducts leftRegularHom coveringOfPresieve Frm IsReflexivePair mongePointWeightsWithCircumcenter ##AndSheafify mvPolynomialOptionEquivPolynomial ##ToPlus hℬs characterSpaceToSpectrum hxfΦ FundamentalSequenceProp ofTensorProductEquivOfFiniteNoetherian ##NormalizedMooreComplex kernMap nonUnitalNonAssocSemiring Hereditary toOneHom✝ toOneHom✝¹ hgexact PrelaxFunctorStruct toENatAux costructuredArrowYoneda irreducibleComponent ¬IntegrableOn toFreeAbelianGroup hU0c hcovBy coneOfCoconeLeftOp coconeOfConeLeftOp IsRightCancelMulZero ##894 hucard IsInvariantSubring ExtendRestrictScalars dualDistribInvOfBasis enumerateCountable KleisliCat homToLift preadditiveCoyonedaObj categoryᵒᵖ addFundamentalFrontier LPμν LPνκ addETransformLeft addETransformRight IsTwoBlockDiagonal 164955 164954 288379 288386 75295 mulEquivOfQuotient gnpow ##OfDet hfngε IsMulOneCocycle scottHausdorff FactorsThruAlong hW₁₃ simplicialCos ##foldr hγt₀ isometryOfOrthonormal ιInvAppπEqMap awayToΓ amalgama toCompleteLattice Literal Nfu Pontryag UCompactlyGeneratedSpace child guess iunfoldr powerSeriesPart sNu ¬univ toConvexCone toBddLat hfexact cardinalGenerate identity CoequalizerRel ##ToSquareZero sumCoords piIcc01 piOptionEquivProd BicategoricalCoherence signBijAux HasStrictTerminalObjects Nullhomotopic PredicateShift HasStrongEpiMonoFactorisations periodizedBernoulli mvPolynomialOptionEquivPolynomialAdjoin ExtendRestrictScalarsAdj amalgamate PontryaginDual 396 48 400 58 7✝ 73 752 7325 97 969 CF Dx Down Fᶜ Hx HA Iα Joint Kβ Kα LD LL₂ Mach Ok Qx Rec Tc Vj VonN Whisker XIdeal Z✝¹ Zeta a⋆ bP d⁄ eF fpos gMulHom hup huo hass hdj hemp iE iCocycles kˣ language mv mab nH od orthonormal pu pv p5 pOrder pprod q1 r₄ reas sing sect sane satisfies sesqForm tg tU tas tend tbs uas x₅ x₆ x₇ x₈ yu y₅ y₆ y₇ y₈ ¬κ ¬In ¬Set ¬Module ¬Submodule ¬root β₃ εx ζ⁻¹ ιv μF ↑ir ↑MF ↥φ ↥𝔭 ⇑N ⇑⊤ ⇑Free ⇑Multiset ⇑Sym ∘ₐ ∼φ ≤r 𝒜✝¹ 𝟭q ##q0 ##eum ##xtendScalars ##nf ##norm ##niz ##dX ##Rig ##soc ##sper 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##LinearIsometryEquiv StarSubsemiring ↑fe closureOperator MonoidalLinear ##BotEquiv ab✝ ##CompSheaf isPrefix isSumSq asString rightAdd preOneHypercover preCantor hrJ hrpos hd1 addValuationDef ##OneHyper ##Preserv ##Precoherent pullbackP1Iso subfamily subordinate leval leib b₂₃ b₁₃ insertRight forall hva hvf PreservesKernel PreservesBinaryBiproduct c₂F c₂J₂ log2 ↑i0 hua ne0 ne✝¹ hlk hlz ##alkLength lim1 ↑m₁ ↑m⁻¹ inrHom exposedPoints ↑b⁻¹ hUl hUx hUA hk✝ ##aryGroup functorInclusion hPM hPpos constComp constFormalMultilinearSeries ##FinsetRange unitHomEquiv LieModuleEquiv hTc hS0 ptsOf StrictWeakOrder whiskerEquiv equivRat equivPolynomial equivBool equivYoneda equivBoundedOfCompact equivEquivIso toLight h1g h12 h1V₂ h2C h2V₂ hab₁ ##MonoOver hquot LocalizationPreserves isoToPlus commut commMon intersper ⇑eα ⇑expMapCircle nonsing hBC ##ConeMorphism NormalMono IsAddKleinFour BoundedSub BoundedGE hFy hFEp inf✝ inf✝¹ InfiniteRk invert IicExtend ##PullbackEquiv hwB colimitLimitIso colimitHomIsoLimit affineRefinement hAC hAK primeIdealOf ##Coverage ##InvUnit 13544 IciExtend hj✝ setCongr setPreimage intU intCast ltb carry hφm pbind dualTensorHomEquiv topObj ##ImageEq ##ImageToKernel 1481 1485 ##RangeEquiv ##PowEq TriangleMorphism tail₂ coeLM coextendScalars HasFiniteColimits basisMatrix uncurryRight hJJ hJp hJsub UnitaryGroup hXp roots1 roots2 RatCast SeqContinuous IH₂ IsMulCentral inclusionTopIso ##IntermediateField a₃₁ a₃₂ a₃₃ LawfulHas hints mΩ✝ Any truncSwap ##covers ##QuotSup ContinuousMapClass args lcomp val✝² nextOr step3 emptyTo h3c h3V₂ monoFactorisation sigmaCurry sigmaUncurry sigmaFiberEquiv IdemSemiring conjeq conjCLE biprodComparison maximally ##Elementary ¬x₁ ubs relEmbedding curryRight finiteSpanningSetsIn 1720 17179 embeddingCongr normalizeAux hhh hp₁o encodeList hE₂ pushoutIsoUnop ##OrderOfST ##CDFReal πi✝ hYp hYm ##NormalSpace reindexFinsetRange FreeGroupBasis ⇑hB nhdsAdjoint ##EquivOfDom ##annAlgebra linearOrderOfST modOf pf✝¹ graphEquiv ##ForkFunctor 199 ##igitsCore ReflectsLimit evenToNeg torsionOrder iV₃ triangleMorphism triangleOfS ##OfIsLimit ##OfIsTrivial changeFunctor hWH rcf cyclesFunctor 2047 hνμ hνinter DiophPFun opcyclesFunctor compContinuousMap finsuppTotal primitiveZMod h𝒜₃ ##VSubWeights b₃₁ b₃₂ b₃₃ hatInv compareOn newCocone ¬↑ε ##Equalizers ##209 A⁻¹⁻¹ ##793 ##CurrySwap weightedVSubVSubWeights ##BiconeFunctor ##BiconeOfIsSplit binaryBiconeOfIsSplit algEquivMatrix ⇑SignType 10050 braidWord IsJordan yonedaEquivFst ##sqb ContentRegular addEquivOp ##Asymptotics ##278 ##270 fiberPullbackEquiv toDigitsCore injectiveResolutions keysLookup PointClass mba ##UnopPushout ##UnopOfCone ##UnopOfCocone spec₁ mkOfPowEq ##OrthonormalBasisIndex CanonicallyLinearOrderedCommMonoid domDomCongrLinearEquiv ##Nones via continuousMultilinearCurryRightEquiv mapTrifunctorMap aeSeqLim toSubordinate riemannZetaSummandHom ##867 toStructuredArrowCone PreservesPullbacksOfInclusions DefinableSet BialgHom BialgEquiv ⇑snf ##LequivOfIsTrivial hssJ 215 2149 elems IsStrictlySupported der1 28304 ↥↑N₁ ↥↑N₂ toIntLinearEquiv vaddAntidiagonal changeFormAux hnd₁ hnd₂ ##DerivedZeroIsoSelf iCondIndepSets hindp initsCore toSubgroupEquiv nondeg✝ NonarchimedeanAddGroup ##lashInvariantForm ##DownwardsPrecomp vecMulLinear sHomComp IsScottHausdorff hapc leftHomologyOpIso Complementeds binaryProductLimitCone biconeMk 69365 69358 69351 mvPolynomialQuotientEquiv ##RightOpOfCone ##RightOpOfCocone componentComplFunctor claim2 moduleCatCyclesIso fillNones dualSubmoduleToDual LightCondensed embedBox zmodEquivZPowers comparisonAdjunction ##8446 hI₀I hI₀fin 24208 ¬IsOfFinAddOrder toLeftMovesMul nilRankAux ¬hausdorff pwv ##EquivQuotMap ⇑normSq subalgebraOf hεs0 TwoUniqueSums costructuredArrowRightwards costructuredArrowDownwardsPrecomp hlen✝ toRightMovesMul toRightMovesAdd hmfng hopi comonEquivalence sheafCongrPreregular sheafCongrPrecoherent IsLocalDiffeomorphOn orderIsoOfPrime NonarchAddGroupNorm hm2n20 pullbackIsoUnopPushout subsemigroup node3R augmentedCechConerve hpaηsqb ##Premetric optionSubtypeNe HasCoproductsOfShape partialFunEquivPointed value✝ GenerateMeasurable Ibad 132220 132224 exponentialPDF lightToProfinite ##ingLeftEquivalence abelianImageToKernel implicitToPartialHomeomorphOfComplemented zg₁ partNums hBIB mappingConeHomOfDegreewiseSplitXIso hbpd 148593 toPushforwardStalkAlgHom ##869184 ofGrothendieck functorExtension₂ dgoEquivHomologicalComplex elementaryDiagram sumLift₂ functorProdFunctorEquiv concatRecAux associatesNonZeroDivisorsEquivIsPrincipal toKerIsLocalization isoCarrier sequentialFunctor 149736 ElementarySubstructure adjoinRootXPowSubCEquiv 13627 CFC Dxs JointEmbedding LDL Machine Recursion VonNeum WhiskeringLeftEquivalence ZetaAsymptotics d⁄dX hassoc mvpz orthonormalBasis puw pvu reassoc sesqFormOfInner tends ¬InjOn ¬rootSpace ⇑SymAlg ##RigidCategory ##PMFReal integrand CommSemiRingCat toAssocList IsCoreflexivePair prodXSubSMul mulAutArrow isPrefixOf preCantorSet ##OneHypercovers ##Preservation leibniz ptsOfPeriod equivRatAlgHom intersperse nonsingInvUnit BoundedGENhdsClass colimitHomIsoLimitYoneda 148131 148596 LawfulHashable hintsum truncSwapFactors finiteSpanningSetsInOpen 17179869184 pushoutIsoUnopPullback linearOrderOfSTO triangleOfSES primitiveZModChar keysLookupEquiv ¬hausdorffEdist VonNeumannAlgebra reassoced 1ᶜ 237 33 38446 464 836 840 844 9321 AF Append Bx Bᵀ Get Hm Hic IC I₅ I0 MN Make Nᵐᵒᵖ On Reduced SI TS Tˣ Tor T35 Uint W4 Wequiv YClass a6 bB bran c₆ dTwo dxy eId fP fine fair gₗ girth hₘ hrank iM j4n ks km lv lZ lle lists llift lYX m₁₂ metrizableSpace ni nontrivial nYZ ont pab punit qt qR rj rz rough sδ uZ uY uux uYZ vu vr vc ¬o ¬⊤ ¬ℵ ¬bit ¬Three ¬Odd ¬Inseparable ¬Antitone ¬CategoryTheory α⁻¹ γS εy ψts ᵈᵐᵃ ↑o →◃ ↥Q ⇑t ⇑Finset ⇑LinearMap ⇑equiv ∂map ##l0 ##elete ##rid ##tinian ##Run ##sOver ##conv ##a₁ ##Augmented ##w₁ ##w₂ ##pass ##Circumcenter ##gle ##GCF ##X₂ ##P2 ##De ##864 ##Imp ##Quiver ##68 ##₃₂ ##stTopology ##orte insertion ##inpoly ##ombo ##onnect ##req IsOrthogonal IsIsomorphic ##odim mapObj mapBinary mapCommMon MeasurablePow toGraph toOne toMono toMon toEquivalence toPartialOrder toMonoidalFunctor toNFA toBundled hfr hfδ hfne ##Eqv InClosure HasAdd HasCompl ##lyDisc ##OrderIsoOf ##HomId ##HomInv ##OnObjects ##MulOfLE Prestructure hsi re₂₃ re₃₂ homological homOfCone homOfCocone hxq hxo hxm hxQ hxP2 compStarAlgEquiv cardCommutator mkFactor mkClasses ofTop ofAlgHom ofPi ofENat ofPNat ofCoprodI ofRowLens ofNormedAddCommGroup ##AddSubmonoid ##AddFlip haa haf ha₄ hamonic FiniteField ##OfSeq ##OfType ##OfInc ##Subordinate op₁ op₂ opUnop invAux ↑n✝¹ ##IsCokernel hgl hgI OrderRingIso coalgebra ##EquivSet Costar CoalgHom CoalgEquiv htα ##RightOpIso hcodim ##OpenCover ##Coalgebra hbJ hbred eq₃ finBasis finprod finAddFlip ##ToFunctor ##ToUnder ##ToAbelian ##ToSubordinate toFunLinear liftBaseChange liftConeMorphism ##FunctorData s₁ᶜ spanFinset spanExt hi₄ hi4 hyy hyα stRun ↑↑1 ChartedSpaceCore p₂o comapEq minCard isEqv asHom hrR hrI MonoidalCategoryStruct AddGroupTopology ##Multiples ##OneCocycles sumInr subNat FreeGroupoid X₂✝ b₁J g₁✝ hey heX shuff shorte piRing piToPi hvo hvv g₂✝ g₂⁻¹ huu huj ##Infi ↑m₂ imageOfD imageUnopOp zeroSection swapRight hU1 hU₂ ##Nonzero hks volumeIoi 1192 hPm t₁✝ Produce ProdAd t₂✝ ##ArrowEquivProd StarRingEquiv ##FinsetOfMem ##ModTorsion hzJ hzw mem1 mem₁ memU LeftUnique LeftCosetEquivalence equivSubtype hμS ##tingHomClass h2n h20 h2ε ##MonoOf hqz isoShift isoTwo isoOneCocycles comm1 comm2 supOfSeq ##ayRefl GradedOne ↑y⁻¹ r₁₁ r₁₃ hFS hF1 hF✝ r₂₃ infSum cs2 v₃₁ ##tends ↑S₁ ↑gf ↑g₀ hwi hwb Artinian hAconv bypass descOfIs ##adicRightAdjoint ##InvHomId h0C ##FactorDvd ih₂ OneCohomology OneCochain OneMemClass OneCocycle reverseRecOn pb✝ hoy lowerSet lowerInv dualLift dualRestrict hKg hKμ hKmem fromMatrix y✝² topM hV₂ ↑denom✝ ##sToPresheaf hMin fderivInner predA predB ↑z1 hR₀ Gamma0 coeEmbedding 1643 totalEquiv basisModTorsion ##ThinSkeleton β₂✝ uncurryLeft a⁻¹⁻¹ hJ₂ hJY hJss sheafOfType flipCompEvaluation ##implicialAugmented tsub cmpβ BiTotal hpq✝ hpql0 onQuot onLine typeEquiv toNatLinearEquiv divBy LipschitzMul ##ConvexHull hδ0 ##CoconeMorphism ExistsMulOfLE toSlashInvariantForm splitSupport ##ComplToSubordinate ##ResidueField toPi toPowerSeries ¬a₁ ringEquivOfRingEquiv coneUnopOfCocone coneRightOpOfCocone τ₁₂✝ steps terminates IsBrid adhs RBSet h3a h3K cols ↥L✝ ##EpiOf toAddUnits ¬x✝ keyB rTensorAlgHom auxLemma curry0 vertices cokernelToAbelian normalizeObj uniformOfFinset coconeUnopOfCone coconeRightOpOfCone FaithfulVAdd lTensorHom stdAddChar ProperlyDisc ##icCompletions reindexEquiv ##EquivOfBasis ##heytingHomClass ##CondSet ##CondensedSet linearDeriv modPart hp₂o revOrderIso germTo nzM assocRight assocInv frobeniusMorphism hσ1 conv✝ hyz✝ NatTransExtension fibRec InducingFunctorData disconnect sbd ##ComposeIso hπT ⅟↑denom✝ baseChangeHom FamilyOfElementsOnObjects hDF homMk₅ homMk₄ ##OfIsColimit acc✝ fbot ¬c₁ cyclesMk IsRegularOfDegree cospanExt twoCoboundaries h₄₃ fst✝⁴ valuationOfNeZero cba₁ sectionsEquiv sheafifyComposeIso hdiv0 reflectionCircumcenter diagSub ##VSubFace precompL HomotopicRel it₂ verticalIntegral ##NumbersUpTo newCone ¬↑i natTransExtension AssocRel prodMapLinear IsLinearOrder ⇑UniformSpace homotopyHomInv homotopyInvHomId ##647 hmeas✝ binaryCoproduct gcombo paths toNonUnitalStarSubalgebra AlgebraicClosureAux toFractionRing✝ ##282 xyab ##Symmetrify ##116 toDelete equivFunL equivFunOnFintype toMulBot firstRow primrec IsWeakAntichain ##VertexOfInc spec₂ toComplexMeasure evenOddRec multicospanIndex htcl 25278 25282 birkhoffFinset hikl Kᗮᗮ rows ##PowerOfTwo ##InnerConst leftOpRightOp BoundaryLE ¬minpoly iWU₁ iWU₂ hss₁ 210 gsum PrincipalSeg sgn δ₀Functor CPRankMax1 limitConeInfi gammaMeasure withTopMap withTopWithBot usu anyM unionComplToSubordinate iCondIndepSet EmptyRelation StrongEpiCategory ##294 StateCpsT hared hnps hnp1 Cancels hxp✝ hxp₁ ##489 toLaurentAlg nXZ nXY components iWX₁ iWX₂ mongePointVSubFace rightShiftAddEquiv hlimint ordConnectedProj fastFibAux hnegζ otherVertexOfInc hp₃p₁ unitGroupMulEquiv sequenceOfCofinals ##1728 CocompactMapClass toBlocks₁₂ ofJ0 ofJ1728 toGradedObjectMap hnotmax 225 48051 48055 48059 hNMK ￢￢b antisymm✝ antisymm✝¹ sigmaIsoGlued Ffu comonadicRightAdjoint composeAndSheafify coneOfCoconeUnop coneOfCoconeRightOp structuredArrowEquiv coconeOfConeUnop coconeOfConeRightOp hsat₁ hsat₂ N₂Γ₂ToKaroubiIso HereditarilyLindelofSpace invertibleOf lem2 haefg delayRefl ##InrIso exch✝ monadicLeftAdjoint ¬Monotone ##OfEqInnerConst GenerateOpen ##CentroidWeightsWithCircumcenter lWZ lWY hKd0 hNxε ##BundledCore algHomUnitsEquiv iZW₁ iZW₂ toBlocks₂₁ toBlocks₂₂ vecAlt1 vecAlt0 OfLocalizationSpanTarget hhdef ofLinearIsometry eLpNormLESNormFDerivOfEqInnerConst squashGCF hE₀fin algHomEquivSigma piLpCongrLeft room₁ ##Append1 toCompHaus forgetToLocallyRingedSpace yonedaCollectionPresheaf Adualₗ isometryEquivMap PreEnvelGroupRel 9373 hazw heEI ¬IsSFiniteKernel wideSubquiverSymmetrify mapToFractionRing InfiniteDimensionalOrder toFilterDistortioniUnion definedAtLeft Coproducts pUnitCocone substructureReduct NormalEpiCategory typeToPartialFun revFindAux costructuredArrowYonedaEquivalence simplicialCosimplicialEquiv children GetElem MakesOver OnRoot SIF T35Space branch finestTopology fairmeas lZX metrizableSpaceMetric onto qR0 roughNumbersUpTo uZW uYW ¬ℵ₀ insertionSort mapBinaryBicone HasAddFundamentalDomain ##OrderIsoOfFactorDvd homologicalKernel cardCommutatorBound mkFactorOrderIsoOfFactorDvd minCardFinsetOfMem shuffle piToPiTop imageOfDf volumeIoiPow 119255 Produces ProdAdicCompletions isoTwoCocycles descOfIsLeftKanExtension OneCohomologyRelation fderivInnerCLM 164386 sheafOfTypesToPresheaf ##ResidueFieldUnits IsBridge cokernelToAbelianCoimage ProperlyDiscontinuous reflectionCircumcenterWeightsWithCircumcenter homotopyHomInvId toDeleteEdges leftOpRightOpEquiv mongePointVSubFaceCentroidWeightsWithCircumcenter otherVertexOfIncident MakesOverArrow mkFactorOrderIsoOfFactorDvdEquiv minCardFinsetOfMemConvexHull 1ᵀ 250 329 450 52 526 650 737 Ai Bᶜ Bmo Cplt Eb Eigen Etale Fderiv GCommSemiring HX HP Hid HSub H₁₂ Hrec Hpos H₂₃ Hlt HL1 Iγ Itop L3 Label MT Ng N₄ Pm PQ Plus Quiv Rt Rgt SNorm Sbd Skeletal T0 Topen VU Xᵒᵈ YIdeal bk binomial bipointed cS cᶜ eβ emax energy fᘁ fam fData h8 hₐ hem hiz hri hSub hrd hunc hperm k0 kre kpos l0 lif lef lig mᶜ mes nullb quo semiring sUnion ssub skeletal tN t✝¹ ust umem vf wd wK wrepr ycc zd ¬R ¬E ¬Y ¬btw ¬Interval ¬coeff ΓIso α₃ η₄ η₃ ι₄ ιₜ ιFunctorObj ψ✝ ℕᵒᵖ ℙ✝ ↑𝓘 ↑RingEquiv ↑inv ⇑ρ ⇑add ⇑hn ∂ℙ ∂if ∃ᵐ ≃ᶠ ⥤ₑ 𝔸✝ ##Fr ##rM ##dry ##dBasis ##sGlue ##Src ##SkyscraperPresheaf ##awful ##Light ##LEquiv ##Lmap ##hrM ##Moment ##12 ##fy ##bim ##Using ##2365 ##733 ##7209 ##61 ##60 ##₃Map ##₃Hom ##VU ##95 ##469 ##Walking ##WalkLength ##inr ##acy ##raDe ##unt ##ingRight ##tienti ##tify ##oller ##CommLeft IsOne IsClassified IsValid Measurab ##gebraCatIso CommMagma mapX mapY mapIntegral mapAux toComm toPrime toSubspace toSeminorm toAlgEquiv toMorphismProperty toHeap toGlue toEdge toCloseds toIntermediateField hfact HasFunctor ##MapHomologicalComplex ##lyConnectedSpace hsF hsδ hsupp hspan NonLindelofSpace unzero hxn hxk hx3 hxV₁ Listβ Listα compQuasi ofHomotopy ofAbelian ofEven ofLimitCone ofIsoLimit ofLower ofComap ofColimitCocone haj haU FiniteIntegral ##OfDiagram ##OfMooreComplex ##OfBinaryBiproducts ⁻¹⁻¹ x✝⁸ x✝⁶ x✝⁻¹ ##aining invf invEmbedding ##IsIso ##IsCompact OrderRingHom Unramified ##EquivSigma ##EquivSelf ##EquivCostar ##EquivWalking ##FiniteFiltered Stalk IsCongr ##IsoKer algebraTensor ##utological ##LeftExtension ##LeftLift ##ueGroup h₁₄ ↑s₀ ##ModuleEquivalence hcF hcos hcompact hconj hclosed hmX hbe ##ToSt ##ToMon ##ToCentroid BohrM mulEquivOfLocalizations restrictHomEquivHom sndHom natEnd liftRingHom hiu hiy hiμ hiYX ##ClosedCompact ##ObjEquiv ##ObjPullbackFstIso evalNeg stoneCechExtend ↑↑c ↑↑ₐ ↑↑𝒰 PartialDiffeomorph isComplete isInt isValid unopMap ##epresent asBoolAlg asBoolRing hrc hrVU OpensLeCover hden ##ShapeOpEquiv ##additiveOfBinaryBiproducts addMap addEquivOfLocalizations sumSet sumEmpty sumsq 1081 pullbackArrows pullbackIsPullback subS sub0 ##algebraCatIso this✝⁹ b₂J singleMapHomologicalComplex g₁₁ g₁⁻¹ ##SumLex shiftr prog g₂₂ huy MonModuleEquivalence ##InfPrincipal getFiber tensoringRight inrRangeEquiv image₁ zero✝ zeroth zeroIso ↑bd hUm hU2 ##NonAssocRing hkj hkpos ↑rx RelHomClass starEquivCostar ##Aux1 ##Aux₂ ##AuxOn ↑e₂₃ ##DualEquivDual ##ArrowEquivalence IsNontrivial hzne hTu hTf hTeq ↑tα numberField numNodes hSuit 127 LeftTotal equivOpposite equivBit equivLax hμ₀ toLawful ##ProdFinsupp habs isoEquiv isoPullback isoPushout isoHomologyπ isoHomologyι ##LEIff hεI det⁻¹ ⇑e₁₂ oneHypercover Bicartesian nonlinearRightInverse adjoinIntegral adjointify hBF ⇑g₀ subtypeHom subtypeClosure hFx infDegree smulTorsor ##SpanOpEquiv y₁✝ ##PullbackStalk RightTotal RightUnique RightCosetEquivalence hC0 hwa hwU colimitEquivQuot hAF hAU descCoconeMorphism inverseAssociator 1320 1347 1319 13864 h0x ##ScalarLeft ihp ih₀ hj2 ##ath01 arrowArrowEquivalence setD ltc pbx pbL ##SuccEquiv hKm fromTypes fromTransported fromMiddle fromCommLeft ValueGroup y₂✝ sq₃ hVc hVf hVmem IsTree ↑den meas0 fsub seq1 predConts ##FromFiniteFiltered ↑z2 ##OpOp hRs 1435 ##Ranges coeTo coeMonoidHom 1618 1641 SymOption ¬IsIso ¬IsQuasiregular sᶜᶜ sᶜˢ throw onDiag toPresheafOfModules IH4 ##LocalizationToStalk hneven hGε typesGlue ##IntEquiv cfcUnits ##wardInduction integralRep factorizationData takeList associatorNatIso inclusionOfMooreComplex ↑N0 anticomm hδpos ↑j✝ ↑j₁ AwayMap w✝³ ##GrpIso outside nilFun diagonalPath diagonalObjPullbackFstIso bitCasesOn ringLmap toLinearMapₛₗ₂ lpTrim lpBC kernelIsoKer h32 sigmaAntidiagonal quotientMul hfi✝ cocycle ⇑b₀ biproductComparison sr1 sr2 findAux findEn k₁t ##uenceSubgroup inducedAddHom k₂t ##HomotopyZero wittOne wittNeg uniformStruct uniformOfFintype centralMoment lieConj ##ivePresentation localmin pushoutSymmetry pushoutDesc ε01 powersHom toProdMulOpposite preimage₁ preimage₂ ⇑hU ↑hom ##KanExtensionUnique whiskeringEquivalence mbles nza foldlIdx snemp hσ2 ##AdjunctionAuxs NonUnitalStarRingHom NonUnitalStarSubsemiring toEn toEventual ##ForkOf bddDefault connectedComponentEquiv 1947 ##CoforkOf algEquivOf finsetWalkLength fr✝ productOfMem sxy ##OfIsColimitCokernelCofork hWc ¬span LiouvilleNumber ¬c₂ ##generacy 2079 20465 20469 hcd0 ⇑i1 ##ersivePresentation cba₂ hequiv ##AnnihilatorEquiv LightDiagram poly✝ polyBinom ##WhiskerRight multicofork sl1 sl2 ##CospanOpEquiv reduct finsuppScalarRight finsuppScalarLeft ##YonedaSectionsEquiv Minpoly ##ToPresheafIso sublistsAux ##693 ##694 Hcont gtc hpm1 LebesgueDecomposition ¬↑I unmopEquiv natTransApp quotAnnihilatorEquiv ExtraDe StableUnderComposition StableUnderCob leftHomologyMapIso ##519 ##velGroup ##1840 piFinsetUnion ##646 toMultilinearMapLinear prl hgmc remaining mrangeRestrict hft2 zmultiplesHom rightHomologyMapIso ##2890 ##AddEquivProdFinsupp lanLeftExtension modifyLast addHaarContent Hdiff i2n ##AsType ##271 ##SplitAt fiberEquiv mapIdIso ##ToLpMeas equivOfRoot equivOfNatIso SemiadditiveOfBinaryBiproducts EquivalenceJ ##421 ##MonCatIso Blunt ↑𝒜ᶜ BinaryBicones mkOfSMul mkOfLax mkOfOplax removeOp multicospanComp ofIsLocalizedModule 2532 localizationMapOf homogeneousLocalizationToStalk hω₁ hωb ##355 fourierIntegralInv cprank ##3926 ##260 toBipointed ofDirectSum toMatrix₂Aux ##360 coeq₃Hom ImpartialAux ##IsoLimitCompLim ⇑ofSubtype ##019 applyId gmint gmcont hB₀J ¬i₁ toCoalgEquiv toCoalgebraCatIso solSpace toMiddle kernelSubobjectMap hdf✝ 287209 limitConeIsLimit conductorSet hpn0 fixingSubmonoid ##DownwardInduction fullBraided homologyIsoSc collapseF LocallyLipschitzOn nondegComplex balancedHull distinctPairs ef0 ranCounit hxp₂ fromSpecStalk vanishes sHomWhiskerLeft sHomWhiskerRight ##LinearIndependentOfCardEqFinrank 3678 orderIsoMapComap ¬eLpNorm ##Adeles leftShiftAddEquiv toSetoid✝ toSetoid✝¹ noZeroDivisors ##include IsTrivialRelation lipsch mopMop srangeRestrict coclosedLindelof toContinuousLinearEquivOfDet optionEquivRight matrixToSt ##ToPGame hlcm ¬lim fromLeftNeg bᶜᶜ ExceptCpsT Corepresent claim1 pullbackConeOfRightIso ##opfAlgebraCatIso √↑k 25159 Cfg₁ gaugeRescaleHomeomorph singleObjApplyIsoOfEq degreeLTEquiv hfn0 CompletelyNormalSpace forgetToPresheafModuleCat isLittleO OppositeShiftAux 34421 ##Truncate wPathDestLeft ##CompatibleFamily toBialgebraCatIso monadMap toLeftMovesNeg toLeftMovesToPGame opcyclesIsoSc IsOrderConnected walkingParallelFamily walkingSpanOpEquiv walkingCospanOpEquiv ##704 functorialityEquivalence strongDownwardInduction avoid hornInclusion quotientKerEquivOfSurjective widePullbackShapeOp functorOfNatTransEq functorOfNatTransComp functorOfNatTransId rightDerivedNatTrans widePushoutShapeOp 1162365 1161840 1162890 5926 ##sEquivMonoOver ##stPrefixDiff structuredArrowEquivalence ##OpensLeCover ##MatricesSubmodule discretePresieve pullbackConeOfLeftIso pullbackConeOfLeftLift quotientInfEquivQuotientProd node4R MaximalSpectrum hsaty hnfd subsemiring ↑u₂⁻¹ lanLiftLeftLift augmentTruncate 6320 homToEquiv linearIsometryBoundedOfCompact ##LESNormFDerivOfEq lem1 ¬¬p leftNegEquiv subtypeCongrHom k2nl ↿γ₁ ↿γ₂ shape₁ shape₂ ofMapLEIff IsTwoCocycle toPNatMultiset egirth skewAdjointMatricesLieSubalgebra HasExplicitFiniteCoproducts ofSigmaCoforkFunctor sumFinsuppAddEquivProdFinsupp dualProdDualEquivDual leftZigzagIso averageMap ##ConjugateSquare toZeroHom squashSeq galRestrictHom 843926 bracket cechNerve cechConerve toHopfAlgebraCatIso toAddGroupFilterBasis hε₂0 hε₂ε 262057 262054 512830 512833 subToKer perf0 toSigmaCoforkFunctor 4380 familyOfElementsOfSection IsSupClosedCompact 108053 toSingleObjEquiv splitAtPred coconePointSMul toUniformOnFunIsCompact threeCochainsLequiv ##filteredClosure Saturate 77901 Foldl SimplyConnectedSpace subterminalsEquivMonoOver indexesOf compatibilityOfZerosOfIsLimitKernelFork 414355 IsMulTwoCocycle 73697 ##SepUniformSpace ##CompSheafToPresheafIso NormalMonoCategory 20473 hmfngE subsemigroupMap shortestPrefixDiff ArtinianObject germToPullbackStalk CoproductsFromFiniteFiltered CpltSepUniformSpace Eigenvalues Ngu SNormLESNormFDerivOfEq bipointedToPointed hizw kreplace nullbdry quotienti ssubsets ycc₂ ¬IntervalIntegrable ⇑addMonoidAlgebra ≃ᶠⁱ ##SkyscraperPresheafAdjunctionAuxs ##bimodule ##₃MapBifunctor ##ollerup MeasurablySeparable mapIntegralClosure toPrimeSpectrum HasFunctorial compQuasiMeasurePreserving ofComapInfPrincipal FiniteIntegralAdeles ##EquivWalkingParallelPair StalkSkyscraperPresheafAdjunctionAuxs IsCongruenceSubgroup algebraTensorAlgEquiv ##utologicalCocone BohrMollerup evalNegHom MonModuleEquivalenceAlgebra getFiberFunctor equivBitIndices toLawfulFunctor BicartesianSq nonlinearRightInverseOfSurjective 132037 131985 161801 164135 SymOptionSuccEquiv ringLmapEquivSelf lpTrimToLpMeas lpBCF findEntry toEventualRanges productOfMemOpens 207926 polyBinomAux1 ExtraDegeneracy StableUnderCobaseChange localizationMapOfSpecializes 367879 mopMopEquivalence toContinuousLinearEquivOfDetNeZero matrixToStdBasis Corepresentable walkingParallelFamilyEquivWalkingParallelPair subterminalsEquivMonoOverTerminal SNormLESNormFDerivOfEqConst quotientiInf 516 581 600 70 719 896 Certi Dg Df Elem FRes Hold Il ID Kclosed Pr Pmin Plat Sᗮ Snd Sali Slim Ul Uc Yint aA a7 alex bq0 cF cIcc e3 eif epimorphisms hΔ hᵣ h𝒰 hite hrec iEx iAll jep l8 nu nst nerve ninj prt pmin parallelFamily qRight rR rra rinv s⋆ same schwartz tn td triv ue uif ultrafilter vsub vsum wa wb wRec wsum xJ xle yC yy yV zh zk ¬H ¬K ¬∅ ¬Sum ¬LinearMap ¬Injective ¬Subsingleton Σˣ ι₀ νi ↑5 ↑Finset ↑of ↑PartialHomeomorph ↑include ↥C ⇑H ⇑I ⇑⊥ ⇑im ⇑Co ⇑ab ⥤ᵇ ##iSym ##ek ##eierstrassCurve ##racket ##Jacob ##xL ##RS ##sFor ##ck ##Strongly ##Tgt ##pred ##Che ##Can ##Choice ##v2 ##ySpace ##ficate ##Eε ##XIsoOfEq ##Bits ##BigO ##⁻ᵐ ##749 ##Iterate ##347 ##551 ##⁺ᵐ ##stle ##tell ##onic ##onempty ##lesum ##icSequence IsId funOfIdeal Finj ##elCan ##atom ##ulator mapSet mapOf mapFunctor mapVal mapPullback mapOpcycles mapBicone mapDesc mapBilinear TopologicalLattice toW toSem toSpan toContDiffBump toUpper toOrthonormalBasis toHomotopyEquiv toInductive toCondensedSet ##setOf hfe hfR hfM ##tert HasPoints ##MapSpan ##HomFunctor ##iestle ##ortho ##MulInv hsne revP reinsert ##FieldEquiv homTensorHomMap unch hxF ##ZeroHom ##ZeroCongr ##ZeroOfNNReal ofSubmodule ofFinsupp ofCoc ofUpper ofAntisymmetrization ofIterate hpz ##AddSemigroup ##AddUnits hae hao IsSpanning ##OfEmbedding ##OfKer ##OfMinPoly Natα symmAt opComm invRot invSelf ##IsInitial OrderAddMonoidHom coxeter coatom ##EquivSpan ##EquivSupQuotient ##EquivPreord ##TopCoe ##izationCongr atLeastTwo ↑xi ↑x₀ hnu hnrp prodCongrLeft ⇑fa ident ##LeftPushout ##anged Coyoneda htI htW htβ hcx hcount hcountable hcfg hmu hmB hmonic hbu hball finsubgraph finChoice ##ToS ##ToId ##ToLimit ##ToMonad ##ToRingEquiv ##ToNormalizedMooreComplex ##ToResidueFieldUnits toFun✝ mulOp restrictRootsOfUnity snd⁻¹ liftLinear liftStar liftOr liftOfIs liftOfSurjective →L⋆ a₁⁻¹ hiC hib evalₗ evalXSelf ↑↑η BorelCan ↑f₀ comk p₁o ##izerCondition ##BotCoe OrderedStructure InjectiveFunction ##CompEq ##CompInv ##CompRot ##CompWhisker isPowerOfTwo isBigO preinc hrss hdq hdF hdisjoint hdprod addCases ##OneCongr ##Prelocal pullbackZeroZeroIso sub1 subsum insertWith heG heφ n✝² ↑I₀ piFieldEquiv ##AddGroupCongr hv₅ huH huG ##InfHom hl₃ hlroot hUeq hkb hk2 projZeroRingHom hIb ##tonicSequence ##plittingField ##Idem ##Ident ##ModIdeal hzC ↑tᶜ mem2 numBits hS₅ hS₄ ##CoeffWithin 129 12400 LeftExactFunctor equivAlgHom equivSigma hμf hμ₂ toLower toLawson ##ProdDirectSum ##Cols autGalois h1P h1U h2v h2P h2U h2D h2k hab✝ hqt isoExt isoLocallyRingedSpace commf comm✝ commRingCatIso interUnion ##LERange ##LENhdsClass sintert encoding withZeroCongr withOneCongr hε2 hε₁₂ auto✝¹ ##LimitToLimit CompactlySupported e₂✝ ##Cones NormalizerCondition IsAddCentral negMap BoundedLENhdsClass hF₀ VectorsProdEqOne ##Curr csY m₁✝ hxyz ##Parameter RightCancelMonoid RightExactFunctor m₂✝ hCpos hw𝒜 colimitLimitToLimit hAx descQ h0q h0₁ h0P ihq ihg ihf ih✝¹ hj₀ cons₂ consRecOn rankGT setCurr ho₁ hKV fromCocone limitBicone hVp MapReverse Endpoint ##FamilyOfElements hRA 1469 1400 hαx n₂₃ ##aceMapComplex ##PowT Gamma1 monomorphisms LiftHom LiftAdjoint Generating IsSeparableContraction inj₀ hN₃ ¬IsIntegral ¬IsPrime ¬IsPrimitive basisAux basisSpanSingleton traceAux ↑c1 ↑c2 hJM hJ₀ hJfin sheafSections tsZ tsY AddCommMagma HomotopyGroup ##ProductsOfShape rootsOfMinPoly hstf generated onCircle onFormula ↑lift ##LocalizationAway yonedaFamilyOfElements toNatSubmodule ##PolynomialQuot LipschitzAdd biUnionPrepartition lines ↑U⁻¹ ##Cocones ExistsMaximal ExistsOneDivLT toSesqForm toSplittingField Anonempty NullMeasurableSpace ¬adj VAddMemClass map₂Left rotCompInv lcongr StrongConcaveOn StrongConvexOn lpPi ##IntegerNormalization h3A monotonicSequence sigmaComparison MonadCont coprodCon recTopCoe recBotCoe ↥s₁ conjBy xl✝ disjs HasLeftResolutions hQx hQ₁ hL✝ xr✝ auxHom vertex ##SurjectiveInjective IsAffineHom wittAdd wittSub hhpred mapBifunctorComp pushoutLeftPushout toAffineIsometryEquiv SubringClass normalizedFactorsEquivSpan ¬f✝ ProperVAdd hYX pushforwardIso linearYonedaObj ##aylorSeries WeakBilin freeAddGroupCongr ##PiType hfs1 hfs2 innerProp snakeInput hfin✝ ∂↑P moduleFilterBasis ##CofaceMapComplex enumIso t2Y isLimitCone ##odularGroup IsNormalClosure hg₁1 ¬sbtw PositiveCone ##DiagonalSucc ¬c₁₂ hfcont ##SubsetProperty 202 HasOrthogonalRows HasOrthogonalCols hgf✝ hgf₁ ⇑i₁ ⇑i₂ ⇑↑n ⇑↑φ PInftyToNormalizedMooreComplex SymmetricCategory condKernelUnit singletons goal polynomialQuotientEquivQuotient commutatorMap minFacProp ##DiscEquivPreord ##327 digitsAux nd₂ ↑↑x⁻¹ equalizerIso ##Outside NonUnitalSubalgebraClass hpos₁ hpos₂ IsNatPowT offsetOf ¬↑j hnormz splittingOf nonunit quotAdjoinRoot quotEquivQuotMap disjointSigma mellinInv ##512 ##795 homotopyP ##180 restrictionMap IsEll mulRightEmbedding taylorCoeffWithin ℤ√↑ ##287 ##289 IsSimpleAddGroup ##MetricApprox toJacobian hcoe ##ExtensiveEquivalence affineOpensRestrict reduceModIdeal toΓSpecMapBasicOpen Aᵀᵀ irred pdiv hsumlesum ##423 spanningSetsIndex ##UnopUnop g1⁻¹ ##LimitsAux RestrictGerm dgb dg0 dgmem large₀ ofIsRightAdjoint coherentExtensiveEquivalence IsTotallySeparated homogeneousSubmonoid hω₂ RingEquivClass toModuleHom mapTrifunctorObj ##267 System toSubMulAction g2⁻¹ hε₁0 SeparatesPointsStrongly normedAddCommGroup ↑↑I⁻¹ peek ##LequivDFinsupp ##TrivialIso scalarRTensor compAEval ##merGroup hfu✝ 288 2836 rIn⁻¹ ##591 hbdiv w2⁻¹ toAddMonoidWithOne grade1 grade0 glueMetricApprox h₅₁ ##548 withTopCongr ##ucasLehmerTest 260 hndf Hfun ##298 IsCancelSMul zmodChar dualTensorHomEquivOfBasis pB₁ hp3p2 hp₂p₄ binaryProductCone Representable ##opfAlgEquiv divModEquiv 29737 29733 6986 colorClasses completeGraph greatestOfBdd isEmptyAlgEquiv sublistsLenAux pullbackDiagonalMapIso NNRatCast ftaylorSeries monoidHom hfyx fastJacob 96113 selmerGroup mapRightHomologyIso TotalComplexShapeSymmetrySymmetry mapLeftHomologyIso equivProdDFinsupp ##PrimitiveRoots hv1v2 unitGroupToResidueFieldUnits 34793 dxeq fR0 InvariantForm ##Universal₁ ##ariant toBialgEquiv vnL nonUnitalSubsemiring S0m withBotCongr NonUnitalNonAssocCommSemiring hgeq strongRecOn hpbar ##EquivQuotPolynomialQuot stolzCone ClopenUpperSet isLt✝¹ dyeq ##873 htends hFnemp toRightMovesNeg toFreeAddSemigroup hexpmul linearizationTrivialIso rightAngleRotationAux₂ finTwoArrowEquiv hsups Extensive IsStableUnderProductsOfShape h₆₂ regulator treeHom toNormedAddCommGroup toNormedDual shiftFunctor₂XXIso ↑u₁⁻¹ IsInvariantBlock quotientInfToPi quotientInfEquivSupQuotient HImp coneEquivInverse cauSeqAbs cauSeqRe cauSeqIm naturalParameter instTopologicalSpaceProd fact1 squareCylinders 27924 27917 lF₀ NormedOrderedAddGroup ofMapSub Mk₁ toTrivialization 34786 MonadicRightAdjoint ReflectsFiniteLimits BlankRel 38366 CreatesLimitsAux hfngEε openness₂ binaryBiproductData shortComplexH2 toMonoidEnd ##Clopens IsMulOneCoboundary recDiagOn constantsVarsEquivLeft h₇₄ abelianizationCongr addEquivOfQuotient fsumeq toHopfAlgEquiv bdA2 hnqp subToSupQuotient equivUnitsAffineMap perf1 37693 67791 67795 comp₂Measurable 123999 123995 csZ✝ realContinuousMapOfNNReal realContinuousMapZeroOfNNReal 96105 96109 448795 12624 topCatAdjunction IHrr nonZ1 moduleCatMkOfKer actionDiagonalSucc ¬LucasLehmerTest unitBallBall psigmaCongrRight toPrenexImp sectl subordinateOrthonormalBasisIndex graphEquiv₁ 21546 orthonormalBasisOneI vcDim lowerSetSupIrred finestTopologySingle HX2 inclusionOfMooreComplexMap toEnvelGroup HasFunctorialSurjectiveInjective Certificate FRespects HoldsFor Priestle Platform Salient SlimChe alexDiscEquivPreord hite2 iExs iAlls rRpos schwartzSeminormFamily ultrafilterBasis νi₀ ⇑CofiniteTopology ##telli mapOfHomotopy mapOpcyclesIso toInductiveLimit ##MapSpanMk reinsertAux unchanged ofCocomplex invRotCompRot coxeterWeight finsubgraphHomFunctor liftOrGet liftOfIsRightKanExtension BorelCantelli preinclusion subsumes 124003 autGaloisSystem commRingCatIsoToRingEquiv interUnionPullbackCone CompactlySupportedContinuousMap colimitLimitToLimitColimit limitBiconeOfUnique EndpointIdent 146934 GeneratingSections ¬IsPrimePow ¬IsPrimitiveRoot rootsOfMinPolyPiType ExistsMaximalSubsetProperty rotCompInvRot lpPiLp monotonicSequenceLimit pushoutLeftPushoutInrIso normalizedFactorsEquivSpanNormalizedFactors polynomialQuotientEquivQuotientPolynomial offsetOfPos quotAdjoinRootEquivQuotPolynomialQuot RestrictGermPredicate fastJacobiSym quotientInfToPiQuotient naturalParameterization moduleCatMkOfKerLERange HasFunctorialSurjectiveInjectiveFactorization HoldsForLocalizationAway PriestleySpace SlimCheck 320 324 44 455 457 419 456 417 470 5✝ 542 649 622 79 87 831 841 822 951 Apos Bc Beq Cᵀ Ceq CFilter CAlgHom DP Eˣ Fa F2 Fˣ Fam Fast Fourier Hj HSpace Hss Hmap HL2 HNot Ix Iy I5 I✝¹ J1 Lf L₁₂ MF Orthoc P₀ PB Rn Ran R₁₂ Ss Sk Sˣ Sct Span SNum SkyscraperPresheaf Uop Vl Vinh Wᶜ Zoom aed bO bid bundle cM cN dk dμ dfin e₀ eas effectiveEpi fk fdd fcd fmem formalMultilinearSeries gj grad gmeas hon hec hub hSup hOdd herase j✝¹ lpos mil may nr n4 ntu oJ ple pid pnt q₃ sS sv sₙ string tH tne tpos ult vo vy v0 wMap xD xₙ xset yH zx ¬T ¬ν ¬Sup ¬Inf ¬AddMonoid ¬Ir ¬Bornology ¬erase Γe Φ₁₂ Φ₂₃ αβ γ₃ γtop γpolish δε δone εK εTo ζe μK μβ νS πFunctorObj τpos χ✝ ϕ✝ ↑Upper ⇑y ⇑ν ⇑Set ⇑Real ⇑Filter ⇑FreeMonoid ∂d ∂p ∂sum 𝒅ₕ ##iary ##irection ##ror ##tl ##tail ##not ##Sol ##SignedMeasure ##StrongEpiMonoFactorisation ##Snorm ##Aug ##wer ##Tprod ##oherent ##partite ##Label ##LEquivProdFinsupp ##most ##mgle ##Main ##gram ##140 ##Zmod ##ZMultiples ##₀Equiv ##G₁ ##PSnd ##be ##Det ##Double ##kg ##786 ##02 ##Ihom ##QIso ##KxL ##535 ##441 ##ιApp ##γσ instModule ##ining ##alRec ##hear ##resentation ##Commute ##CommShiftIso IsEven funMulInv FinVec mapHom mapAlg mapsTo mapCech mapOfSurjective mapIic mapFr ##ableFiltration toK toGroup toMeasurableSpace toImage toNeg toRows toColumns toNonneg toThinSkeleton tower ##ild ##iliary hfj hfK hfloor hfAB Inverse HasAbs HasSize HasTwo HasProp ##MapsTo Subbimodule ##lyCover ##ricSystem ##InType ##InBasicOpen ##InDouble ##Ones Preirreducible PrelocalPredicate hsT hsB hs₄ hsxp hsxy uninf MulDiv hxw compMeasurable compatible compCoyoneda cardDist ##FinBasis rangeKer mkHomeomorph mkPostcomp mkSol mkLabel ofCone ofMeasurableSpace ofExact ofBox hph hp₄ hpα ##entricSystem haL hag IsSkeleton LieHom ##OfComp ##OfThree ##OfNot ##OfFlip ##OfBadSeq ##OfTprod ##SubPow ##SubLower op₃ opHom invOf invOne ##IsSheaf ##IsPushout hgo OrderMonoidHom OrderMonoidWithZeroHom codd ##EquivNat ##EquivSubtype ##EquivSigmaCofork ##EquivCoprodI ##FiniteCompact ##FiniteSpan u₂₁ ##MeasureFamily ↑xn ##IsoSwap ##IsoBinaryBiproduct ##IsoCurrySwap prodOpEquiv ⇑fb Coalg CoheytingHomClass CofilteredClosure IsPFilter ##RightTo hcn hcv hmod hby hbf hbφ eq3 finsum ##ToD ##Toπ ##ToAlgebra ##ToOfIso ##ToPartOrd ##ToCoalgebra toFunAux sndOfNot nat✝ natMod nat✝¹ liftLie spanx spanFinBasis ##vPowerSeries hiD ##DiffWithinAt hyn hyS hym hyf ##Catch ##ObjFlip stVar stableFiltration ↑↑φ leftSection leftFixedPoints leftRetraction StarHomClass coeffIntegerNormalization ifr ifkg α✝² SubmonoidPresheaf abel abcd comapEquiv minBadSeq ##IntegralPowerBasis ##SupHom ##CompMono isFraction isKernel isCokernel isRep isRed isSuccLimit isAdjoinRoot unopSymm ##epr rightSection rightFixedPoints rightRetraction preord hrw hrz SumEval impro hdu hdegree hdfg ##ShapeUnop AffineOpenCover ↑p₂ ##Multipartite ZeroCochain 102 104 10489 ##atedBy pullbackSpec ##AssocReparamAux singleFunctors indiscrete ##SumDistrib heval piLinearMap piQuotient piDiag piEquivalenceFunctor piIsoPi closedIhom hvc Component shiftZero hlu hl3 hlzero hlhs limy lim2 lim⁻¹ castNum castOrderIso inrComp imageFactorization zeroHom V₂✝ swapLeft V₁✝ hU3 hUAB hkmul ↑rg 1113 ##CompactToT functorL₁ functorL₂ hPs hPa hPp hP₄ hP₇ hI₁ hI₂ ##Aux₁ ##Auxiliary Productive ##DualPairing unitCofork unitBackward unitAuxAux hzl hzd hzR hT₅ hT₄ ↑tβ mem₀ hSx hSs hS✝ ##ClosureOperator C₂ᵒᵖ equivHom equivAdj equivNum equivCongrLeft equivariant equivSignedMeasure toLoc ##ProdAdjoint hab₂ habne hq✝ isoLimit isoSucc isoIsPushout commTensor GradedNatTrans enrich error b✝⁴ b✝³ oneSub nonemp ##LimitMapsTo p✝² ta1 ta2 tautologicalCocone ##enceFunctor ↥S₀ transRefl transAssocReparamAux subtypeOr subtypeSubtype ##inaryBiconeFunctor aevalEquiv hFt M₀✝ smulOfNeZero a1p SecondObj hCB hwR hw✝ hw0 hw₃ hwreal colimitCoyoneda hAd hAm hAmeas hAps ##TypeEquivIs primeCount descMap ##InvRotateIso 139 1337 bound1 hj1 hjf cartesian hφG₁ eqToEquivalence extendCone extendCocone hobj ##ickB h₀✝ h₀₁ hKx fromAffine fromSingle₀ sq✝ sqFrom limitUncurry topTo topDualPairing hVs ##Induced ##sToVar w₂✝ IsWide hMF hMT hMg upperSet upperSubLower ↑Kg ↑Kf hij✝ ↑z✝¹ ##OpUnop ##OpMop monToLax DistribMulActionHom tailD coeEquiv 167 169 ##CancelClass injRS injKxL centerToCentroid hNe ¬IsZero ¬IsFixedPt ¬IsUnramified ¬IsCoprime basisSingleton targetAffineLocally ↑c⁻¹ ↑circle uncurryObjFlip sheafIso flipMultilinear flipₗᵢ flipIsoCurrySwap thickB hstep this✝¹⁰ hpq0 toListAppend SeqCompactSpace IHl IHx ##CoproductCofan ##MonEquiv φ₁✝ φ₂✝ ↑v₁ ↑v₂ takeI ##PFst inclusionInDouble ##EquivalenceSet ↑NT corepr orthogonalGroup LawfulGet hinl hinr toScott toSkyscraperPresheaf w✝⁵ ##QuotTo ##ltP ps₁ ps₂ IsStandard conePoint coneOfHom constantsToVar smn smth toLinHom LTCmp hmn✝ EmbeddingLike forget₂Mon kernelIsLimit ↥Kᗮ empty✝ empty✝¹ h3C h31 monoOver sigmaπ sigmaSet sigmaEquiv Encoding quotientEquivQuotient quotientQuotientEquivQuotient coprodEquiv biprodIsoProd ##DivAux orbitEquivQuotient ##EpiComp ds✝ hQy ↥↑x s2✝ rTensorBot ub1 ub2 ν₂✝ ν₁✝ auxInv currySum Q₁✝ 1727 1777 1719 17551 hhmgle Q₂✝ compl✝ compl✝¹ encodePosNum ua1 ua2 PullbackCompatible normalized✝ normalized✝¹ coconeOfHom coconePointsIsoOfNatIso hEpos lTensorBot ULiftable lawson locality pushoutZeroZeroIso structureSheafInType toAffineIsometry ProperConst ##Normalizer preimageIso ##vdxy pushforwardToOfIso ##EquivOfLe ##EquivOfPrimitiveRoots realRingEquiv γ₁⁻¹ modDivAux ##UniqueIso symgen ↑hu ↑hr ↑hs mapHomologicalComplexXIso hfmono powCoprime countableGenerating toEDist evaluation₁ evaluation₂ evaluation₄ evaluation₃ t1✝ moduleEquiv toEmbedding✝ toEmbedding✝¹ cofree cofinal hlt₁ hlt₂ bddA 1939 submoduleMap ctop hπ₂ gaugeSeminorm hnmcp isLimitEquivSections isLimitOfFlip strInv iVZ iVX ha₁a₂ hΦ₂ triangleOfDegreewiseSplit IndexFunctor ##OfIsCocontinuous fbd fbb ##TorsionPolynomial changeInverse ##Defining hW₂ decomposeProdAdjoint ¬sin ##PreimageEquiv snd✝⁴ hκκ ¬cmp 206 hgf₂ twoTorsionPolynomial ⇑i2 rrss opensOfIdeal stabilizerSubmonoid fp₁ fp₂ hbc0 uc1 Bicones polyEquivTensor hg₂1 hdiva dedupKeys hf0ε adjunctionOfEquiv ##DerivationToSquareZero ##OutOfThree ↑↑self botEquiv bottom ##OddFEPair h4v derivedLength evtl pseudofunctor ##6946 regularCoverage HomotopicWith it₁ cofan₃MapBifunctor ¬↑MF toOrderBot quotLeftTo ↑φ₁ ↑φ₂ NonUnitalStarSubalgebraClass hxz✝ ##SimpleGraph ##181 ##186 rootsOfUnityEquivOfPrimitiveRoots m₀✝ prr ##Original hβγσ hsubW equivalenceLeftTo equivalenceRightTo ##248 toFractionRing✝¹ h₁₃₂ lanAdjunction hfx0 runCatch hcoeff Hdrop ##274 ContDiffBumpBase complexRingEquiv ¬MixedCharZero CorePresheafOfModules dflt integerMultiple IsCoatomistic ##508 ##500 ##503 toMulOneClass Hsum pdvdxy hsumltP hgt₁ hgt₂ quotientMapOfLE ##425 hp₀✝ ##Leads ##Impl mapTriangleIso mapTriangleCompIso mapTriangleIdIso mapTriangleRotateIso mapTriangleCommShiftIso mapTriangleInvRotateIso ht1m ##460 m2✝ restrContDiff mkOfHom mkOfHas underToAlgebra JordanHolderModule ofIsClopen hmin✝ initialBound hw₁✝ extensionToFun hmgEc pretopology ##LengthCost EventuallyMeasurable mapTrifunctorMapObj hB₁I leftOpRightOpIso toBinaryBiconeFunctor uniqueDiffWithinAt ↑Dr ↑D1 ↑D2 ##497 iWV ##AddOrderEmb ht2m vcompb ##014 hssu imageSubobjectMap toLocallyRingedSpaceCoproductCofan 216946 pointIndexEmbedding sg1 sg2 AddMonCatMax IsStrictWeakOrder hdfma nextCoeffUp 284 overToCoalgebra ↑E2 hvp✝ IsGeneratedBy hpn1 glueMorphisms gammaCDFReal 2679 ea₁ ##inctFactors ιTotalOrZero allOnes eventually equivFinOfCardEq mergeIdem FilteredClosure repOfTprod ##403 bicomp ##ZPowOfHom hlip✝ ppredA ppredB addMonoidHomLequiv 40512 leftHomologyFunctor verschiebungPoly xa₁ cantorSet 292 2927 2946 r₀✝ liftedLimitMapsTo rightHomologyFunctor rightHomologyOpIso sectionInBasicOpen hv2p relabelEquiv completeMultipartite ¬l₂ ##MinpolyMap iter₃ coimageIsoImage subOneIntegralPowerBasis ndrecOn ft1 claim3 ##OfLeftIso moduleCatHomologyπ hgu✝ leastOfBdd XIsoOpcycles dualSubmodulePar hurwitzOddFEPair unitsSMulGroup cancelLeads CompletelyDistribLattice optimalGHDist comparisonForget IsLowerModularLattice revAtFun maxGenEigenspaceIndex 345 575 5719 pq0 natTransEquivCompatibleFamily ##SemiNormedRing ##ForallMem ##EquivPiFork sumLexAssoc monadMonEquiv toLocalizationWithZeroMap mmnn toLeftMovesAdd toLeftMovesNim withBotMap hJlz 66933 Dependent εb0 hmt1 hifg strongInduction hnotone AddGroupSeminormClass functorCategoryEquivalence transitionMapLE HeytingHomClass rightDerivedDesc toRightMovesNim CNFRec multiforkEquivPiFork contractibleTriangleIso 5950 59749 hmf0 IsProjectiveMeasureFamily sigmaCongrRightHom homeomorphCircle ofEquivFun tc1 hsrc✝ IsLocalDiffeomorphAt longest indefiniteDiagonal orderIsoOfRightInverse trianglehMapOf openCoverOfRight openCoverOfBase ##Precompose subsingleton equivQuotientZSMul dropSliceTR differenceFunctor Universally BinaryBiproductData OfLocalizationFiniteSpan 64849 64855 64843 9011 fact2 toAddComm pathComponentIn hpy₁ hpy₂ liftOfDerivationToSquareZero strictMono SplitEpiCategory nullSetᶜ shortComplexOfDistTriangleIsoOfIso 94618 ¬Monovary symmetrifyStar symmetrifyCostar implicitFunctionOfComplemented autEquivZmod quotQuotMkₐ conesEquivInverse 75509 ImageMap LocQuiver ContinuousAffineMap mulEquivOfMulEquiv tb1 tb2 succNthDefining sumFinsuppEquivProdFinsupp sumFinsuppLEquivProdFinsupp hqd0 ##Postcompose ##PostcompQIso pushoutCoconeOfRightIso pushoutCoconeOfLeftIso 88321 Finsubgraphᵒᵖ 10890 12795 12799 linftyOpNormedRing linftyOpNormedAlgebra linftyOpSemiNormedRing 46503 addEquivOfAddEquiv 31880 31876 84186 sdiv zg₂ ##ZSMulOfHom compHausToTop mappingConeHomOfDegreewiseSplitIso monoidalAdjoint 68429 68425 room₂ zn0 hfkl hgδ₂ forgetToScheme boxProdLeft boxProdRight fullyFaithfulOfReflective IsSupFiniteCompact 108099 toSingle₀Equiv quotQuotEquivQuotOfLEₐ 69657 69654 𝒜ᶜˢ singleTriangleIso mcfab heI₀i binaryProductTriangleIsoBinaryBiproduct hheadtail 211386 211385 35289 306779 306786 ↥w✝ ↥w✝¹ homQuotientZPowOfHom homQuotientZSMulOfHom ##OfMapOfLE ##ToLaxBraided 102700 121497 266427 266431 mapBifunctorHomologicalComplexShift₁Iso mapBifunctorHomologicalComplexShift₂Iso walkingParallelPairOp walkingParallelPairOpEquiv pointedToTwoPSnd pointedToTwoPFst 88317 88315 23191 23198 goodτ sjx ¬AntivaryOn inductivePremetric toDilationEquiv endMonoidalStarFunctor identityToΓSpec 97646 ⇑FreeAddMonoid commMonToLaxBraided RecursionMain rz₁ ¬ThreeGPFree hfδ₁ ##NonzeroSingleton 22533 ProperlyDiscontinuousSMul skeletalFunctor isValidChar 108100 12767 isoEquivHomeo fromCommLeftInv quotientMulEquivQuotientProd multicoforkEquivSigmaCofork ¬liminf lpTrimToLpMeasSubgroup ↑ofComplex ↑includeLeft ⇑abv toWeierstrassCurve toSpanNonzeroSingleton condKernelUnitBorel fastJacobiSymAux 64946 84190 Bcbl Hmaps OrthocentricSystem Rn₀ RanIsSheaf SkyscraperPresheafFunctor Zoomed aedisjoint bidirection bundled dμκ dfinsupp easy effectiveEpiOver milgram maybe ¬Irrational Γevaluation εToSingle₀ ↑UpperHalfPlane ∂dirac ##Augment IsEvenlyCover funMulInvSnorm HasTwoOutOfThree PreirreducibleSpace hsxps MulDivCancelClass compCoyonedaSectionsEquiv cardDistinctFactors rangeKerLift ofBoxProd IsSkeletonOf invOneSubPow CoalgHomClass sndOfNotNil minBadSeqOfBadSeq isFractionPrelocal isRepresentation isSuccLimitRecOn improve pullbackSpecIso singleFunctorsPostcompQIso piQuotientLift piEquivalenceFunctorDiscrete 111346 ##CompactToT2 equivAdjoinSimple transReflReparamAux subtypeSubtypeEquivSubtype colimitCoyonedaHomIsoLimit primeCounting 133780 cartesianComon fromSingle₀Equiv limitUncurryIsoLimitCompLim monToLaxMonoidal flipIsoCurrySwapUncurry inclusionInDoubleDual LawfulGetElem IsStandardSmooth constantsToVars monoOverEquivalenceSet quotientEquivQuotientMinpolyMap quotientQuotientEquivQuotientAux orbitEquivQuotientStabilizer 172711 177771 countableGeneratingSet 193906 bottomMap quotLeftToQuotSup equivalenceLeftToRight equivalenceRightToLeft IsGeneratedByOneHypercovers repOfTprodIso liftedLimitMapsToOriginal completeMultipartiteGraph dualSubmoduleParing trianglehMapOfHomotopy equivQuotientZSMulOfEquiv UniversallyClosed succNthDefiningPoly binaryProductTriangleIsoBinaryBiproductTriangle RanIsSheafOfIsCocontinuous bidirectionalRec IsEvenlyCovered HasTwoOutOfThreeProperty 246 47 420 440 410 900 AX Brec Basic CLM Effective G₁₂ Hk Hfg Hmem Hinj Ibot IinS JD K⁰ Kₘ LEquiv LL₁ MS M0 NO Pu Psup Princip Qf RR RL US Vop WY XW Zlattice aU a8 bct b⁻ᵐ b⁺ᵐ cnd case cne cIoo dμν f⁺ frange fille gₘ h9 hane hidl jj l✝¹ lnonneg mOf m⁻¹ nM nin name oe pP pac pois qpp ry rω rin rho sT series spos sneg slt sZMod ul uκ uinf wU xF yE