Hom

📁 Source: Mathlib/Topology/VectorBundle/Hom.lean

Statistics

Metric	Count
Definitions Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, fiberBundle, topologicalSpaceTotalSpace, vectorPrebundle, continuousLinearMap, continuousLinearMapCoordChange, continuousLinearMap, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom, Hom	76
Theorems memTrivializationAtlas, vectorBundle, isLinear, continuousLinearMapCoordChange_apply, continuousLinearMap_apply, continuousLinearMap_symm_apply, continuousLinearMap_symm_apply', continuousOn_continuousLinearMapCoordChange, baseSet_continuousLinearMap, continuousLinearMap_apply, clm_bundle_apply, clm_bundle_apply₂, clm_apply_of_inCoordinates, clm_bundle_apply, clm_bundle_apply₂, clm_bundle_apply, clm_bundle_apply₂, clm_apply_of_inCoordinates, clm_bundle_apply, clm_bundle_apply₂, continuousAt_hom_bundle, continuousWithinAt_hom_bundle, hom_trivializationAt, hom_trivializationAt_apply, hom_trivializationAt_baseSet, hom_trivializationAt_source, hom_trivializationAt_target, inCoordinates_apply_eq₂	28
Total	104

AddCommGrpCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

AddCommMonCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

AddGrpCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

AddMagmaCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

AddMonCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

AddSemigrp

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

AlgCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

AlgebraicGeometry.LocallyRingedSpace

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

AlgebraicGeometry.PresheafedSpace

Definitions

Name	Category	Theorems
Hom 📖	CompData	1 math math: map_comp_c_app

AlgebraicGeometry.Scheme

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

AlgebraicGeometry.Scheme.Cover

Definitions

Name	Category	Theorems
Hom 📖	CompOp	—

AlgebraicGeometry.Scheme.Modules

Definitions

Name	Category	Theorems
Hom 📖	CompOp	—

BddDistLat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

BddLat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

BddOrd

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

BialgCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	1 math math: Hom.toBialgHom_injective

Bimod

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

Bipointed

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

BoolAlg

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

BoolRing

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

Bundle.ContinuousLinearMap

Definitions

Name	Category	Theorems
fiberBundle 📖	CompOp	19 math math: Bundle.ContMDiffRiemannianMetric.contMDiff, vectorBundle, Bundle.ContinuousRiemannianMetric.continuous, ContMDiffVectorBundle.continuousLinearMap, inCoordinates_apply_eq₂, mdifferentiableAt_hom_bundle, IsContMDiffRiemannianBundle.exists_contMDiff, IsContinuousRiemannianBundle.exists_continuous, contMDiffAt_hom_bundle, hom_trivializationAt, hom_trivializationAt_source, ContMDiffCovariantDerivativeOn.contMDiff, hom_chart, hom_trivializationAt_apply, hom_trivializationAt_baseSet, memTrivializationAtlas, mdifferentiableWithinAt_hom_bundle, hom_trivializationAt_target, contMDiffWithinAt_hom_bundle
topologicalSpaceTotalSpace 📖	CompOp	23 math math: Bundle.ContMDiffRiemannianMetric.contMDiff, vectorBundle, Bundle.ContinuousRiemannianMetric.continuous, ContMDiffVectorBundle.continuousLinearMap, inCoordinates_apply_eq₂, mdifferentiableAt_hom_bundle, IsContMDiffRiemannianBundle.exists_contMDiff, IsContinuousRiemannianBundle.exists_continuous, contMDiffAt_hom_bundle, hom_trivializationAt, Bundle.Trivialization.baseSet_continuousLinearMap, Bundle.Trivialization.continuousLinearMap_apply, hom_trivializationAt_source, ContMDiffCovariantDerivativeOn.contMDiff, continuousAt_hom_bundle, continuousWithinAt_hom_bundle, hom_chart, hom_trivializationAt_apply, hom_trivializationAt_baseSet, memTrivializationAtlas, mdifferentiableWithinAt_hom_bundle, hom_trivializationAt_target, contMDiffWithinAt_hom_bundle
vectorPrebundle 📖	CompOp	1 math math: vectorPrebundle.isContMDiff

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
memTrivializationAtlas 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	MemTrivializationAtlas ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup AddCommGroup.toAddCommMonoid topologicalSpaceTotalSpace fiberBundle Bundle.Trivialization.continuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup
vectorBundle 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	VectorBundle ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule AddCommGroup.toAddCommMonoid ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction MonoidWithZero.toMonoid Semiring.toMonoidWithZero SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid Module.toDistribMulAction ContinuousSMul.continuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing SMulZeroClass.toSMul NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid DistribSMul.toSMulZeroClass AddMonoid.toAddZeroClass DistribMulAction.toDistribSMul ContinuousLinearMap.toNormedAddCommGroup ContinuousLinearMap.toNormedSpace CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing topologicalSpaceTotalSpace ContinuousLinearMap.topologicalSpace fiberBundle	—	VectorPrebundle.toVectorBundle IsTopologicalAddGroup.toContinuousAdd smulCommClass_self ContinuousSMul.continuousConstSMul