ylt ¬U ¬W ¬if ¬Monoid ¬Un ¬Pro ¬Multi ¬ord ¬fin ¬Abs ¬of ¬Sq ¬ring ¬True ¬Associ ιfin ρs ψφ ωb ωUnit ⁺ᵐ ↑NNReal ⇑η ⇑Finsupp ⇑change ⇑MeasureTheory √r √Real ∼ψ ⊤⁻¹ ##rfl ##tra ##Rid ##sLT ##square ##sInfHom ##cε ##Am ##Acyclic ##AugmentedCech ##pode ##Lit ##Coind ##CMapSpanMk ##vize ##m1 ##MvPolynomial ##1p ##Gluing ##Bracket ##Drop ##₄₅ ##66 ##63 ##330 ##₆₅ ##416 ##WType ##Wide ##Write ##πApp injOn instTopological ##alLinearEquiv ##len ##leN ##ormation ##tiplicative ##array ##relation ##easurable ##CommIso IsFixed IsElementary ##idLines ##geq funInv Fint ##ultiplicative mapSubmodule mapOfLE mapSquare mapAugmentedCech toAddCommGroup toIso toBounded toHomotopy toCycle toVectorBundle toStarSubalgebra toNonAssocRing ##ilinearMap hfN hfun hfLp hfcd hfzero ##EqZero ##EqLocus HasCo HasCore ##MapCMapSpanMk Subarray Subrelation ##lyPositive ##otmax objSup ##Fun₂ ##WithOneClass LinearLocally PreSubm PreSt hsr hsν hsW hsinf repre reLm NonNeg hom✝ hom✝¹ uni unary MulLE MulOption hxC hxmem ##ZeroExtend compUnit compQuadraticMap compCounit ContinuousOpen ContinuousOrderHom rangeOf mkInv mkOfUnit mkInductive mkCoind ofProd ofLinearEquiv ofSubring ofSym ofSubset ofFintype ofInvolutive hpo hpv hpg hpQ hpV hpW hpdeg RingInv ##AddOpposite ##AddHomClass ha₅ ha3 Submultiplicative ##OfNon ##OfComplete ##OfSpecializes ##OfFiniteType ##OfNeighborSet ##OfImageEq ##Subtra opComp opSymm opOpEquivalence hgM hgLp hgker hgtends ##EquivList ##EquivMvPolynomial ##FiniteOrder ##TopEquiv ##calate M₁⁰ clg hnX hnng ##IsoRange ##IsoSource algebraToUnder prodFst prodSnd ⇑f₃ ⇑fₐ fst⁻¹ ##LeftMul Coherence htε htrans htsub h₁₀ ##RightMul ↑sg ↑s⁻¹ hcong hmd hmain hmlen ##Conformal hbZ hbI hbz a✝⁵ eq₄ ##₁₂CommIso finFunction ##ToA ##ToType ##ToLocalization ##ToSubtype ##ToModuleCat ##ToSupQuotient Locale toFunBilinear restrictOpen ##ormalAdjoint liftH liftNormal hiJ hiw hiT hyd hyj hyB hyK evalᵢ stWrite ↑↑2 ↑↑γ s₂ᶜ leftComp leftSide leftHomologyMapData leftDerivedZeroIsoSelf combo ↑a1 ↑a₁ ↑a2 ↑aI abLeftHomologyData minus isZero isrfl asFunctor asLimitCone rightHomologyMapData rightDerivedZeroIsoSelf NonUnitalAlgEquiv preLeft preRight imLm Opensᵒᵖ hdiag AffineIsometry sumMap 1011 pullbackComparison subcategory leSy QuotientDiff upFunctor heU he0 LocallyOfFiniteType SmoothMap ↑If filterLinearMap filterAddMonoidHom PreservesImage PreservesPushout CompEval shiftAdd ↑i₁ ↑i₂ hu✝ huU hust ##Information ofRealAm hlF hlx hlp hlv hl4 limLax tensorQuotEquiv imageMono imageSheaf imageObjIso imageIsoImage deriv₂ swapCore positi hU4 hUcover hku hklt ↑rTensor 1127 1130 functorP ediv shiftFunctor₁₂CommIso hPb hPQ hPirr starLift ProdPreserves ↑ev ##TensorEquivQuot ##ContinuousAt LieModuleHom ##OrderedAddCommGroup hzp hzM hTU mem₂ hSf hS4 12⁻¹ 1296 1210 LeftRigidCategory equivIcc equivSetoid hμT ##Constraint autAdjoinRoot h1✝¹ habcd hqreq sourceᶜ isoP isoComp isoN₁ isoΓ₀ isoIsPullback commg supSpanSingleton supIrred intercalate hεu hεpow F₂₃ ↑y1 ↑y2 ⇑eι onePoly noncenter nonsquare ##LimitDist Pi1 tau ##retrivialization DiscreteMeasurableSpace hF0 BicategoryCoherence ##UnionInfty infIrred coequalizerComparison TotallyS sSupHomClass ↑SignType a1m ##LiftT RightRigidCategory hCg hwu affineBasicOpen genEigen hAA descH ##adicMap 1324 1390 h0✝ ih1 hjx cons₁ counitCo counitCofork β✝² setRed hφi hφw extendWith charFn pbc ho₃ host h₀i h₀₀ fromAppend1 sInfHomClass ofNatList ofNatMultiset AddSubmonoidWithOneClass hVsymm sign⁻¹ LatticeOrderedAddCommGroup hijk bijection ##FromSubtype hRp hR₃ ##RangeEq hα₁ hα₂ monToMonad eval₂AlgHom 1680 1699 openToLocalization centerAnd hN✝ hN0 ¬Isδ₀ HasFiniteWide basisRepr ExactFunctor downFunctor sheafYoneda sheafOfTypes hXint restrictScalars₁₂ cmpUsing toMatrixAux toMatrixₛₗ₂ 1581 1584 hstn generalLinearEquiv hpqf utf8Prev PathStar typeToPointed antipode hinner rs₀ toScheme ##GroupoidFunctor ↑w₁ ↑w₂ splitAux ##QuotSMul ##NthVal toPretrivialization bitm1 coneOfPreserves coneOfAdj toDualProd toDualBotEquiv toDualTopEquiv hτbdd stalkPullback stalkCongr GeneralizingMap hmn0 hmncp left✝² forget₂ToModuleCat ↑Js h3D ↑R₀ sigmaCofan quotientSubgroup quotientOut ⇑bs ⇑b₁ MonadIso MonadLiftT recC recolor OfSequence PerfectSpace fourierSubalgebra join₂ k₁l ↥↑s ##FreeAlgebra ##sonPMFReal tl2 tᶜˢ inducedOrder ↑H₂ k₂l ↑T₁ 17464 17460 NegMemClass embeddingUp hha hh1 complOrderIso ##to0 normalizedMooreComplex lbot succAboveEmb coconeOfPreserves casesAuxOn MonoidWithZeroHom GridLines lawful localPreimage pushoutComparison ##ConnectedLimits reindexLie ##EquivOfImageEq rotateHomotopyEquiv linearYoneda linearHomEquiv linearCoyoneda hp1s1 freeSection ↑ht ↑hv ↑h₁ ↑h₂ ##CorePresheafOfModules innerₗ hfm✝ decomposed h₁₂₄₅ evaluationEquivOfIs ofAddEquivOfDom hlt✝ connectedComponents ##irrfl ##aneConformal sbo MulSemiringActionHom hπip hπc₁ hπc₂ hD₁ hD₂ hD₃ zpowersHom ofFnRec ofFnTR ofFnNthVal toPartialEquivOfImageEq finsetEquivSet finsetClopens scMap homMk₂ ##OfIsLocalization smoothCoordChange smoothLeftMul smoothRightMul decomposeLinearEquiv decomposeOption hιY hg₁r hintf ##ArithmeticFunction twoPow h₄₁ h₄₂ ##CardEq zipWith3 ⇑↑gf opensLeCover ##SigmaZMod BEqCmp fpow Grpd sectionsFunctor powerBasisAux formula heq1 polynomials ##320 hdivb ##PushforwardStructure codiag ndvd ↑↑x✝ equalizerComparison corec₁ h4w hψ₃ ComonadIso ##StalkEquiv hposbdd isoOfEq isoOfComponents isoOfRangeEq trStAct compareLex ##Differentials ##LieModuleHom hxU✝ ↥I₁ AlgEquivClass ¬↑x ¬↑M ##Fibers hcontra natTransP natTransHomologyπ natTransHomologyι quotTensorEquivQuot disjointUnion transposeAddEquiv StableUnderInverse ##511 subgroupMap hp2s1 ToRel ##188 IsEuclidean hgmn unitsEquivAut pathStar pathEquivList TM1to0 coprimes iYW bd0 ##OriginIndexEquiv intros ht₂s IsSolvableByRad addEquivProdDirectSum alter ofMulEquivOfDom ##963 ⇑measurable hac0 equivOfCardEq ##sentative ##507 HasWideCoequalizer HasWideEqualizer parity optionElim IsWeakUpper IsWeakLower isColimitCocone specStalkEquiv monotoneCurry monotoneUncurry lfs extractLsb iZU iZU₁ hmgi ##352 4974 49535 ##Coevaluation colimitCoconeOfUnique colimitCoconeιApp toPartialHomeomorphOfImageEq EventuallyMeasurableSet hB₁mo diracProbaInverse huniq ιMapBifunctorOrZero ##006 ##009 toRelIsoLT takeWhileAux iWZ hcard✝ vcomp1 precomposeEquivalence ##862 n₁₂₃ eapproxDiff ##478 husub hξ₁ hξbdd wpRec ##592 erasePTR BundledCorePresheafOfModules boundedFormula limitConeOfUnique limitConeπApp ##575 toAddMonoidEnd extendScalarsOfIsLocalization h₅₃ whiskeringRight₂ anyAux Hfa dartOfNeighborSet toEuclideanCLM fmla findIdxs ⇑γ₁ ⇑γ₂ secondRow ##297 homeoCompactToT2 hu₀s ⇑D₁ IsCancelVAdd rightAdjointOfEquiv toComplₗᵢ ##FintypeEmbedding shiftLeftZeroExtend finsuppTensorFinsuppRid FGModuleCatEvaluation FGModuleCatCoevaluation postcomposeEquivalence leftRegularHomEquiv transferFunction oreMin oreSubtra CondensedMod 363 orderIsoOfFin hcs₀ hcs₁ addSubgroupMap hfba LeftFraction₂Rel binaryProductLimit ##IsoProdEqLocus scanr hconst equivRealProdLm colorClass toComonad hiφi mapLMultilinear coimageObjIso ##AdjoinIntegral submonoidMap cnK ⇑MvPolynomial hnφi moduleCatLeftHomologyData summands 960 hpd2 maxTrivEquiv leftAdjointSquareConjugate sheafPushforwardContinuousCompSheafToPresheafIso 611507 hfnleN liftHom₂ HasExplicitPullbacks Quasicoherent 57464 ##ftLim ##SemilatticeSup h₃₂₆₅ iV₂U monadToMon multiplesHom ¬leftLim 66927 66935 66939 66947 66931 66943 ##OfFiniteDimensional hmt2 diagramIsoSpan hnot1 hJuz localizationLocalizationSubmodule dyadicMap splitOnPTR 32694 AlternatingCofaceMapComplex rightAdjointSquareConjugate boolArrowEquivProd IsPartialInv skyscraperPresheafFunctor toInf✝ replaceFTR h₆₃ SlashInvariantFormClass MagmaCat shiftFunctor₁XXIso orderIsoOfNat frequent h2g₂ h2g₃ quotientInfToSupQuotient ##PointsIsoOfEquivalence 45519 HI₁ ##OfCardLE coneEquivFunctor coneEquivUnitIso cauSeqConj lanLiftUnit 28063 ¬¬Is ¬¬ContinuousAt argminOn 27982 dZeroArrowIso ##ToHomRTensor ##ToHomLTensor strictlyPositive addSubmonoidMap inrNonUnitalAlgHom quotientEquivSigmaZMod ↑univUnitBall hgEcε derivationToSquareZero zipWithLeftTR restrictedYoneda lcRow0Extend hnbq StarAlgEquivClass coconeOfDiagram Drirrfl place planeConformal ⇑W₀ IsFormalAdjoint takeDTR directSumLeft 23250 23254 232416 GLPos hNN₀ npowRec toOplaxFunctor readAux rightZigzagIso exponentialPDFReal ihxyn shortComplexH1 shortComplexH0 quotQuotEquivCommₐ hInotmax metricSpaceAux ##ingLeftToKaroubiIso beckCofork epiComp h₇₅ h₇₆ partitionFiltration mapActionLax ofBraidedObj IsTruncLE UniformContinuousConstVAdd dirichletSummandHom GroupNormClass piLpCongrRight 2186 89275 89276 nv2 sortedUniv toComposableArrows prodLift₁ hTv✝ 148403 am1p dXY✝ ##uffix hfIJ mkFinConsOfLE universalMulHom iteratedSliceForward iteratedSliceBackward toPseudoFunctor toPseudoMetricSpace takeWhile₂TR 377010 377006 piTensorHomMapFun₂ hkp✝ ##filteredLimitsOfSize mapBifunctorMapHomotopy nsmulCoprime hπiC hπiδ Saturated CSLiftVal coproductIsoCoproduct ¬toLex preLiftAlgHom 12154 nonZ2 geometricPMFReal sides✝ goodδ ¬Antivary φψs MeasurableInf₂ inductiveLimitDist unitOfTensorIsoUnit tailings rTensorHomToHomRTensor endMonoidalStarFunctorEquivalence 39620 39627 40064 40068 752508 752511 96949 96953 huopen ofRelIsoLT toLightCondSet h1g₂ h1g₃ commuting commutant monoFactorisationZero binaryBiconeOfIsSplitMonoOf binaryBiconeOfIsSplitEpiOf viaEmbedding viaFintypeEmbedding IsStrictlySupportedOutside fillNonesTR subalgebraOfSubring subalgebraOfSubsemiring ⇑equivRealProd ofPiForkFunctor ofPNatMultiset opUnopIso coalgebraToOver isoShiftZero toPiForkFunctor lTensorHomToHomLTensor binaryCoproductCocone delayReflLeft yonedaCollectionPresheafToA IsOneCocycle hspan0 tensoringRightMonoidal isoHomologyπ₀ isoHomologyι₀ adjointifyη coeToPowerSeries sigmaAntidiagonalEquivProd NonUnitalStarRingHomClass subsemiringClosure hrecOn mapSetEmbedding revPerm ##CompWhiskeringLeftToKaroubiIso vertexSubgroup enumIsoOut homotopyPToId ftaylorSeriesWithin nonUnitalSubsemiringClosure offsetOfPosAux 45523 FastSubsingleton ##1408 hcnz equivariantProjection centerToCentroidCenter derivedLengthOfIdeal longestOf subsingletonEquiv 4719 440575 MSx NONote PrincipalIdealRing filler mOfFn poissonPMFReal ¬Multipliable ¬finrank ¬Absorbs ¬ofSuppBddBelow ¬Squarefree ¬ringChar ¬Associates ψφs ⇑changeOriginIndexEquiv ##sLTMul ##DropLast instTopologicalRing IsFixedBlock funInvIdAssoc HasCofilteredLimitsOfSize objSupIsoProdEqLocus LinearLocallyFiniteOrder PreSubmersivePresentation PreStoneCech representative MulLEAddHomClass MulOptionsLTMul ContinuousOpenMap rangeOfWType mkOfUnitCounit mkCoinductive RingInvo SubmultiplicativeHomClass ##OfNondegenerate opCompYonedaSectionsEquiv htransvec finFunctionFinEquiv NonUnitalAlgEquivClass subcategoryAcyclic leSymb tensorQuotEquivQuotSMul imageMonoIsoSource positivize hkltp ProdPreservesConnectedLimits 12961 121039 equivIccQuot supIrredLowerSet infIrredUpperSet TotallySeparatedSpace genEigenrange fromAppend1DropLast 168006 169944 centerAndRescale sheafYonedaHom sheafOfTypesBotEquiv utf8PrevAux reindexLieEquiv evaluationEquivOfIsGalois opensLeCoverCocone quotTensorEquivQuotSMul IsWeakUpperModularLattice IsWeakLowerModularLattice QuasicoherentData frequently planeConformalMatrix binaryBiconeOfIsSplitMonoOfCokernel binaryBiconeOfIsSplitEpiOfKernel 0ᵀ 269 224 242 216 235 229 2270 337 316 371 313 334 3260 451 435 55 524 527 511 599 590 5266 6✝ 620 635 77 7⁻¹ 718 711 775 705 7275 71408 827 95 919 9464 Al Aₙ Are Altern BY B♯ B⁄ Crec Del Eval Emem F̂ Fclosed Hr Hens Hrd Hneg Henstock Hinv I6 J2 Jᵛ Ku Ks Kc Kne Lc L✝¹ Lclosed MutuallySingular Nᵀ Nᴴ RS Sw Sp Supp Sopen Tt T5Space Tpolish Uᵢ Vᵢ Vsymm W1 Wrepr Y✝¹ Zp Z₇ ant apos b3 b4 bY call cr₂ dq dd dz dep dνκ eμ eγ epos emp fj fC fE f⁻ f4 fss fseq fok fdiff ftop ginj hall hep hInf iF ig istr kᵐᵒᵖ kill lty mF mM mN mle nt pat pth pmeas rρ sC shar sfin sMk skew shear trivializationAtlas tbot uh uU vg wk wV wim wInv wnorm winl winr x3 x4 zb z𝖣 ¬⋯ ¬ω ¬η ¬Real ¬add ¬Ideal ¬Countable ¬MDiff ¬List ¬Free ¬Algebraic ¬mem ¬ClusterPt ¬Pairwise ¬SupIrred ×ₖ Φ₀ Φcomp α0 αθ βˣ βᵃᵒᵖ γi γ⁻¹ δc δlim εr ζ✝¹ η₅ ηα ιF ι2 νU πr ρFunctorObj φlim ψl ψr ᵀ⁻¹ ᶜˢ ℚ∞ ⅟f ↑𝕜 ↑ub ↑val ↑Up ↿h ⇑w ⇑ξ ⇑Cl ⇑Semid ⇑sqrt ⇑Quaternion ⇑Fintype ⇑MulOpposite ⇑CategoryTheory ⇑SimpleGraph ⇑AddOpposite ⊕ᵥ ⥤ᵣ ⥤ₗ 𝕜ˣ ##ext ##FZero ##FOne ##r0 ##ns ##nakeInput ##nEc ##RIn ##RamificationIdx ##s₂ ##s₃ ##sAux ##cl ##cru ##Sk ##Symmetric ##SnakeInput ##aves ##T2 ##otent ##path01 ##Lid ##CC ##Corner ##Coreflexive ##vant ##hift ##MMem ##MEqTop ##ModularGroup ##flip ##E₂ ##EMetricSpace ##ENNReal ##GO ##₁XIso ##₁a₂ ##₁E₂ ##PLift ##ball ##UV ##ULift ##269 ##Bu ##Bipartite ##₂XIso ##₂U₁ ##Dart ##73 ##730 ##752 ##03 ##Iter ##ε₀ ##618 ##625 ##346 ##316 ##541 ##91 ##μs ##446 ##4423 ##WF ##ₐᵢ instAlgebra instApplicative ##insupp ##onvex ##levant ##ets ##SpaceEmbedding ##rator ##unif ##relevant ##blem SetNot funSplitAt funext ##RingOfIntegers mapPresheaf mapGen mapComon mapHomotopyEquiv mapSpanning mapNeighborSet mapOfIsLimit mapSnakeInput toF toRing toOf toSeq toConst toDist toRestrict toCore toDiffeomorph toWOT toSeminormed toShrinkHoms toInit toElementary toBiconeFunctor toArithmeticFunction toSemilatticeSup ##osing hfL hfac hfge hf✝¹ hfreq ##EqUniv HasCoreflexive ##omplete ##efault ##InCommRing objPairwise objAppend1 ##FunOnFintype ##MulEquivOf hsj hsign homologicalComplex homotopic homTensorHomEquiv unip unfold unflip hxε hx32 ##ZeroSMulDivisors compInverse compExact compAddEquiv ##Unmop ContinuousSem ##SetAux ##SetCondition ##iftable mkNormed mkPoint mkArray mkMMem ofComp ofClosure ofCountable ofGen ofSets ofElement ofSurjective ofUnique ofBdd ofComposition ofRingEquiv ofTensorHom ofSelfIso ofNull ofFullyFaithful hpure ##oinMonic FieldAxi ##AddRel ##AddAux haT haeb IsSolid ##OfContinuous ##OfStructure ##OfExists ##OfSelf ##OfNatIso ##OfLinearIndependentOfCardEqFinrank ##OfClosureOperator ##OfForallMem ##OfRamificationIdx M₂✶ ##Realization Semigrp opObj opHomeomorph opInverse ↑n⁻¹ hgS hgL hgle hg✝¹ hgunif ##UnitDet ##EquivClass ##EquivFunctor ##EquivSum ##EquivUnder ##EquivOver ##EquivLieModuleHom ##EquivRingOfIntegers GroupAlgebra ##ProductEquiv valA valFrom M₁✶ cls clo clf IsLittleO IsLiftable hnj hnh hny hnY hnge hnsep hnzero hngn ##IsoTo ##IsoFlip algebraQuotient algebraEquivOfIso algebraEquivUnder algebraMapInv algebraMapCoeffs ##LikeToTop prodIso prodSumDistrib condd ⇑finsupp fstHom univᶜ ##WithCancel ##Shane htff h₁⁻¹ hcst hclo hcinf hcμs hmzero ##Convolution ##Covolume hbm hb₃ ##ToSum ##ToTensor ##ToFinset ##ToHomologicalComplex ##ToCenter ##ToWeak ##ToCos ##ToGood ##ToEquivalenceFunctor ##ToString ##ToLight ##ToOpensLeCover ##ToIter maxIdeal FunctorPushforwardStructure mulSpan mulKer mulHead restrictTotalDegree restrictTopIso natDeg natAddOrderEmb HomClass liftₐ liftSup liftLimit liftMagma liftHomotopyZero ##FunctorIsoN₁ hiU hyi hyq hyk ##ClosedGraph ##ClosedCompl ##SMulAux ##ObjSingle₀ ##ObjOfMap evalₐ evalCompEq ↑↑R ↑↑K ↑↑ModularGroup ##SeriesSummable Icc01 leftComm leftInverse leftRes leftKanExtensionUnique SMulBracket ##trongLT support✝ ##NatSum ##NatEquivNat abstract comapComp ContFract ##CompHaus ##CompEval ##Compatibility ##CompCoyoneda ##CompProj ##CompForget ##CompBipointed isReal isKan isTrue isFalse unopEquivalence unopUnop rightSide rightKanExtensionUnique hrm hrδ SumSq implicitFunctionData hdy hdm hdis ##rankEq ↑p₁ addHom addAux addSpan addTorsion addMonoidalFunctor addCovolume ##OneConst sumDual sumArrow sumProd sumArrowEquivProd sumEquivSigma sumToIter ZeroMemClass 1079 1045 ##Prefunctor pullbackTotal pullbackSnd subobject le1 less R✝¹ R✝² upath01 ##AssocTensor singleOne singleCompEval ##SumOfLE height piIso piLinearEquiv piFan piCurry piSplitAt hvμ hv₁₂ hvcard forgetCone forgetBraided trNum trCont PreservesOneHypercovers EquivMon CompFst CompSnd shiftRight CountableCategory huf huI hlr hl5 kerᶜ lim₁ limAux castAddMonoidHom getOrElse tensorComm tensorMonoidal imageMap imageMonoFactorisation ##ativeDifferentials derivLB ##izedBy posConvolution hU₀ ↑rj 1119 11180 functorL functorEquivalence hPJ starAddEquiv starCenter hIF hIA hIf ##DualAntid ##TensorQuot constSMul constRingHom AdjoinMonic ##ContinuousSheafification unitor hze hz✝ hzU ↑tl mem3 numLe hSp hSU 128 1242 ##ClosureRange equivMeasure equivQuot equivDFinsupp equivNatSum equivTensorQuot hμu hμp hμB hμV hμuv ##ProdArrow ##ProdLEquiv ##LinearMapEquivLieModuleHom autMulEquivOf h1B h2y h2m h2B h2✝¹ habk hab0 habove hqb hqV hqrd hq₁₂ isoTriangle isoCongr isoBiproduct commZ commX commensu GradedMul withLength hεδ F₁₃ b✝⁵ ⇑e⁻¹ orderUnits orderLHom non0 nonZeroSMulDivisors presheafToType CompactT2 hfgC hfgX adjoinEquivRingOfIntegers hBA hBB ##Valued ↑kj cont✝ transported factoring subtypePreimage subtypeQuotientEquivQuotient subtypeₐᵢ TopCatᵒᵖ hFeq coequalizerColimit M₀⁰ smul₀ hxyi hxyj sSupClosed ##econdRow ##PullbackOfPreserves ↑gn hCC hwp hwv hw₄ colimitInv colimitAddAux colimitSMulAux affineLocally hA1 hAX ##TypeEquivFunctor descFun descent descHomotopyZero 1338 h0₂ iha ihN ihb ih2 ihα rank✝ rankTR ¬p₂ setNormalizer ##PresheafInCommRing hφψ hφle updateRIn extendIso extendComp extendId extendXIso ##ickCmp lowerEquivalence dualDual dualAntisymmetrization hK1 hKE hK2 hKpos fromAddMonoid fromULift sInfClosed decPred limitIsoSwap ofNatHom hVS hVb hV0 hVne hVopen ##StarTransform ##EndTo ##EndSelf MapFactorizationData EndMonoidal ##Bytes ↑default Caratheodory LECmp LE₁E₂ measM hMl hMs seq2 LatticeHomClass ##DistEq ##OpNatIso 141 149 1446 1478 14465 14347 asIdeal✝ asIdeal✝¹ ##AdjointOp LpToLp monFunctorCategoryEquivalence coeAlgHom coeAddHom coeWithTop coePNat inj₁ inj₂ pure✝ pure✝¹ totalOn continuousMap ¬IsAlgebraic ¬IsCorner hJc hJ✝ ContinuousLinearMapWOT ##AlgHomOfSplits sheafToTypes restrictScalarsₗ restrictScalarsEquiv 1522 rootsExpand ##RestrictCLM generators this✝¹¹ onSentence ##MkEq ##MkCLM utf8SetAux degMatrix hnext hnezero hGcard typeOf ↑v⁻¹ toNatIso toNatLinearMap toNatCast divExact ##Values d₁a matroid ↑NF antitone hδs hδδ hin✝ rsize toSections ↑w₃ AsType splitMonoOf splitEpiOf ##BiproductToSubtype ##BiproductFromSubtype w✝⁴ SolutionSetCondition G₁₃ ##QuotQuotMk argPartialEquiv lsize ##MovesEquiv coneOfSection coneOfDiagram constantCommute ##IndepMatroid condb smeas kernelBiprod kernelForkOf kernelUnopUnop step0 stepRet IsSheafUnique IsSheafPairwiseIntersections IsSheafOpensLeCover ↑RCLike mono✝ mono✝¹ pairSelfAdjoint quotientBot quotientEquivProd quotientEquivPi MonadFunctor coprodComm coprodCongr OfInv OfCoimage ↥sm biproductIsoPi biprodXIso xlim ##Div2 hasShift fourierTransform join₁ ¬x₀ hQzero key1 key0 Upto hL₀ rTensorHomEquivHom permMatrix rel✝ rel✝¹ relativeDifferentials aux3 auxGroup auxLTensor curryEquiv vert inducedStructure cokernelBiprod cokernelUnopOp cokernelCoforkOf ↑H1 complement ##UnitsMulHom WellFoundedRelation wittZero wittNSMul wittZSMul uniformContinuous hhb hh2 PullbackObj mapBifunctorShift L✝² chosen coconesEquiv hE₃ insertNthTR casesDiag lieAlgebra lTensorHomEquivHom ##PartitionSet structurePresheafInCommRing ##OrderOfEq ofHomInv toAffineSubspace ↑↑↑n ↑↑↑p normalizedFactorsEquivOfQuotEquiv rightUnitorEquivalence rightUnitorNatIso hYE hY✝ ↑11 RegularMono ⇑hA ⇑h₁ ⇑h₂ foldrm nns pushforwardContinuousSheafification ##EquivOfInjective b⁻¹⁻¹ realLinearIsometryEquiv hp1a hp1✝ chainub ##TotalEquiv freeGroupoidFunctor ↑hg ↑hfin leftUnitorEquivalence leftUnitorNatIso mapHomologicalComplexIdIso hfsA nzm foldlm foldlAux assoc✝ assoc✝¹ frobeniusFun powEquiv LinearEquivClass notNil pfa countableGenerate ##OfFinrankEq ##MemAdjoin evaluationAdjunction evaluationRightAdjoint evaluationLeftAdjoint decodeSum huv₁ huv₂ moduleEndSelf ##SubtypePerm bddmax 187 hHL ReflectsLimitsOfSize hs₂s₃ lowerCentralSeriesLast denom✝¹ ↑L₁ ↑L₂ rootSpaceProduct hπδ hρball homologyMapIso ≃ₗᵢ⋆ algEquivOfEq hs₁0 hs₁s₂ ↑↑n₁ isLimitOfHas isLimitForkOf truncateAugment hD₀ struc boxes₁ boxes₂ scov PredLast hΦinv productEquiv triangleRotation H1✝ ¬b₁ coyonedaLemma pp0 pprime ##DiagramOfDiagram ##CofanSum decomposeAux ##Monads toAddMonoidHomEquiv quickCmp hκη toMonoidHomEquiv facets 205 hgfC hgfX ##MultiplicativeIntEquiv rrb ##PUnitSumLex ##AutGalois singletonMonoidHom singletonAddMonoidHom singletonAddHom singletonMulHom sheafifyHomEquiv ##CompIsoWhisker ##324 hg₂r hdivn hdiv2 ##WhiskerRightIso adjunctionToTypes hγγ ##sOfShape ##IdempotentOfIsLimit ##IdempotentOfIsColimit hscv hsc₀ compContinuousAlternatingMap finsuppProdLEquiv boddDiv2 primitiveCharacter CoeTC fu0 iterateTR mno mapCoconePrecompose HasBiproductsOfShape precompEquiv hμνs ##RingEquivOp isoOfHomotopyEquiv isoOfMkEq ##LimYonedaIso ##696 ##695 Hconn compareEquiv φ₃⁻¹ toTopCatMap hnormeq toOrderRingHom toOrderMonoidHom unmopFunctor unmopBraidedFunctor quotQuotTo proper₁ proper₂ ↑x✝² ##514 hp2a iU₂U₁ ¬y✝ dvd2 homotopyFrom restrictionXIso ##640 ##643 factorThruCoimage binaryCofanSum mapConePostcompose hgm₁ ss✝ sshift unitsLift canonicalTopology nonzero✝ cyclesMapIso hβα equivalenceJ equivalenceOfEquiv equivalenceUnitIso equivalenceCounitIso 1009 braidedFunctor ##244 ##edFunctorTypeEquivFunctor ##283 ##AddEquivDFinsupp himp him✝ lanDesc hfxy opcyclesMapIso ##MagmaCatIso addHaarProduct edgesFinset hZa hZ₀ sheafificationIso complexLinearIsometryEquiv toQuot✝ toQuot✝¹ fiberBinary hx12 ⇑σ⁻¹ toDFA equivOfEquiv finSuccEquivLast integerLattice IsOrderedSMul IsOrderedVAdd fundom HasWideEqualizers singleObjXIsoOfEq ##BoolAlgOp irrelevant optionEquivalence hextends ##377 bcount isColimitCoforkOf wfst ##EqualizedBy BinaryBiconeMorphism mkOfObjOfMap removeUnop removeRightOp hdegP large₁ ofIsUnitDet hpsa hST₁ 2553 25330 nodup✝¹ domDomCongrₗ sortEquiv deleteMin initialSeg extensions extensionValuation ##16618 hyp2 toModuleEnd hvsY gxeq ##392 ##3916618 ##262 MaxToGood nN✝ msn ##0000 hr₀✝ ##Bilimit ##494 leftAdjointOfEquiv leftAdjointConjugateSquare leftHomologyDataOfIsLimitKernelFork skewAdjointLieSubalgebra lowerCrossingTimeAux vcomp2 ##CenterToCenter ##861 ##8667 ##015 ##5552 toHomeomorphOf ##LequivProdArrow arrowCongrSL 2177 2121 21759 21752 cotangentToQuotient ##3147 conjTransposeAddEquiv modifyNthTR ##OfMemClosureRange IsCentralVAdd rightHomologyDataOfIsColimitCokernelCofork fy₁ ##419 toMvPowerSeries intble₁ intble₂ hξm ##ToTopCat ##595 ##594 toNNRat⁻¹ cc₂ δ₀pos limitConeX hpnr0 ##OfLeConst partialHomeomorphCoe toZModSubmodule endos selfAdjointMatricesSubmodule continuousLinearMapToWeak extendScalarsOfSurjective gluePremetric natIsoEquiv 2688 268667 homothetyUnitsMulHom AddSemigrp alls karoubiHomologicalComplexEquivalence karoubiUniversal₁ hμm₁ ##4083 rightAdjointConjugateSquare har1 quasiregular finsuppTensorFinsuppLid CancelMonoid ##773 ##774423 ↑fs₁ ↑fs₂ ##OfIso₁₂ topologyOfClosureOperator 36647 36643 363916618 Cᴹᵒᵖᴹᵒᵖ orderIsoOp orderIsoIic orderIsoSumLex orderIsoPUnitSumLex evalEvalRingHom hfbdd binaryProductEquiv 29894 693147 hconc hconv hconvex equivRealProdAddHom H3p mopEquiv mopFunctor mopBraidedFunctor mopRingEquivOp McShane matrixEquivTensor completeSpace completeBipartite ##Reducible ##215 ringEquivOpMop iterToSum scanlTR irrfl claim4 pullbackConeIsLimit √↑q √↑z functorObjSrc functorObjTgt ##GeneratorsData mapBifunctorHomologicalComplexObj 51400 6070 6074 Cfg₂ subtypeEquivRight subtypeEquivToFinset subtypeEquivSubtypePerm measurableEquivPi measurableEquivRealProd measurableEquivIoc ##AlternatingFaceMapComplex addUnitsLift h𝒢ℋ hpd3 maxTrivLinearMapEquivLieModuleHom mapRightEq mapRightComp mapRightId upperCentralSeriesStep unitsSMulWithCancel 27894 ba₁a₂ cancelAux mapLeftEq mapLeftComp mapLeftId equivProdNat totalShift₁XIso totalShift₂XIso ##Subgraphs hv1p Quasicategory 34429 ##CompLimIso pqq ⇑Tropical hprimes ##SemiRingCatIso 24358 h𝔖₃ sumLexDualAntid beq1 beq2 liftToInitial liftToTerminal bifunctorComp₁₂Obj bifunctorComp₂₃Obj tfG ⇑Aₘ ##44116 hmt3 functorialityComp diagramIsoParallelPair build wittMulN avg ##874 ##InvertibleEquivInvertible permsOfFinset widePullbackShapeOpEquiv widePullbackDiagramOfDiagram 3236 ##AddOrderOfEq widePushoutShapeOpEquiv dnK ##OfHasKernel ##OfHasCokernel R₁✝⁰ hi₃₁ hi₃₂ boolProd quotKerTotalEquiv contractibleTriangleFunctor Ffs hmfnEc skyscraperPresheafCocone GradeMaxOrder GradeMinOrder hcccru toInf✝¹ ##MulEquivAutGalois hpoweq comonEquiv comonFunctorCategoryEquivalence pairwiseNode pairwiseToOpensLeCover toRatLinearMap ##₂₃MapObjIso gelfandStarTransform HJs bxor discreteQuotient hpk₁ hnoet orderIsoOfSurjective pullbackConeOfLeftFst hucount toArrayAux DevosAddRel 4569 45429 45377 1066 1065 ##ImageComparisonIsIso sigmaFinsuppLequivDFinsupp lanLiftDesc fastGrowingε₀ 28006 28005 280548 280541 63269 63275 63272 63266 dpq wsnd ∂count equivIcoMod laurentAux toPrelaxFunctorStruct toKaroubiNondegComplexFunctorIsoN₁ ¬StrongLT rightInverseUnitor oneCocyclesLequivOfIsTrivial algebraFunctorOfMonadHomEq algebraFunctorOfMonadHomComp algebraFunctorOfMonadHomId humeas ηs₁ ηs₂ quotientEquivSumOfLE 94624 94612 Hnext ¬MonovaryOn ##7601 ##enom✝¹ primeSpectrumProd ##olem₁Reduct finSuccAboveOrderIso conesEquivFunctor 36651 36635 36639 36655 36631 mappingConeCompTriangleh ImageFactorisation unitizationAlgEquiv mulEquivOfOrderOfEq ↑↑j₁ ↑↑j₂ pointwiseRightKanExtension pointwiseLeftKanExtension doublingConstant 39294 39346 76625 h2xs totalFlipIsoX directSumRight 3839 CreatesLimit ngnpos ##MopIso exponentialCDFReal ihyxn 78773 lightDiagramTo φmono 108266 108270 108274 recDiagAux algHomOf simpleGraphOfStructure linearEquivFunOnFintype beckCoequalizer ⇑x✝ ofBoolList addEquivOfAddOrderOfEq eLpNormLESNormFDerivOneConst eLpNormLESNormFDerivOfLeConst basisOfLinearIndependentOfCardEqFinrank freeGroupEquivCoprodI algHomEquivAut algHomEquivAlgHomOfSplits zsmulAddGroupHom 231592 ##Ecε compHausLikeToTop ##WhiskerLeftMap ##WhiskerLeftIso monoidalFunctor simplicialToCos AddGroupNormClass suma✝ 110759 110262 1107601 equivUnitsEnd yonedaCollectionPresheafMap equivalence₂UnitIso isometryOfInner isometryEquivBoundedOfCompact quotQuotEquivQuotSupₐ ιInvAppπApp 43710 43714 ofGradedObject universalHom 119294 119287 iteratedSliceEquiv toPseudoEMetricSpace dgoToHomologicalComplex elementarySk pnatDen matrixDecompositionAddEquiv ofHasKernelOfHasCokernel ofHasCokernelOfHasKernel triangleRotateShortComplexSplitting 230696 4485 62184 ¬IsSolvable wideSubquiverEquivSet toUInt64 mapIdxMAux dXZ✝ 22022 22013 77909 825552 Foldr Scount SimpContFract ¬toTriangle ##igrpIso composableArrows₃ pullbackFstFstIso subterminalInclusion tensorDistribEquiv indexesValues 136948 136952 136944 homotopyEquivNormalizedMooreComplex 25950 25982 pointedToBipointedCompBipointed iseqv✝ iseqv✝¹ compatibilityOfZerosOfIsColimitCokernelCofork 29683 29676 ¬LSeriesSummable finEquivPowers 101327 functorMapSrc psigmaEquivSigma hπU✝ inclLiftTo adjointDomainMkCLM 9744 Tcount pprodCongr pprodEquivProd instUniformSpaceProd commMonFunctorCategoryEquivalence 17202 triangleMorphismId mapTrifunctorMapNatTrans mapTrifunctorMapFunctorObj abelianImageToKernelIsKernel RecursionBase MNT punitProd punitCoprod ¬AntitoneOn toPartialOrder✝ ofPiFork ofPNatList opUnopEquiv coalgebraEquivOver finBasisOfFinrankEq divByNat toPiFork valuationOfNeZeroToFun firstRowToS limitConeInfiIsLimit delayReflRight ¬MonotoneOn cokernelToAbelianCoimageIsCokernel 45092 45088 52509 52667 52674 73757 73761 ##LightProfinite toGlueR toGlueL equivLaxMonoidalFunctorPUnit equivLaxBraidedFunctorPUnit 138641 138648 hVconvex 14353 14359 takeListTR cocycleOfDegreewiseSplit 194755 194754 algEquivOfAssociated remainingToString remainingBytes fiberEquivKer 25322 25326 fullBraidedSubcategory fullBraidedSubcategoryInclusion strongDownwardInductionOn widePullbackShapeOpMap widePushoutShapeOpMap 592611 592608 hsaty₁ hsaty₂ 632041 632038 43805 43809 bipointedToPointedFst bipointedToPointedSnd toLawfulFunctor✝ toLawfulFunctor✝¹ findEntryP 367879441 36787944116 quotientiInfEmbedding 7079 71935 trivChange 129704 generatedNormal mapBifunctorComp₂₃MapObjIso ⇑↑φ₀ splittingOfFunOnFintype IsEllSequence 288867 topCatAdjunctionUnit toPrenexImpRight interUnionPullbackConeLift CompactlySupportedContinuousMapClass 4190 79019 83140 ¬SupPrime toKaehler toImagePresheaf ##ToDGO isKernelCompMono isCokernelEpiComp preordToPartOrd 10428 inrCompHomotopy equivHomset commTensorLeft enrichedFunctorTypeEquivFunctor toLinHomAux₁ cofan₃MapBifunctorBifunctor₂₃MapObj mkOfHomPrefunctor addMonoidHomLequivInt strongInductionOn 4103 mkInductiveAux₂ 101120 imageSheafι autAdjoinRootXPowSubCEquiv ##UnionInftyEmbedding 158177 forget₂ToModuleCatHomotopyEquiv quotientSubgroupOfMapOfLE inducedOrderRingIso embeddingUpInt decomposedTo connectedComponentsLift natTransPInfty ⇑equivRealProdLm mkCoinductiveAux₂ 26953 2244083 227041 337009 52726 52660 7784 71899 71152 77547 70551 82739 AreEqualizedBy Alternative DelProp Henselian KuratowskiEmbedding Kconn Lcompact SuppPreservation callCC dds depth istrns killCompl patches pthRoot sharp skewProd uhpath01 ¬addWellApproximable ¬MDifferentiable ¬memPartitionSet ηαθ ↑Upto ⇑CliffordAlgebra ⇑SemidirectProduct instApplicativeComp SetNotation mapSpanningSubgraphs toOfLists toConstProd toRestrictTop toSeminormedAddCommGroup HasCoreflexiveEqualizers objPairwiseOfFamily homologicalComplexToDGO unipotent unfolds compInverseIso compExactValue ##UnmopIso mkNormedAddGroupHom ofClosureMEqTop ofGenMemAdjoin ofUniqueOfUnique ofNullHomotopic FieldAxiom haebdd ##OfRamificationIdxNeZero valFromGraph algebraQuotientOfRamificationIdxNeZero algebraEquivOfIsoMonads liftSupQuotQuotMk evalCompEqToEquivalenceFunctor leftInverseUnitor SMulBracketCommClass SumSqIn