Bundle.Pretrivialization

Definitions

Name	Category	Theorems
continuousLinearMap 📖	CompOp	5 math math: continuousLinearMap_apply, continuousLinearMap.isLinear, continuousLinearMap_symm_apply, continuousLinearMap_symm_apply', continuousLinearMapCoordChange_apply
continuousLinearMapCoordChange 📖	CompOp	4 math math: continuousOn_continuousLinearMapCoordChange, contMDiffOn_continuousLinearMapCoordChange, mdifferentiableOn_continuousLinearMapCoordChange, continuousLinearMapCoordChange_apply

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuousLinearMapCoordChange_apply 📖	mathematical	Set Set.instMembership Set.instInter Bundle.Trivialization.baseSet Bundle.TotalSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup Bundle.TotalSpace.proj	DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul ContinuousLinearMap.funLike continuousLinearMapCoordChange toFun' Bundle.TotalSpace AddCommGroup.toAddCommMonoid Bundle.TotalSpace.proj continuousLinearMap symm ContinuousLinearMap.zero	—	ContinuousLinearMap.ext SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd smulCommClass_self UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul RingHomCompTriple.right_ids RingHomCompTriple.ids ContinuousLinearMap.comp.congr_simp continuousLinearMap_symm_apply' RingHomInvPair.ids Bundle.Trivialization.coordChangeL_apply Bundle.Trivialization.coe_linearMapAt_of_mem
continuousLinearMap_apply 📖	mathematical	—	toFun' ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.TotalSpace AddCommGroup.toAddCommMonoid ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup Bundle.TotalSpace.proj continuousLinearMap ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.right_ids Bundle.Trivialization.continuousLinearMapAt RingHomCompTriple.ids Bundle.TotalSpace.snd Bundle.Trivialization.symmL	—	SeminormedAddCommGroup.toIsTopologicalAddGroup
continuousLinearMap_symm_apply 📖	mathematical	—	PartialEquiv.toFun ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.TotalSpace AddCommGroup.toAddCommMonoid PartialEquiv.symm toPartialEquiv ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup Bundle.TotalSpace.proj continuousLinearMap ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.right_ids Bundle.Trivialization.symmL RingHomCompTriple.ids Bundle.Trivialization.continuousLinearMapAt	—	SeminormedAddCommGroup.toIsTopologicalAddGroup
continuousLinearMap_symm_apply' 📖	mathematical	Set Set.instMembership Set.instInter Bundle.Trivialization.baseSet Bundle.TotalSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup Bundle.TotalSpace.proj	symm ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule AddCommGroup.toAddCommMonoid ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.zero continuousLinearMap ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.right_ids Bundle.Trivialization.symmL RingHomCompTriple.ids Bundle.Trivialization.continuousLinearMapAt	—	SeminormedAddCommGroup.toIsTopologicalAddGroup RingHomCompTriple.right_ids RingHomCompTriple.ids symm_coe_proj symm_apply
continuousOn_continuousLinearMapCoordChange 📖	mathematical	—	ContinuousOn ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul ContinuousLinearMap.addCommGroup NormedRing.toRing NormedCommRing.toNormedRing ContinuousLinearMap.topologicalAddGroup continuousLinearMapCoordChange trivialization_linear AddCommGroup.toAddCommMonoid Set Set.instInter Bundle.Trivialization.baseSet Bundle.TotalSpace Bundle.TotalSpace.proj	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd smulCommClass_self UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul ContinuousLinearMap.topologicalAddGroup ContinuousLinearMap.smulCommClass ContinuousLinearMap.continuousConstSMul RingHomCompTriple.right_ids RingHomIsometric.ids ContinuousLinearMap.continuous RingHomCompTriple.ids RingHomInvPair.ids trivialization_linear continuousOn_coordChange ContinuousOn.congr ContinuousOn.clm_comp Continuous.comp_continuousOn ContinuousOn.mono ContinuousLinearMap.ext

Bundle.Pretrivialization.continuousLinearMap

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
isLinear 📖	mathematical	ContinuousAdd AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup AddCommGroup.toAddCommMonoid ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	Bundle.Pretrivialization.IsLinear ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule AddCommGroup.toAddCommMonoid ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup ContinuousSMul.continuousConstSMul Bundle.Pretrivialization.continuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd smulCommClass_self UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul ContinuousSMul.continuousConstSMul ContinuousLinearMap.comp.congr_simp ContinuousLinearMap.add_comp ContinuousLinearMap.comp_add ContinuousLinearMap.comp_smulₛₗ