implicitFunctionDataOfComplemented sumDualDistrib sumArrowLequivProdArrow sumProdDistrib sumArrowEquivProdArrow sumEquivSigmaBool pullbackTotalSpaceEmbedding numLeaves equivQuotTensor autMulEquivOfFullyFaithful isoTriangleOfIso₁₂ isoBiproductEmbedding commensurator transportedMonoidal subtypeQuotientEquivQuotientSubtype ##PullbackOfPreservesLimit colimitInvAux 1338774423 limitIsoSwapCompLim 14468 147899 LpToLpRestrictCLM coePNatMonoidHom splitMonoOfIdempotentOfIsLimit splitEpiOfIdempotentOfIsColimit constantCommuteCompose kernelForkOfFork IsSheafUniqueGluing pairSelfAdjointMatricesSubmodule quotientEquivProdOfLE OfCoimageImageComparisonIsIso rTensorHomEquivHomRTensor cokernelCoforkOfCofork chosenProd casesDiagOn lTensorHomEquivHomLTensor pushforwardContinuousSheafificationCompatibility notNilRec isLimitOfHasPullbackOfPreservesLimit isLimitForkOfKernelFork quotQuotToQuotSup sshiftRight fiberBinaryProductEquiv isColimitCoforkOfCokernelCofork mkOfObjOfMapSucc 255346 cotangentToQuotientSquare ##OfMemClosureRangeCoe continuousLinearMapToWeakSpace 363916618873 orderIsoSumLexPUnit completeBipartiteGraph functorObjSrcFamily functorObjTgtFamily ba₁a₂F sumLexDualAntidistrib widePullbackDiagramOfDiagramOver simplicialToCosimplicialAugmented 1107598 yonedaCollectionPresheafMap₁ elementarySkolem₁Reduct wideSubquiverEquivSetTotal homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex pointedToBipointedCompBipointedToPointed firstRowToSecondRow 3678794412 splittingOfFunOnFintypeSurjective mkOfHomPrefunctors AreEqualizedByLocalization 133877442384 splitMonoOfIdempotentOfIsLimitFork splitEpiOfIdempotentOfIsColimitCofork 1ᵛ 1∗ 1✝¹ 228 239 233 2266 2276 31 311 355 317 378 3337 426 449 487 56 539 547 548 519 5869 655 614 74 755 787 7267 815 8867 986 929 933 921 991 Ax A2 A⋆ Aesop ACounit Bₙ Bind Cx Can DE HK Hsep IRec Ki KL KU LA LU LK Lmul Labelling MNF Np N✶ NBu Pure Pinf Pbot RM Rem Range S₀ T1 T₀ Til U1 U2 Uᗮ Vo Ver Vis Wri Xᵢ Xᵒᵖ XXIsoOfEq YE Yᵢ aC a9 addCommMonoid ablem bj cyc dum dse divisionRing densely double eₒ eve eEE gF gE glo hor hset hTo hrows iH i5 icc i⁻¹ j42 ke kx ky ly l₄ led limits lind liouville lequiv lnot me modu mus mmap mr₂ nne om o1 o2 omap operate pF pY pₗ pythag qe q2 rU sF sM sX som seg sInter tS tm t⋆ tₙ tfin vl vPullbackCone wv wpos wmeas wint xx xc xw xab xpos yf y𝖣 ypos zi ¬F ¬D ¬δ ¬θ ¬𝓝 ¬ψ ¬χ ¬Mul ¬Fin ¬Measurable ¬Li ¬Con ¬Sigma ¬Bijective ¬Euclidean γδ δx δγ εxp μ₀ πid πir πip πComp ρAut φs ψtr ω00 ϕ₁ ϕ₂ ⅟B ↑χ ↑ℝ ↑em ↑an ↑is ↑il ↑ri ↑Algebra ↑Nat ↑ind ↑hy ↥l ↥e ↥v ↥ϕ ⇑o ⇑With ⇑Fin ⇑Is ⇑Nat ⇑NNReal ⇑Matrix ⇑AddMonoidHom ⇑cs ⇑ENat ⇑lift ⇑WithTop ⇑LatticeHom ⇑AddSubgroup ⇑WithBot ∂f ∅ᶜ ⊤ᗮ ⊥ᶜ ⊥⁻¹ ⟶ᵐ 𝔖✝ ##qn ##e₁ ##Far ##rv ##rase ##x₀ ##total ##nal ##RId ##sat ##sCon ##sible ##clo ##Skeleton ##StrongEpi ##airing ##wInvariant ##LId ##Cop ##vr ##ville ##vLex ##hing ##hase ##himp ##my ##match ##gHomClass ##E₄ ##E₃ ##Epim ##Estimator ##Erase ##₀⁰ ##₀Homotopy ##₁₃ ##XAdd ##P₂ ##bal ##211 ##254 ##Bial ##BLE ##₂G ##₂E₃ ##Dvr ##822 ##8489 ##728 ##07 ##ISMul ##62 ##637 ##633 ##671 ##6266 ##350 ##341 ##383 ##343 ##₃ObjExt ##₃E₄ ##520 ##589 ##VT ##V₀ ##433 ##4366 ##ι₀Homotopy ##𝖣a infinite inCircle instLE ##onst ##oryModel ##etim ##unique ##ols IsFunc IsBound ##ddCommute ##apb ##GroupEquiv ##ogx ##ologous ##atUnionInftyEmbedding ##ivSequence mapLift mapLe mapFn mapHomotopy mapEval mapAddHom mapDifferential mapCochain mapDerivedCategory mapArrowFunctor mapCoeffs mapOfIsColimit toIs toUnit toCat toGame toExp toCoc toBool toTransported ##ontal ##osite hfσ hfX hfU hfad hfab ##terT ##ocus ##Map₁ ##MapOfEquiv ##ument ##HomRel objUp objPreimage objDown ##izontal ##WithInjective ##MulRight hsing hsSup ##ational re✝ re✝¹ ##rimrec unC hxN compMono compCLM compYonedaSectionsEquiv composite ##Unsat rangeSingleton mkCone mkCocone mkOfIs mkLine ofC ofSub ofMeasurable ofPred ofPow ofBase ofSequence ofSigma ofCompIso ofExists ofUnitHom ofNSMul ofSums ofFiberEquiv ofPreimageEquiv ofErase hpj hpL hpne hpapb RingAut ##AddUnit ##AddCyclic haw ha₇ SubmersivePresentation ##OfRel ##OfChar ##OfLift ##OfAlgHom ##OfTendsto ##OfRightInverse ##OfInvertible ##OfNonempty ##SubZero ##Subcover symmComp opos opInv opMulEquiv ##IsImage hgw ##UnitSMul ##UnitSubmonoid ##UnitInterval ##EquivL ##EquivFin ##EquivIcc ##EquivTuple ##TopLe ##TopHomClass ##asisDivisor ##keToReal ##ComplexShiftIso ##ComplexOfComplete ##valXAdd atImInfty ↑x₁ ↑x₂ ↑x₃ clt clos IsList hnC hnin hnum hnam ##IsoLeft ##adToFunctor algebra✝ prodP prodFunctor prodUnique prodLex construct conformal ⇑fe f₁⁻¹ idRestr fst⋆ fstKernelFork ##LeftHomology ##LeftEmbedding ##LeftKanLift succRecOn htS htM htne h₁i h₁w₁ hcG hc3 hcab hcell hcond hcpos hcPos hconnected hcuv hcols hmv hmas hbl hbv hbb hbad a✝⁶ eqn eqc eqz eqZero ##₁₂MapObj finAntidiagonal finPi ##ToW ##ToList ##ToLinearEquiv ##ToInjective ##ToiUnion ##ToCommMon R₂ˣ h₂w₁ h₂w₂ restrictComp restrictDvd restrictFullyFaithful snd⋆ sndKernelFork natLE liftι liftMonoid liftAlgebra liftFrom liftInclusion spand spanEval hyu hy3 ##SMulRegular ↑↑P ↑↑3 leftFunc leftKanExtension ##LinearIsometry FiniteDimensionalOrder Modify ↑fr ↑fn coeff✝ coeff✝¹ ifs supportᶜ ##NatAbs abU comapFun comapMetricSpace minNatAbs InjectivePresentation ##NNRealReal ##IdealRingEquiv ##IntegrallyClosed ##ComposableArrows exs isSub isImage isPerm isOption isMaximal isLowerSet isSemi isPredLimit isIsomorphic isBilimit isUnsat isUnitSMul unopInverse unopOpIso unopUnitIso unopCounitIso asEmbedding asSubtype asOrderHom rightComp rightKanExtension premap presentation hru hrε im✝ im✝¹ impos hdt hdPos hdrv ↑pt ↑p₃ addEmpty addValuation ##OneMonoid 105 1038 subadd subthe subring subrel lex le2 le12 RingHomId Quotientˣ singleAlgHom singleZeroRingHom heπ hest forward shrink ##wiseLimit profinite piComm piMap closedUnit closedCounit hvi hvN Cᵒᵖᵒᵖ PreservesCoproduct PreservesEqualizer PreservesBinaryBiproducts ##babilityTheory shiftAddHom logHomeomorph logOrderIso ↑i✝ huA huw hl6 hloc hlogx kerCotangent lim₂ castFree castOrderEmbedding getLit tensorAssoc tensoringLeft tensorRId tensorLId inrCokernelCofork imageHom imageStrongEpiMonoFactorisation imageIsoRange zeroMul zeroProd ##ativeDimension expHomeomorph ##KernelSubobject derivUB ##izedTypes hUi hUs hUk hko 1169 1179 1124 1157 1140 1177 1143 11266 11269 projKer ##CompactOperator RelHom hPZ hPnon hPmonic hPnot hPunique starInitial starₗᵢ ##EmbeddingEquiv inlRingHom inlCokernelCofork hIe hIterate ↑eX ##Tensor₃ObjExt gcdAux ##oveNone unit✝ ##OrderedSentence hzt hzn hzK hTs hTx₀ ↑to hSn hSd hSne hSfin hSgen 1230 1292 whiskerVer equivLT equivHomotopy equivFixedPoints equivFreeAlgebra equivSubZero hμ₁₂ toLE ##radedMonoid ##ProdEq autMulEquivAutGalois h2i hqzero normComp isoH isoProduct isoProd isoCoproduct isoCoprod isoSheafedSpace isoStrongEpi isoToLinearEquiv ##AlgOfEq p₃₄ GradedSMul hεx hεy eraseZ detMonoidHom detRow detInvertible ##TransSymm ⇑eη orderBornology one₁ one₂ non1 ##LimitEval ##LimitPairwiseIntersections e₁₃ negISMul IsDivSequence ⇑g✝ hFε infi TotalBLE smulOneHom hxy4 ##SpanEquivQuot ##SpanOfCardEqFinrank archim array ↑Spec hC✝ hwC hwz colimitPresheaf colimitFlipIso colimitBundledCore colimitAuxiliary affineHomeomorph Matroidᵣ descToInjective h✝² A₁ᵀ 1389 13014 h0r h0d ##FactorAt ##rectness hζ₁ hζ₂ counitNat counitAlgHom counitBackward counitAuxAux setBasis setValue intF intSpanEquivQuot reverseInduction reverseOpEquiv hφq hφpos eqToEquivalenceFunctor ##FinsuppSurjective extend₂ ##ColimitEval charPoly ho✝ lowerBasis dualCop hKA reflTransSymm fromUnit fromInitial fromStalk fromNext fromThinSkeleton fromInduced fromSkeleton limitOpIso limitIsoPi limitRightOpIso limitBundledCore limitAuxiliary hVj hV✝ hV₁ hVortho hVtotal K₁✝ ##Endo ##EndEquivAut basicOpenSection IsDedekindDomainDvr K₂✝ K₂ᗮ ↑denom✝¹ ContMDiffMap ##sToAffine ##sToConstants signExtend hMq hMmatch hMVT h₃w₁ h₃w₂ head✝¹ ##ImagePreimage bihimp blur ↑z⁻¹ ##OpNorm B₁✝ hRt 144366 hαt ##AffineRefinement Domᶜ LiftObj LiftPred coeRingHom coeEmb coeMulHom coeNNRealReal 1639 1697 16591 16014 totalDesc hNT hNε ¬IsTop ¬IsFiniteMeasure ¬IsLeftRegular ¬IsRightRegular ¬IsAddCyclic ¬IsSMulRegular ↑Aₙ uncurrySum hJs hJv sheafForget sheafIsoOfIso hXR hXZ restrictScalarsBundledCore that whiskerLeftFunctor 1555 158489 BiheytingHomClass ##ComponentwiseLimit hstop hstart j₁✝ toListTR hGF yonedaPairing ##oleanisation ##Booleanisation hμsc hμs✝ ##ouville j₂✝ z₁ᶜ π₁Toπ ↑N₀ antisymmetrization correctness LawfulCmp hinz ↥M₀⁰ ##NegMonoid z₂ᶜ ↑w✝¹ splitMono splitEpi ProjectivePresentation d₂a w✝⁸ InvMemClass dimension ClosedPredicate varsToConstants ##QuotMapCMapSpanMk argument toPointed lsb lsbs ##alyticGroupoid conePoints coneOfHas coneOfIsSplit conePointsIsoOfEquivalence diam0 constantMap StrongHomClass IsMaximal✝ IsMaximal✝¹ cond2 π₂Toπ nextFixed kernelUnopOp kernelIsKernel kernelOpOp kernelOpUnop adc IsSheafPreserves μ₁✝ μ₂✝ h3lt ↑R⁰ sigmaUnique sigmaPUnit sigmaOpens sigmaComposition sigmaTR sigmaOrthonormalBasisIndex sigmaPreimageEquiv sigmaToiUnion defaultExpansion defaultCost xn1 xn0 quotientAddSubgroup quotientCotangent quotientEquivOfIsCompl colimits coprodObj directionOfNonempty recur recAux recAuxOn ↥s₂ conjNeg ##DivSequence orbitZPowers orbitZMultiples weightCost ##compTrans hasOpNorm disj✝ InfTopHomClass HasLeftInverse HasLeftTensor₃ObjExt dsm key2 ↥↑J hLc hL₁ hL₂ Squash replicateTR toContinuousAffineMap toEndHom toEndRingHom tl₁ tl₂ cokernelCocone cokernelOpUnop finiteSubspace finiteSubcover 176 17215 17211 ↑M⁻¹ ↑ModularGroup KaroubiUniversal₁ ##MonoidalToMon hhf encodeNat ⇑φ₀ ##Pushouts p₀✝ lb₁ lb₂ IsPrecomplete coconePoints coconeOfHas coconeOfIsSplit toTopsp la₁ la₂ localGeneratorsData IsCohom RevLex ↑↑↑A toProdHom rightUnitorBimod ¬f⁻¹ πiH toAlgebraIso naturalityProperty hYJ respects ##Normalize reindexGroupEquiv fractRestrict foldrAux foldrRecOn ⅟↑ad linearHom realizedTypes hp1m chains freeMap symInsert leftUnitorBimod vecEmpty hfmgle nzero powMonoidHom hσ3 nothing ##SquareIsPullback measurableSet idealMap decodeNat ##PermIncl NN0 bddsup toAlgHom✝ toAlgHom✝¹ ReflectsFiniteProducts rootSpaceWeightSpace IsHered IsRelational IsZeroAtImInfty hπn comulAlgHom ↑GradedMonoid HasRightInverse hx₁B prevFixed IsIncompTrans ⇑OrderIso ⇑OrderEmbedding yn1 yn0 g₀L ##aternionBasis front productTR triangleMap acca accb H1LequivOfIsTrivial ¬basisDivisor coyonedaPairing AllAg hWY fxclo n0l quaternionBasis toMonoidHom✝ toMonoidHom✝¹ rcli ¬constant ¬const hfc2 cyclesIsKernel ¬Primrec ##ticalIntegrable 200 2006 fixAux fixToW ¬Gᶜ PreservesColimitPair hcd₁ ⇑↑p ⇑↑z ##ramSchmidtNormed opensCongr opensImagePreimage hx₂B submatrixEquivInvertible αᵒᵈᵒᵈ condKernelCountable SemigroupWithZero singletonOneHom singletonZeroHom sectionsMk heq✝ polynomialEquiv supportedEquivMvPolynomial mixedChar opcyclesIsCokernel ##3228 compactOperator toPrev toPreOneHypercover ##lySatisfiable whiskeringLeftFunctor finsuppLequivDFinsupp nd₀ botEquivOfInjective ↑μs hψφ gluedIsLimit hx₀s g₃⁻¹ EffectiveEpiStruct ##Birational UVl ##StalkOfSpecializes L₀X₂ precompRelation isoOfQuasiIso MeasurableSMul₂ ##691 ##6964 f18 hpmqn quotMapOfEquiv transposeLinearEquiv ##790 ##799 hp2m pmapImpl adjugateᵀ pullbackCoverAffineRefinement postComp SpecialLinear Specializes ##SimpleOrder ##189 ##1808 restrictionLT groupCohomologyπ ##641 factorThruKernelSubobject algEquivAe algEquivComplexOfComplete unitsEquiv unitsEquivProd unitsNonZeroDivisors unitsTypeEquivIs unitsEndEquivAut pathToList castLEEmb hres toNonUnitalSemiring toNonUnitalNonAssocRing equivalence₀ H0LequivOfIsTrivial toFractionRingRingEquiv ##2828 isSuffix AugmentedCech LawfulMonadCont DivInvOneMonoid hco✝ addEquivBoundedOfCompact almost algeq hZI hZW ##273 ##irectLimit ##1157 equivOfInverse equivOfRightInverse ##502 ##505 hadd✝ optionEmbeddingEquiv ##volutionExistsAt quotientMapₐ InitialSeg toMeasureEquiv isColimitWhiskerEquiv ##leteFar ↑σ₁ ma⁻¹ replaceTopology mkOfClosure mkOfPoint mkOfNhds mkOfHomEquiv ofIsIsoLeft IsTotalPreorder 25867 25874 256266 ¬gramSchmidtNormed tmulEquiv ##8023 fieldEquivOfRingEquiv fieldOfChar hik2 ContextInformation hωpos hωneg ##Braiding hw₁w₂ ##168 497 494 4901 cpow ##TupleEquivTuple ##268 hfpB toSubstring toSubNegMonoid uniqueProd analyticGroupoid ↑Dl expMapCircle⁻¹ ClosedUnderColimitsOfShape ClosedUnderLimitsOfShape vcompd asIsoHomologyπ asIsoHomologyι precomposeHomEquiv ##863 apply₂ BialgHomClass hm₀✝ ##470 MeasurableVAdd₂ ht₀s ht₀o compContinuousLinearMapEquivL imageSubobjectCompIso hdvdx conjTransposeLinearEquiv awayMapₐ fy₂ hyxu iCyclesIso ofInjectiveEndo EffectiveEpiFamilyStruct ofSetoid fintypeOfAlgHom hbdc BundledHom DifferentialsCon hermiteTheorem ##576 endEquivSections selfAdjointEquiv changeFormEquiv 2677 268023 hgauge hysy pOpcyclesIso initsTR hcpn explicitCokernelIso hcomp✝ he₂e₁ ##293 mkContinuous₂ mkContinuousMultilinear ##404 ↑ζe ##SectionsIso constrL tailsTR LevenshteinEstimator 40520 bezout sHomFunctor ¬restrictScalars 362828 ##192 ##334 leftShiftLinearEquiv hμUk binaryProductFunctor firstDiffPos noTopOrder IsMonotone hrpq0 divModAux 2905 frobeniusPolyRat IsSepClosure ##OfFinsetProdEq toContinuousLinearEquivOfContinuous cmn cmd sectionOfCone msbs ofIdComp isEmptyRingEquiv rightShiftLinearEquiv NoetherianObject SupBotHomClass coimageStrongEpiMonoFactorisation ndrecC claim5 √↑x ##999 25131 curryLeftLinearMap ##523 ##HomeoI addUnitsTypeEquivIs ##IcoMod hpd4 hpdvd Hnot ##109 otherMap 2779 27192 61164 61156 61160 hef✝ hfnEcε cyclesIsoX₂ cyclesIsoLeftHomology comparisonLeftAdjoint hδ₁pos IsPointwiseRightKanExtensionAt 57647 57423 57419 57595 57189 dxlt directLimitRight ##SemilatticeInf kerLiftAlg homologySequenceComposableArrows 2432 2418 2458 rangeSRestrict ##EquivPiFinsupp monadToFunctor stdSimplexEquivIcc bigSquareIsPullback mm₁ opcyclesIsoRightHomology opcyclesIsoX₂ ##BraidedToCommMon isoOfIsoLift DeleteFar fvu hifs1 autMapHom 2251 ⇑natUnionInftyEmbedding ⇑a₀ compRightAlgHom compRightContinuousMap ##ToProdFunctor coeFnRingHom coeFnAlgHom coeFnMonoidHom compContinuousMultilinearMapL alternatingProd⁻¹ extensiveCoverage widePullbackShapeUnop IsFinitelySatisfiable preStoneCechExtend widePushoutShapeUnop RayVector ##8269 ##OfHasFiniteProducts selectPoly 59015 ¬ContinuousOn eqLocusM hII₀ hScl skyscraperPresheafStalkOfSpecializes oxl oxr ##LogLengthCost toInfTopHom ##ObjIsoComponentwiseLimit comonadToFunctor IsStableUnderFiniteProducts cobddmax ##itarilyLindelof hesu ##898 hpk₂ orderIsoOfIso bijInv collectedOrthonormalBasis HasImageMaps liftToFinsetColimitCocone ExtendBy hCFk 4583 45694 eₙ₂ eₘ₂ ofIsoComp hprodZ coneEquivCounitIso instTopologicalSpaceUnits mapBifunctorRightUnitorCofan 64879 64871 90392 ¬Sbtw ¬¬a φ₁₂₃ ofModuleMonoidAlgebra LiftpPreservation DilationEquivClass 64863 classNumber quotientEquivAlgOfEq foldrIdxSpec 42593 42589 hdpq IsTwoCoboundary GenerateHas hp₁s₁ hp₁s₂ hp₂s₁ hp₂s₂ 3041 30188 eGG r₁₂₃ εa0 hsq₁ hsq₂ mapBifunctorLeftUnitorCofan 3910 IsFwInvariant SubadditiveHomClass LiftPPreservation kernelSubobjectIsoComp 23232 CreatesConnected toOplaxMonoidalFunctor mkDerivationₗ implies ¬↑n₁ ColimitCoconeIsColimit 61695 functionField toPushforwardOfIso NonarchAddGroupSeminormClass grothendieckTypeToCatFunctor grothendieckTypeToCatInverse 4626 PushQuiver bgu bfu beckAlgebra epiWithInjective toZeroAtInfty ¬IsBoundedUnder hπ₁U raiseCone quotEquivOfEqBot sheafPushforwardCocontinuousCompSheafToPresheafIso ¬AEStronglyMeasurable liftOfRightInverseAux restrictedYonedaObjMap₁ toAddGroupSeminorm leftpadTR selfProdPermIncl monoidalCounit δlastFunctor 21818 21810 21814 εc0 cosimplicialToS fixFC equivalence₂CounitIso IsPointwiseLeftKanExtensionAt 37168 4341 eE₂E₃ eE₃E₄ ePP₂ eP₂G fullyFaithfulForget hbj✝ universalAddHom isPrime✝ hqy₁ hqy₂ orderEmbeddingOfSet orderEmbeddingToFun flipEquivalenceUnitIso flipEquivalenceCounitIso quotientPiLift awayToSection openCoverOfLeftRight combineCones combineCocones 23635 23631 23606 37783 toAdjoinMonic sumLiftRel functorProdToProdFunctor hzsz nsmulRec equivalence₁UnitIso equivalence₁CounitIso associatesNonZeroDivisorsEquiv toUInt8 toUInt32 toUInt16 220633 35297 62618 62626 62630 62622 Hloc coproductColimitCocone dYZ✝ hencard laxMonoidalToMon laxBraidedToCommMon ¬toIcoMod mapToSelf composableArrows₅ pointedToBipointedFst pointedToBipointedSnd definedAtRight IsFraisseLimit 41420 mapMonFunctor symmetricSubalgebra finEquivZPowers 109347 1093228 1091157 functorMapTgt functorExtension₁CompWhiskeringLeftToKaroubiIso unitOfInvertible equivIocMod 16018 IsMulTwoCoboundary rotateLeftAux rotateRightAux gnpowRec ##OfDetInvertible sectr subordinateOrthonormalBasis huai toLightDiagram 17207 17203 graphEquiv₂ 199793 199790 triangleMorphism₁ triangleMorphism₂ dgoEquivHomologicalComplexUnitIso dgoEquivHomologicalComplexCounitIso functorProdFunctorEquivUnitIso functorProdFunctorEquivCounitIso Machine₀ 23741 23745 237519 46486 46482 46478 rz₂ ¬ThreeAPFree mapObjFun mapCommMonFunctor toMonoIsImage toMonoidalFunctorOfHasFiniteProducts hfnew hgI✝ ##ToFunctorProd hV₂x pathsHomRel invertibleOfInvertible invertibleOfNonzero ProperlyDiscontinuousVAdd 25079 329271 52304 semiring✝ IsOneCoboundary toSubspaceUnit adjointifyCounit sigmaAntidiagonalTupleEquivTuple toProdMulOppositeHom foldlIdxSpec toMiddleHom forgetToPresheafModuleCatObj subsemiringMap skewAdjointMatricesLieSubalgebraEquiv 51659 58132 58135 60069 Ucne toSemilinearMap finChoiceAux equivSigmaTuple mapBifunctorComp₁₂MapObj isLimitConeOfCocone splittingOfFinsuppSurjective IsEllDivSequence 283606 283613 260737 260730 topCatAdjunctionCounit 320996 320999 324358 324351 45702 45682 542640 542637 95150 95146 dkk gradg gradf stringLengthCost stringLogLengthCost vyx ¬InfPrime ¬InfIrred ##mostMono mapCechNerve mapCechConerve toRows₁ toRows₂ toColumns₁ toColumns₂ HasAbsLeftKanExtension HasAbsLeftKanLift isAdjoinRootMonic 102181 1048911 1048914 subtypeOrEquiv subtypeOrLeftEmbedding 139799 topToPreord IHxl IHxr currySumEquiv 17195 17199 ProperConstSMul ProperConstVAdd adjunctionOfEquivLeft adjunctionOfEquivRight mkOfHasColimits mkOfHasLimits toLocallyRingedSpaceCoproductCofanIsColimit 284404 bicompl bicompr 292784 292787 ndrecOnC 34532 34536 57581 57588 571927 571930 595057 595060 597491 597494 OfLocalizationFiniteSpanTarget conesEquivInverseObj 1089086 1089083 127678 127674 bundledInduced maybeNormalize ofBoxProdLeft ofBoxProdRight IsStandardSmoothOfRel 246298 9007 EffectiveEpim ¬Wbtw ¬Uncountable ¬ProbabilityTheory mapAugmentedCechConerve toBoundedContinuousFunction unaryCast 112788 11305 132496 counitCoalgHom HasFiniteWidePullbacks 158486 stalkPullbackHom recolorOfEquiv linearHomEquivComm ⇑measurableEquivPi 36381 96011 derivationToSquareZeroOfLift coconeOfDiagramInitial hrecOn₂ 24237 37155 62056 95502 AlmostMono z𝖣x ¬AlgebraicTopology toRingAut toElementaryEmbedding toSemilatticeSup✝ ofCompId ofCountableUnion ##OfForallMemZ singleOneRingHom 128478 14964 quotientEquivPiOfFinsetProdEq fourierTransformCLE inducedStructureEquiv lieAlgebraComponent 217769 6931471808 algHomOfDvd mapIdxMAuxSpec adjointDomainMkCLMExtend embeddingUpIntGE 22662 227632 31133 35536 31752 53917 54716 54871 51945 58695 65549 61456 815509 98653 92908 93383 99132 CanLift DET Npq RemoveNone Tilde VerticalIntegrable VisClopen WriterT dummy divisionRingOfFiniteDimensional denselyOrderedSentence doubleFactorial eEE₂ global horizontal iccHomeoI j42n ledx liouvilleNumber modulus sometim segm ¬MulDissociated ¬Liouville ¬ConvolutionExistsAt ¬SigmaFinite ¬EuclideanDomain εxpos πCompι₀Homotopy φsur ↑emax ⇑liftLatticeHom infiniteTheory IsBoundaryPoint mapEvalEquiv mapDifferentialObject mapCochainComplexShiftIso toIsIntegrallyClosed toUnitMono toCocompactMap toBoolUsing hfadp hsSupJ mkOfIsCompactOperator ofPowEqOne ofNSMulEqZero ##AddUnitAddSubmonoid symmCompOfNondegenerate ##TopLeSpanOfCardEqFinrank ##valXAddC prodFunctorToFunctorProd constructLeftAdjoint conformalFactorAt idRestrGroupoid finPiFinEquiv natLERec liftFromProjective ModifyWF isSemireal isPredLimitRecOn isIsomorphicSetoid addEmptyConstants 103896 subtheoryModel subrelIso kerCotangentToTensor castFreeCommRing zeroProdIso 116938 112486 projKerOfRightInverse hPnonzero whiskerVertical isoStrongEpiMono detRowAlternating colimitPresheafObjIsoComponentwiseLimit colimitFlipIsoCompColim colimitAuxiliaryCocone 138915 intSpanEquivQuotAddOrderOf eqToEquivalenceFunctorIso dualCopairing reflTransSymmAux fromInitialModel limitOpIsoOpColimit limitRightOpIsoOpColimit limitAuxiliaryCone basicOpenSectionsToAffine 163940 155546 π₁Toπ₂ toPointedCone coneOfHasLimitEval coneOfIsSplitMono π₂Toπ₃ IsSheafPreservesLimitPairwiseIntersections sigmaCompositionAux sigmaOrthonormalBasisIndexEquiv quotientCotangentIdealRingEquiv orbitZPowersEquiv orbitZMultiplesEquiv coconeOfHasColimitEval coconeOfIsSplitEpi IsCohomologous respectsIso symInsertEquiv rootSpaceWeightSpaceProduct IsHereditarilyLindelof AllAgree rclikeToReal ¬constantCoeff opensImagePreimageMap L₀X₂ToP isoOfQuasiIsoAt quotMapOfEquivQuotMapCMapSpanMk pullbackCoverAffineRefinementObjIso algEquivAevalXAddC unitsEquivProdSubtype unitsNonZeroDivisorsEquiv unitsTypeEquivIsUnitSubmonoid isSuffixOf AugmentedCechNerve ofIsIsoLeftRightHomologyComparison 49012 fintypeOfAlgHomAdjoinIntegral DifferentialsConstruction endEquivSectionsFibers noTopOrderSentence addUnitsTypeEquivIsAddUnitAddSubmonoid homologySequenceComposableArrows₅ 245881 epiWithInjectiveKernel cosimplicialToSimplicialAugmented mapBifunctorComp₁₂MapObjIso IsStandardSmoothOfRelativeDimension EffectiveEpimorphic globalSectionsIso sometimes 1ᴴ 2∗ 248 364 342 346 331 322 381 382 388 3304 477 484 4464 4270 4360 4862 4324 53 5⁻¹ 500 584 585 567 558 5873 67 63 65 6⁻¹ 651 627 639 601 630 610 684 667 682 623 6275 6287 6283 731 753 771 734 709 7594 7470 86 85 826 821 806 875 872 8019 8704 803 86964 8576 94 950 980 906 970 9429 9360 A1 A0 And Amalgamation Acover Bint Bracket Ci Cn Cm Cᴴ Cartan Cech Cnonneg Dᴴ Dper Dnonempty Ene Eᵐᵒᵖ Eᵒᵈ F✝¹ Family Frobenius Gx GT Gy GH G0 GMulAction Gdistrib GUV He Hh HV Hre Him Hat Hist Hprod Hsub Half HAB Iu Ifin JA Jᶜ Kt Kφ Kst Kum LC L4 Lcomp Lequiv May Nᵃᵒᵖ Oˣ Opera OddCommute PT PContinuous QP Qiso Rl RP Ref Roo Sg Sε TC Tᵒᵖ Trailing UP UW Vx VP VD VW Vᗮ Vct Vne Vsub Vcl W⁻¹ Y₀ Z₃ aB aε aₙ aₘ addCommGroup aca ainl b⋆ bod bne bpos bilinear b𝖣a du eI esto fG fφ fα fct fep four gᘁ geq gath gray gradient hΘ hed hdd hig hUn hho hInv happ ip iv ici lk lra lti lcurry lr₂ mW moment nR nᶜ nop ot oS oβ oα oyl pS pK phase qc rK sG sle sim sof simp tR tT tid trichotomy tsets um vp vInv vonN vanish we ww weak walkLength xV yq yw ym yac ycs ymem ¬⨆ ¬st ¬in ¬up ¬is ¬tr ¬Add ¬Algebra ¬cd ¬Complete ¬Surjective ¬Small ¬range ¬Ca ¬Dense ¬Step ¬multi ¬Monic ¬Line ¬OfNat ¬HomogeneousIdeal ¬Ordinal ¬NeZero ¬Dvd ¬WellFounded ¬Commute ¬SimpleGraph ¬Booleanisation Σₗ βα δy δm εUV ιι ιPi κ✝¹ ᗮᗮ ᘁg ℕˣ ℝˣ ⅟m ⅟1 ⅟k ↑7 ↑al ↑ed ↑ur ↑ax ↑ab ↑ry ↑ux ↑Prod ↑Int ↑Multiset ↑Character ↑Valued ↥a ↥b ↾Sum ⇑Y ⇑τ ⇑Normed ⇑Comp ⇑Ex ⇑mul ⇑Homeomorph ⇑Subalgebra ⇑Function ⇑Opposite ⇑Prime ⇑map ⇑UpperSet ⇑RingEquiv ⇑AddEquiv ⇑Ordinal ⇑NNRat ⇑Weak ⇑li ⇑Specialization ⇑MulEquiv ⇑TensorAlgebra ⇑AddConst ⇑oi ⇑AffineMap ⇑inl ⇑AddSubmonoid ⇑inr ∂fun ∅⁻¹ ⊤ᶜ ⊥ᗮ ￢f ￢⊤ ￢∂ ￢⊥ ￢Order 𝔸ˣ 𝔸ᵐᵒᵖ 𝕆ᵒᵈ ##l₁ ##l₂ ##losure ##lag ##iet ##iler ##qr ##qs ##u⁻¹ ##utral ##Fix ##Focus ##rk ##right ##ries ##tTop ##tBasisNumber ##ngth ##det ##dHom ##RUnitIso ##snd ##sInter ##sSurjective ##sentedGroup ##sSupHom ##cur ##SR ##ScalarTower ##Sco ##Sorted ##SeparationQuotient ##Shear ##autologicalCocone ##Ty ##TProd ##TautologicalCocone ##pon ##powers ##LimitsOf ##Laurent ##LEquivOfIsCompl ##LCounitIso ##LEquivPiFinsupp ##LtTop ##CQuot ##Copy ##CBasicOpen ##ved ##yr ##yne ##mOfExists ##Mac ##MvPowerSeries ##ger ##gTo ##128 ##146 ##135 ##101 ##Hy ##Ge ##Gm ##GModuleCat ##XSubC ##beta ##bras ##264 ##229 ##2500 ##BE ##Bucket ##Dl ##Dedekind ##kU ##827 ##896 ##857 ##899 ##890 ##887 ##711 ##069 ##Iterator ##65 ##632 ##396 ##336 ##zne ##Kleisli ##↑γ ##VW ##Vortho ##Viet ##906 ##479 ##πIso ##ιIso ##ιTo ##ωSup ##pes ##oris ##orec instM instSemiring instFunLike instBEq instMonoidalCategory instFintype ##alge ##left ##access ##roSco ##asheaf ##edNatIso ##erfect ##erViet ##ingLimYonedaIso ##ormulation ##arger ##icPt ##olut ##CommShift ##CommonNeighbors IsωSup NormedLinearOrdered ##idClosure ##GroupIsom ##GroupEquivCoprodI ##GroupIsoTo ##ogram ##atInfCat ##RingOf ##RingProd ##RingSeminorm ##isSupHom mapZero mapSubgroup mapLinearMap mapMonoidHom mapPushout mapAddMonoidHom mapNatIso mapTR mapKey mapOrderEmbedding mapDart tot toCon toBot toAbs toRegular toGrp toProp toUnique toAut toDistribMulAction toCocycles toSheafification toModel toNonAssocSemiring toBornology toRingCatIso toGrpIso toMonCatIso toClopens tosInfHom toMagmaCatIso toSemiRingCatIso ##ilure ##ilinearMapClass ##ilDl ##ilatInfCat ##osOf hfh hfπ hfri hf₁₂ hfalse ##EqEquiv ##EqBot ##istent HasEquiv HasSplit ##MapZero ##MapGenerate Subset Subterminal ##lyDiscrete ##OrderEquiv objOpOp objAsType ##OnRange ##FunEquiv ##WithUpperSet ##MulSelf hsin hsingle hslt hssub homFrom homOfElement unif unone unbeta MulRingSeminorm hxL hx₅ hx₄ hx4 hxeq hxab hx✝¹ hxym hxneg hxfg ##tedConnected ##ZeroRing ##ZeroCoe ##ZeroAtInfty ##ZeroEquivIso compAlgebra compIso compLimit compRingHom compLinearEquiv compAlgEquiv compRingEquiv compPMap cardGe ##Uncur ##FinTwo ##Finitary ##Finsubgraph ##FinBoolAlgOp rangeFin rangeInl rangeInr ##ightProfinite ##SetMem mkEmbedding mkOrderEmbedding mkIterator ofLeft ofRight ofRoot ofComplete ofMono ofSheaf ofStar ofPolynomial ofPushout ofDense ofSpanSingleton ofRightInverse ofStarAlgHom ofPreserves ofPullbackCone ofFinitary RingTopology RingNorm ##AddRight ##AddPrehaar ##AddCosetEquivalence ha₆ ha✝¹ ##urjection ##reeGroupEquivCoprodI ##nds IsSuffix ##OfReal ##OfSub ##OfFunctor ##OfId ##OfProd ##OfMono ##OfInv ##OfStrict ##OfImage ##OfOp ##OfAdjoint ##OfAffine ##OfLocalization ##OfOrthogonal ##OfPi ##OfNonUnital ##OfBijective ##OfStructuredArrow ##OfDiscrete ##OfCmp ##OfOfLe ##OfConj ##OfKernelFork ##OfCokernelCofork ##OfCostructuredArrow ##OfSpanning ##OfClosedCompl ##OfTopLeSpanOfCardEqFinrank ##OfMulSelf ##Reals x✝⁷ symm₂ symmetry symmHomeomorph op1 opSpan opCospan opOrderIso opUnitIso opCounitIso opAdjointOp invEquiv invFunctor invVal invAct invOrderIso invENNReal ##IsKan ##IsSome hgsupp NonemptyFinite ##AlgebraIso Unbundle ##EquivMap ##EquivLinear ##EquivSem ##EquivMatrix ##EquivLift ##EquivAlgHom ##EquivNth ##EquivUnits ##EquivSym ##EquivEven ##EquivPUnit ##EquivAnnihilator ##EquivDerivation ##EquivRep ##EquivBoolAlg ##EquivCoe ##EquivRealProd ##EquivProj ##EquivPowers ##EquivDirectSum ##EquivGenerate ##EquivFixedPoints ##EquivNeighborSet ##EquivIntermediateField ##EquivDet ##EquivFreeAlgebra ##EquivCommonNeighbors ##FiniteBase ##FiniteBiproducts ∂μa CompleteCopy ##thHomotopy IsCryst cliffordAlgebra clmOfExists clAddPrehaar ##allographic IsLT IsLE hnN hnote ##IsoIso ##IsoRight ##IsoModule ##IsoNat ##IsoCone ##IsoEnd ##IsoSheafify ##IsoEval ##IsoSubobject ##IsoLowerSet ##IsoToDual ##IsoPartialFun ##IsoCentroid ##IsoFibers ##IsoMapGenerate ##IsoAlgebraIso ##adIso prodLeft prodRight prodContinuous prodEquivOf prodPi prodEquivPi prodBinaryFan prodZeroIso prodShear prodZeroRing conc congTo ##xpPartialHomeomorph ⇑freeGroupEquivCoprodI idTransformation idZeroEquivIso fstEquiv fstCLM univ⁻¹ univPi ##LeftOfNatIso atTop⁻¹ Coex succFunctor htp htν h₁t h₁w ##RightMoves ##RightOfNatIso ##ModuleEquiv hcyc hcxy hmq hmlt hmsb ##Coex ##Cokleisli ##CofilteredClosure hbM hbU eqHom eqOfHom finProd finsub ##ToComplex ##ToRight ##ToObj ##ToPre ##ToPoint ##ToRoots ##ToUnits ##ToPath ##ToSnd ##ToOrderIso ##ToCondensedSet ##ToFr ##ToAsType ##ToCompHaus ##ToFinBoolAlgOp LocalRule distance h₂i h₂t mul₁ mulFunc mulMon mulInitial mulMulHom mulIsInitial restrictₗ restrictSupport restrictRestrict restrictVar restrictIndepMatroid sndEquiv sndCLM natSum ##ipLeft Ordset liftFun liftCompact liftQuotient liftEquivOf liftExpand liftFZero liftFOne liftZeroAtInfty ##FunctorIso ##FunctorCompEvaluation ##FunctorToComplex f✝² spanOp hi✝¹ hyl hyC hy✝¹ ##ObjObjSingle₀ evalN evalAlgHom evalLatticeHom st⁻¹ ##astOrderEmbedding ↑↑d ↑↑to ##perCrossingTime EqOfCmp adjToComon adjToMonad leftIso leftFraction leftAssocTensor leftMovesEquiv leftToRight a₂⁻¹ ##NNDistEq ↑fl ↑f✝ MonoidalNatIso ##tension ab✝¹ abCyclesIso comapId comapSubgroup comapSubtype comapEval lengthTR ##IdealQuotient ##elSpaceHomeomorph ##CompMap ##CompSum ##CompCompose ##CompDiagram ##CompYoneda ##CompEss ##CompYonedaIso ##CompHomotopyEquiv ##CompToDual ##CompPreord ##CompToOver ##CompToUnder ##CompIsIso is₁ is₂ isPair isCompl isInitial isIdempotent isIm isPrincipal isRightAdjoint isClopen asType asFork asCofork asGroupHom rightComm rightIso right⁻¹ rightFraction rightFunc rightRes rightAssocTensor rightMovesEquiv hrS hrv hr2 hrk hr₄ hr3 hr₃ hdx hd₃ hdown hdmem hdVW ##ShapeUnopOp ##RelQuotient ↑pqr addFunc addAddHom addKer addNormalizer ##OnePart ##OneBirational sumᵀ sumᴴ sumAux sumAlgEquiv sumEquivOfFintype sumOfConj ZerothHomotopy 1099 10594 10523 ##PresentedGroup pullbackLimitCone subInv ley le23 leOnePart ##HomologyFunctor insertNe insertSorted singleHom toRealAffine toRealLinearIsometryEquiv toRealLinearIsometry heV filterBasis filterTR pia piπ piPi piMeasurableEquiv piQuotientEquiv hvV hvpi forgetful forgetCocone forgetEval trident ##Stack ##LatticeOfComplete ##actorization ##actorSetMem CompNondegComplex Compiler shiftl shiftFun shiftUp shiftEval hug huφ neK hlq hlA hlf someVector somePath someContDiffBumpBase