Bundle.Trivialization

Definitions

Name	Category	Theorems
continuousLinearMap 📖	CompOp	4 math math: hom_trivializationAt, baseSet_continuousLinearMap, continuousLinearMap_apply, Bundle.ContinuousLinearMap.memTrivializationAtlas

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
baseSet_continuousLinearMap 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	baseSet ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.TotalSpace AddCommGroup.toAddCommMonoid ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace Bundle.TotalSpace.proj continuousLinearMap Set Set.instInter	—	SeminormedAddCommGroup.toIsTopologicalAddGroup
continuousLinearMap_apply 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	toFun' ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.TotalSpace AddCommGroup.toAddCommMonoid ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup Bundle.TotalSpace.proj Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace continuousLinearMap ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.right_ids continuousLinearMapAt trivialization_linear RingHomCompTriple.ids Bundle.TotalSpace.snd symmL	—	SeminormedAddCommGroup.toIsTopologicalAddGroup

CoalgCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	1 math math: Hom.toCoalgHom_injective

CommAlgCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

CommBialgCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

CommGrpCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

CommMonCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

CommRingCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

CommSemiRingCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

Continuous

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
clm_bundle_apply 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing Continuous Bundle.TotalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace RingHomIsometric.ids Bundle.TotalSpace.mk'	Continuous Bundle.TotalSpace Bundle.TotalSpace.mk' DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike	—	RingHomIsometric.ids ContinuousOn.clm_bundle_apply
clm_bundle_apply₂ 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing Continuous Bundle.TotalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul ContinuousSMul.continuousConstSMul Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace ContinuousLinearMap.toNormedAddCommGroup RingHomIsometric.ids ContinuousLinearMap.toNormedSpace ContinuousLinearMap.addCommGroup NormedRing.toRing NormedCommRing.toNormedRing Bundle.ContinuousLinearMap.fiberBundle Bundle.ContinuousLinearMap.vectorBundle ContinuousLinearMap.topologicalAddGroup ContinuousLinearMap.continuousSMul RingHomSurjective.ids Bundle.TotalSpace.mk'	Continuous Bundle.TotalSpace Bundle.TotalSpace.mk' DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike ContinuousLinearMap.topologicalSpace ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing ContinuousSMul.continuousConstSMul UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero	—	IsTopologicalAddGroup.toContinuousAdd smulCommClass_self ContinuousSMul.continuousConstSMul SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul RingHomIsometric.ids Bundle.ContinuousLinearMap.vectorBundle ContinuousLinearMap.topologicalAddGroup ContinuousLinearMap.continuousSMul RingHomSurjective.ids ContinuousOn.clm_bundle_apply₂

ContinuousAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
clm_apply_of_inCoordinates 📖	mathematical	ContinuousAt ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.inCoordinates AddCommGroup.toAddCommMonoid Bundle.TotalSpace	ContinuousAt Bundle.TotalSpace DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike	—	SeminormedAddCommGroup.toIsTopologicalAddGroup continuousWithinAt_univ ContinuousWithinAt.clm_apply_of_inCoordinates
clm_bundle_apply 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing ContinuousAt Bundle.TotalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace RingHomIsometric.ids Bundle.TotalSpace.mk'	ContinuousAt Bundle.TotalSpace Bundle.TotalSpace.mk' DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike	—	RingHomIsometric.ids ContinuousWithinAt.clm_bundle_apply
clm_bundle_apply₂ 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing ContinuousAt Bundle.TotalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul ContinuousSMul.continuousConstSMul Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace ContinuousLinearMap.toNormedAddCommGroup RingHomIsometric.ids ContinuousLinearMap.toNormedSpace ContinuousLinearMap.addCommGroup NormedRing.toRing NormedCommRing.toNormedRing Bundle.ContinuousLinearMap.fiberBundle Bundle.ContinuousLinearMap.vectorBundle ContinuousLinearMap.topologicalAddGroup ContinuousLinearMap.continuousSMul RingHomSurjective.ids Bundle.TotalSpace.mk'	ContinuousAt Bundle.TotalSpace Bundle.TotalSpace.mk' DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike ContinuousLinearMap.topologicalSpace ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing ContinuousSMul.continuousConstSMul UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero	—	IsTopologicalAddGroup.toContinuousAdd smulCommClass_self ContinuousSMul.continuousConstSMul SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul RingHomIsometric.ids Bundle.ContinuousLinearMap.vectorBundle ContinuousLinearMap.topologicalAddGroup ContinuousLinearMap.continuousSMul RingHomSurjective.ids clm_bundle_apply