someDecidable castDef castLEquiv castAddOrderEmb getEquiv getIso getEquivOf tensorIso tensorFunc inrCLM imageAddHom imageMulHom imageMonoOver zeroFunc zeroCoprod zeroRingProd swapAt ##ShiftOfLocalization pos₂ posOf posSubgroup ##FormOfReal hUy hUz hUW hkq hkU ↑rng 117 1129 1153 11500 11446 11135 projₗ functorComp hPL starLinearEquiv starAe inlHom inlCLM inlCompSum hIK hImax chooseᶜ ↑eL ↑eI ↑eY ↑expPartialHomeomorph ##DualIso ##DualNumber constL constₗ constAlgHom constMonoidHom constAddMonoidHom constLim constCompEvaluation ##ContinuousLinearMap Schemeᵒᵖ ##FinsetFunEquiv ##SemigrpIso unitSphere unitEquivUnits HasFactorization ##IdCancel ##ModPrincipal ##ModelSpaceHomeomorph hzi hzA hzan hT0 ↑t₀ ↑t⁻¹ mem4 numDenom 125 1269 1264 1211 1216 1270 1209 12116 12704 12494 ##ClosureRealization whiskerHom whiskerOfComp whiskerOfId whiskerIsoMapGenerate whiskerIdCancel equivSMul equivFinsupp equivList equivFn equivSym equivAddCircle equivPUnit equivBaseChange equivIsoLimit equivIsoColimit equivAdjoin equivOrbit equivDirectSum equivClosureOperator equivIsoIso equivPresentedGroup toLT toLarger ##SubgroupOfEmbedding ##ConstMap ##ConstInitial ##ConstTerminal ##ProdIsometry autIsoFibers h11 h1δ h13 h1728 h1V₀ h2h h21 h2V h2Φ habu habv habz hq3 hqnd normGroup TopHomClass TopCommRing sourceHomeomorph isoPresheaf isoInverse isoCoequalizer isoDiag isoOver isoTarget isoSource isoOpEquiv isoBiprod isoBinaryBiproduct commClosure comminl comminr commsnd commGroupIsoTo commShiftOfLocalization supOfBasis ##HomeomorphUnitInterval intermediateField internal sinOrderIso hε0 eraseAddHom b✝² ##SubalgebraOfNonUnital ⇑ea ⇑eb oneFunc oneLE oneLe ##SheafCondition r₁✝ ##LimitNatIso ##iscreteEquiv ##BoundedImage hfgrk reformulation e₁⁻¹ adjoinZero adjoinOne hBN hBAB ↑k✝ reprx reprX reprW negFunc negOrderIso contZ contX cont✝¹ contdiff ⇑g⁻¹ subtypeSupport hFortho r₂⁻¹ infTo infIcc infIoo coequalizerIso smul✝ smulLeft smul✝¹ smulMulHom hxyne ##SpanXSubC ↑StieltjesFunction a1✝ ##PullbackMap ##LiftIso ##Locale ##LocalRing ↑g1 hweq hwuv colimitNeg colimitFlip colimitEquivQuotient colimitCurrySwap colimitIsoSwap colimitIsoFlip colimitConstInitial affineIsometry n₁₃ hAN hAD AntiSymmetric prime✝ descMapObj descUniq descCApp descFZero descFOne inverseCompIso h✝³ ##adicLeftAdjoint ##InvOfPi 131 130 1332 1328 1356 13400 13229 h0n h0m ##FactoredNumbers ih₃ hjt hjm hj₃ consCases ##LegendreSym counitBial setSymm setTR int✝ intMax bindTR reverse∗ reverseEquiv reverseIso ltx lts ltLe ltAddSubgroup carries ##PresheafToSheaf ##PresheafToOver hφn hφ✝ edistLtTop extendFan lowerBound dualEquivDual dualIndepMatroid ##possible CoverByImage hKr hKt hK4 hKW fromList fromZeta fromIntEquiv fromMultiplicativeIntEquiv fromKleisli fromCokleisli sqf sqTo limitFlip limitOfS limitFlipIso limitCurrySwap limitIsoFlip limitCompCoyoneda limitEquivFixedPoints limitCompYonedaIso limitConstTerminal ↑uy ofNatIsoRight toFinsetᶜ I₂✝ top✝ hVy hV1 hVAB hVkU multiplicative ##Parts ##EndRingEquiv MapIso MappingCone ##Indefinite ##sToFunctorToComplex hM1 hM✝ hM2 hMdet ##Uniformity upperBound ↑Kβ ↑Kᶜ ↑Kᗮ ↑Kα ##Imageι ##ImageEquiv ##ImageInclusion SmallModel CliffordAlgebraDualNumber ↑zero ##OpCycle ##OpToFr 1437 1480 1416 1436 1415 14383 ##RangeOfInjective lastCases z₀✝ de₁ de₂ dead homologyOpIso tail✝¹ LiftCommShift 1611 1631 1617 1690 1670 1667 1625 1672 16894 16898 ##CancelRight pureMonoidHom pureAddMonoidHom pureAddHom pureOneHom pureMulHom pureZeroHom totalFunctor centerCircle centerUnitsEquiv continuousGroupoid hNn hN3 hNκ ¬IsOpen ¬IsCompact ¬IsLimit ¬IsTorsion ¬IsPeriod ¬IsLindelof ¬IsBadSeq basisSingle basisMonomial foldTR ↑A0 uncurryBilinear down✝ hJt hJB ord₁ ord₂ sheafPullback sheafOver hX₁ moved restrictScalarsL restrictScalarsIsometry HomotopyLike toMatrixOrthonormal whiskerLeftRUnitIso whiskerLeftLCounitIso 1518 1547 ##ProductsOfHas hstg ##Inverseπ ↑l✝ iteratedFDerivComponent IHe IH₁ IHyl IHyr ##SingletonHomeomorph ##BundleModelSpaceHomeomorph hne✝ hGH yonedaMap yonedaEvaluation yonedaCompLimIso typevec toNatHom castSuccFunctor castSuccOrderEmb inclusionBool antilipschitz hδm ncf ↑U✝ ↑U₁ ↑U₂ jacobian ↑j₂ convexAddSubmonoid LawfulFix hincl ↥M⁰ ap✝ ↑w₄ ##BiproductIso ##BiproductComparison ##BiproductπIso ##BiproductιIso w✝⁷ w✝⁶ InvOneClass InvTy truncFun truncCycle G₁✝ varFinset tensorObjDesc generateFamily generateSingleton argEquiv IsGE diagonalRingHom diagonalAddMonoidHom diagonalInvertibleEquivInvertible toPure toPFilter toPerfect ¬a₂ ringQuotTo psp coneMorphism coneOfCone coneCompEvaluation diam1 lcomm constantBase a0✝ condensedSet toLinOfInv nextPowerOfTwo kernelFork kernelZeroIso kernelIsIso kernelCompMono kernelBiproductToSubtype kernelBiproductπIso step4 terminated adicTopology IsSheafIff ↑J⁻¹ emptySum h3t h3b h3μ antidiagonalEquivFin pairEquiv pairSep sigmaL sigmaCongr sigmaSigma sigmaImp sigmaOpenCover sigmaSumDistrib sigmaFinsetFunEquiv Entry quotientRel quotientPath quotientSpanXSubC cocountable MonadHom coprodMap coprodUnit coprodSubtype coprodPUnit coprodZeroIso toLpHom f₃₂ G₂✝ ↥L₁ biproductUniqueIso biproductBiproductIso ##InitialsAux jacobiMatrix maximality hasPrev hasMac toAddGrp toAddGrpIso toAddMonCatIso toAddMagmaCatIso toAddSemigrpIso toAddConstMap ¬xs ¬x✝¹ toLinearEquivRight tangentBundleModelSpaceHomeomorph hLt hLU domx ##TwoEquivCommonNeighbors ubnd smulRightₗ smulRightDual relIso BoundedOrderHomClass auxs aux0 auxIso tanPartialHomeomorph StandardSimplex cokernelCofork cokernelZeroIso cokernelIsCokernel cokernelOpOp cokernelUnopUnop cokernelEpiComp cokernelIsoRange cokernelBiproductFromSubtype cokernelCompIsIso cokernelImageι cokernelBiproductιIso ComonadicLeftAdjoint tensorRightIso tensorRightTensor tensorRightMopIso tensorRightUnmopIso ↑H₁ 1769 17548 17320 ↑M₁ ##FilteredClosureRealization embeddingLiftIso ##UnitsCenter normalizeCoeffs normalizeConstraint wittPow uniformPDF hhJ hhx hhc hp₁✝ PullbackSelf mapBifunctorObjSingle₀ mapBifunctorObjObjSingle₀ ##IccSup ##IccZeroCoe parallelPairDiagram succAboveOrderEmb IsPrecongr coconeOfLE coconeOfCocone coconePointsIsoOfEquivalence hE✝ lieCharacter lieEquivMatrix lTensorf renameSymmetric lazy homEquivOfIs bernoulliPowerSeries ↑Bₙ localPredicate locallyDiscrete pushoutInl IsMprojection toAffineAddEquiv HasColimitOfHas powersMulHom powersEquivPowers ↑↑↑a ↑↑↑0 ↑↑↑↑γ ¬false I₀✝ b0✝ hYB resComp resId unitIsoAddEquiv ##AbelianOfIdeal ##ermatLastTheorem preimageHomeomorph preimageSingletonHomeomorph ⇑hVortho ##OrthogonalEqBot nnqs ##EquivOfLeftInverse ##EquivOfMapZero hxs✝ attachFin ##CokernelFork ⅟↑n sinhEquiv sinhHomeomorph sinhOrderIso chainSup modEq ⇑isoP WeakSpace LocallyRingedSpaceᵒᵖ symEquivSym ↑hI ↑hSR ##TerminalFrom ##TerminalsAux whiskeringObj whiskeringLimYonedaIso mapHomologicalComplexIso hfsi hfsj g⁻¹⁻¹ tensorLeftIso tensorLeftTensor tensorLeftMopIso tensorLeftUnmopIso powMonoidWithZeroHom powLog ↑Float point✝ pointToPoint hσ4 notMem graphFunctor idealTo evaluationUncur hyzx decodePosNum ##starAddEquiv huvx boxProdComm ##InftyToId ##CoproductsOfHas IsAbsKan 181 1892 1920 1926 1955 1957 1971 sb✝ sbdd ReflectsEffectiveEpiFamilies iaᶜ evenEquivEven toContinuousMapLinearMap toContinuousMapAlgHom toContinuousMapAddHom t2Setoid torsionAddEquiv torsionMulEquiv hnm1 hnm✝ IsInaccess ⇑OrderHom hs₁fin hs₁card ↑↑n₂ isLimitEquivIs hDC ##opyObj L₄✝ iVY ynmem ha₁✝ zpowersMulHom failure linearMapEquivDerivation finsetI circlesInter scMapIso frbdd productUniqueIso NNRealˣ ##SingleIso hc₁p ##OfIsScalarTower coyonedaEvaluation coyonedaCompLimIso ##ElemEquiv HasLimitOfHas ##Cofan₃MapBifunctor decomposeAddEquiv ¬single ¬sSup ##NonUnitalRingHom ##NonUnitalAlgHom fxs vectorEquiv hsC✝ ¬cos ¬closure ##SubsetSource ColorFocus ¬rl ¬r₁ ¬Principal 2032 2048 2010 2017 2071 2044 2070 20591 20862 20343 20146 20711 20906 homologyFunctorIso homologyFunctorSingleIso hcd✝ ##subl cospanOp zipWithAux zipWithTR ⇑↑H ##Neutral acx acb ##AlgEquivOp ##AlgEquivDirectSum opensEquiv opensRestrict gramSchmidtBasis ##SigmaTuple stabilizerEquiv stabilizerIsoEnd condKernelReal condKernelBorel singletonFinsubgraph snocCases rotationOf ##L2OfOrthogonal nonemptyTheory semilinearMap ##CompIsoSelf BiconeMorphism ##323 ##329 f⁻¹⁻¹ ##SelfAs ##SelfOfHas hmulright hmulleft hγ₀ formPerm⁻¹ sl₂ finsuppLEquiv ndeg ↑↑x✝¹ inclDesc inclCompMap ↑↑s✝ H2✝ CoeFun adjointOfOp diagAddMonoidHom h4s ##ProfiniteToLight iterateEquiv derivedAbelianOfIdeal mapCoconeOp mapCoconeWhisker mapCoconeToOver rla ##BaseSetProd ComonadHom precomposing ##TargetEqUniv ##RingEquivDirectSum event ##699 ##areReals mapDomainRingHom mapDomainNonUnitalAlgHom cauchy⁻¹ ⇑LowerSet ¬↑u ¬↑t ¬↑s ¬↑c ¬↑b ¬↑num zetaUnit natTransOfLe natTransOpCycle quotOfList quotToD quotMapCMapSpanMk quotEquivAnnihilator disjoint₁ disjoint₂ WalkingCospanᵒᵖ ##203 transpose⁻¹ transposeAlgEquiv transposeRingEquiv transposeOrderIso transposeInvertibleEquivInvertible BotHomClass alternatingCofaceMapComplex toLinearIsometryEquiv induceUniv ##510 subgroupCongr ##796 IsPrefix ##ConsSMulTop ↑γ₀ hp2✝ adjugate⁻¹ ¬yR ¬yL extFunctor fixedByFinite mapIsoOfIsLimit mapIsoOfIsColimit mapIsoToOrderIso ##CastSucc hxzne b1ne0 ¬μ₁ ToSet ##185 ##1855 ##1834 restrictionFunctor hmeasℱ toHomPerm toHomAddUnits subgroupOfEquivOfLe gci rootsOfUnityEquivNth algEquivOpMop algEquivEquivAlgHom algEquivIsoAlgebraIso prf mapConeOp mapConeWhisker mapConeToUnder hgm₂ hnonmax sieveOfSub unitsCentralizer unitsCenterToCenter unitsModPrincipal pathComposition liftsRing castLEOrderIso castLEOrderEmb hmeml hmem✝ toNonUnitalRing toNonUnitalStarAlgHom filterMapTR hχ₁₂ s⁻¹⋆ equivalenceSingleObj equivalenceSelfOfHas zmultiplesAddHom ##241 ##242 ##ContinuousMapHom ##280 ##AddEquivDirectSum f27 arrs lanCompIso lanCompIsoWhisker hfxv p⁻¹⁻¹ √x⁻¹ sym2Map al✝ ##AsFunctor ##AsBoolAlg ##AsBoolRing sheafificationNatIso sheafificationWhiskerRightIso sheafificationWhiskerLeftIso complexOfFunctor affineOpensEquiv toJordanDecompositionEquiv ⇑mk hacc ⇑σ₁₃ toDirectLimit equivOfComm equivOfEquivalence nullHomotopy ##5050 firstDart ##SieveCompatible ##SieveCompatibleFamily toΓSpecCBasicOpen Hs1 Hsmul hη₁ hη₂ ##Paths ##PathCategory optionIsSome ↑2⁻¹ listToPath ##3706 toLocalized PointDerivation ##461 ##466 ↑↑hx ↑↑hζ isColimitEquivIs isColimitTautologicalCocone isColimitCofan₃MapBifunctor CartesianClosedFunctor mb₂ restrOpen special ofNNRealHom factorMultisetEquiv replaceBornology replaceUniformity mkOfBound mkOfDiscrete mkOfDistEq mkOfNNDistEq mkOfOrthogonalEqBot recOnSubsingleton removeLeftOp CanonicallyLinearOrderedSemifield toContinuousLinearMap₁ BasedNatIso large₂ ofIsClosedGraph hps₁ hps₂ 25⁻¹ 2557 2585 25254 ¬IsMaxChain ⇑B₁ ##803 ##textFree IsBlockSystem preservesColimitsOfShape preservesLimitsOfShape preservesLimitNatIso extractP initialMul postcompPostcomp postcompIsoOfIso postcomposing extension₂ extensionHom ##356 WalkingSpanᵒᵖ 4981 colimitCoconeComp colimitCoconeOfComp gxs ↑δ₁ EventuallyEq cpm ##391 ##390 mapTrifunctorMapIso hfp₁ hfp₂ ##SourceEqUniv toQuadraticMapLinearMap ##363 ##3638 toSubbimodule ⇑c₁ ⇑c₂ ⇑castOrderEmbedding ⇑toTriangle ⇑toContinuousMapHom ##003 ##0017 ⇑↑f₁ ⇑↑f₂ ⇑↑f⁻¹ ¬mk leftAdjointOfNondegenerate leftAdjointOfStructuredArrow ⇑ofReal ##OfConeCompDiagram ⇑PicardLindelof ##CenterPow ##entialImageInclusion precomposeWhiskerLeftMap ##860 ##5539 apply₁ applyₗ toHomeomorphOfFiniteDimensional toStructuredArrowCompProj toStructuredArrowCompToUnder 509 ⇑sign forkOfKernelFork cramerMap embDomainRingHom ⇑ContinuousMapZero arrowCongrEquiv 214 21572 21316 21323 toCokleisli conjTransposeRingEquiv sol1 solidClosure tropEquiv tropOrderIso gradedHomologyFunctor iicInfHom iicsInfHom system ##415 cs₂✝ smoothNumbersᶜ hyxb ##merDedekind repeatTR isoMk₀ isoMk₁ isoMk₂ isoMk₅ isoMk₄ isoMk₃ isoMkSucc ObjAsType completionHom completionSeparationQuotient 28461 ##308 ##305 ##309 fintype✝ fintype✝¹ fintypeToFinBoolAlgOp ↑E1 ##590 RightFraction₂ hasseDualIso piFinCastSucc IsAdicCauchy ##SndIso limitConeComp limitConeLift limitConeOfComp mapBifunctorMapObjDesc his✝ xᶜᶜ toZModLinearMap selfAdjointSubmodule ##OrderIsoIoo ##OrderIsoIccSup linearEquivOp linearEquivTuple linearEquivIsoModule ##545 natIsoLift 26113 26109 hndeg HasProjectiveResolution extendDomainHom anyTR homothetyHom all₂ allTR karoubiUniversal hsnfg fmono EmptyCollection LimitBicone ##AddSubgroupOfEmbedding hcomp1 restrictFunctorΓ ↑a✝² ##295539 homeoEval mkContinuousLinear mkContinuousOfExists toLieEquiv ##407 ⇑DFinsupp rightAdjointOfCostructuredArrow hnpq incidenceSetEquivNeighborSet trivialFiltration postcomposeComp postcomposeId postcomposeWhiskerLeftMap CentroidHomClass ##770 leftRegularTensorIso addMonoidHomOfMemClosureRangeCoe transferCenterPow 4031 4089 40899 36295539 hapos HasInjectiveResolution hxV₂ orderIsoMultiset orderIsoSubtype orderIsoColex orderIsoIccZeroCoe M✶✶ YonedaSheafCondition ¬evariance toModuleCatMonoidalFunctor toModuleCatBraidedFunctor IsSupportedOutside addSubgroupCongr v2✝ ##SmoothNumbers htriv noBotOrder ##AndBinary involuteEquiv hm₁✝ finTwoEquiv HasWidePushouts ManyOneReducible 2951 2947 2943 29963 29822 acceptsFrom mopAlgEquivOp mvPolynomialEquivMvPolynomial commonSection commonRetraction matrixEquiv v1✝ ⅟a₁ ⅟a₂ cs₁✝ relabelAux completeLatticeOfComplete preservesColimitNatIso ¬lm ##813 isEmptyEquiv ringEquivCauchy mr₁ ##Pretopology ##0625 ya₀ ⇑discreteEquiv ##SMulTopInner curriedAssociator addSubgroupOfEquivOfLe Hpv between monoidEndTo toSup✝ toSup✝¹ toWeakSpace compLinearMapₗ claim6 extensionOfMaxAdjoin Hbdd √↑v moduleCatHomologyIso 5143 51691 51003 60429 60184 60274 60433 60273 60827 ##561 ##562500 distribLattice toCostructuredArrowCocone toCostructuredArrowCompProj toCostructuredArrowCompToOver dotProductᵣ fastFib fastLegendreSym ##525 ##OfEpiZero hgbdd idem✝ idem✝¹ addUnitsCenterToCenter DartAdj hxa✝ ofMulActionSelfAs hpd5 orderEmbOfCard ofTensorProductInvOfPi upperCentralSeriesAux unitsSMulEquiv 61158 61162 cancelBaseChange surjective✝ surjective✝¹ compMeasurePreservingₗᵢ ofSubsingletonₗ ofSubsingletonₗᵢ isMinimal subtypePermOfFintype hVWU cyclesIsoKernel CircularPartialOrder ↥carrier comparisonN eq✝³ eq✝² hzbm ##CompColimIsoColimitCompColim ##CompColimIsoColimitCurryCompColim 34208 5749 57896 57069 57632 ##CompLimIsoLimitCurryCompLim ##CompLimIsoLimitCompLim directLimitLeft BfactorSetMem mkRingHomOfMulSelf liftAlternatingEquiv 24341 24334 24510 h⁻¹ᘁ lrb ofSeqClosedGraph nonUnitalRingHom nonUnitalSubalgebraOfNonUnital stdSimplexHomeomorphUnitInterval GaussianFourier ¬j✝ ##BiprodComparison liftToPathCategory multiplesAddHom opcyclesIsoCokernel wronskianBilin ¬length ins1 ins2 ins3 toSheafedSpaceHom mulEquivEnd functorOfMonoidHom functorialityUnit functorialityCounit diagramIsoPair diagramIsoParallelFamily toGradedObjectFunctor lxor ##EquivQuotSMulTopInner