ContinuousOn

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
clm_bundle_apply 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing ContinuousOn Bundle.TotalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace RingHomIsometric.ids Bundle.TotalSpace.mk'	ContinuousOn Bundle.TotalSpace Bundle.TotalSpace.mk' DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike	—	RingHomIsometric.ids ContinuousWithinAt.clm_bundle_apply
clm_bundle_apply₂ 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing ContinuousOn Bundle.TotalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul ContinuousSMul.continuousConstSMul Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace ContinuousLinearMap.toNormedAddCommGroup RingHomIsometric.ids ContinuousLinearMap.toNormedSpace ContinuousLinearMap.addCommGroup NormedRing.toRing NormedCommRing.toNormedRing Bundle.ContinuousLinearMap.fiberBundle Bundle.ContinuousLinearMap.vectorBundle ContinuousLinearMap.topologicalAddGroup ContinuousLinearMap.continuousSMul RingHomSurjective.ids Bundle.TotalSpace.mk'	ContinuousOn Bundle.TotalSpace Bundle.TotalSpace.mk' DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike ContinuousLinearMap.topologicalSpace ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing ContinuousSMul.continuousConstSMul UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero	—	IsTopologicalAddGroup.toContinuousAdd smulCommClass_self ContinuousSMul.continuousConstSMul SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul RingHomIsometric.ids Bundle.ContinuousLinearMap.vectorBundle ContinuousLinearMap.topologicalAddGroup ContinuousLinearMap.continuousSMul RingHomSurjective.ids ContinuousWithinAt.clm_bundle_apply₂

ContinuousWithinAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
clm_apply_of_inCoordinates 📖	mathematical	ContinuousWithinAt ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.inCoordinates AddCommGroup.toAddCommMonoid Bundle.TotalSpace	ContinuousWithinAt Bundle.TotalSpace DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike	—	SeminormedAddCommGroup.toIsTopologicalAddGroup continuousWithinAt_insert_self FiberBundle.continuousWithinAt_totalSpace congr_of_eventuallyEq_of_mem clm_apply IsOpen.mem_nhds Bundle.Trivialization.open_baseSet FiberBundle.mem_baseSet_trivializationAt' Filter.mp_mem Filter.univ_mem' RingHomCompTriple.right_ids RingHomInvPair.ids trivialization_linear instMemTrivializationAtlasTrivializationAt RingHomCompTriple.ids ContinuousLinearMap.inCoordinates_eq Set.mem_insert
clm_bundle_apply 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing ContinuousWithinAt Bundle.TotalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace RingHomIsometric.ids Bundle.TotalSpace.mk'	ContinuousWithinAt Bundle.TotalSpace Bundle.TotalSpace.mk' DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike	—	RingHomIsometric.ids clm_apply_of_inCoordinates SeminormedAddCommGroup.toIsTopologicalAddGroup
clm_bundle_apply₂ 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing ContinuousWithinAt Bundle.TotalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul ContinuousSMul.continuousConstSMul Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace ContinuousLinearMap.toNormedAddCommGroup RingHomIsometric.ids ContinuousLinearMap.toNormedSpace ContinuousLinearMap.addCommGroup NormedRing.toRing NormedCommRing.toNormedRing Bundle.ContinuousLinearMap.fiberBundle Bundle.ContinuousLinearMap.vectorBundle ContinuousLinearMap.topologicalAddGroup ContinuousLinearMap.continuousSMul RingHomSurjective.ids Bundle.TotalSpace.mk'	ContinuousWithinAt Bundle.TotalSpace Bundle.TotalSpace.mk' DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike ContinuousLinearMap.topologicalSpace ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup ContinuousLinearMap.module smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing ContinuousSMul.continuousConstSMul UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero	—	IsTopologicalAddGroup.toContinuousAdd smulCommClass_self ContinuousSMul.continuousConstSMul SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul RingHomIsometric.ids Bundle.ContinuousLinearMap.vectorBundle ContinuousLinearMap.topologicalAddGroup ContinuousLinearMap.continuousSMul RingHomSurjective.ids clm_bundle_apply

DistLat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

FinBddDistLat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

FirstOrder.Language

Definitions

Name	Category	Theorems
Hom 📖	CompData	37 math math: Embedding.ofInjective_toFun, Hom.domRestrict_toFun, Substructure.coe_comap, Hom.ext_iff, Function.emptyHom_toFun, Hom.instStrongHomClassOfIsAlgebraic, Hom.mem_range, Hom.mem_range_self, Hom.id_apply, Embedding.toHom_injective, Hom.map_fun, Hom.mem_eqLocus, Substructure.coe_map, Hom.comp_apply, Embedding.coe_toHom, Hom.toFun_eq_coe, Embedding.toHom_comp_injective, Embedding.coeFn_ofInjective, Hom.map_rel, Hom.range_coe, Equiv.coe_toHom, Hom.range_eq_top, HomClass.toHom_toFun, Substructure.map_closure, Hom.map_constants, ElementaryEmbedding.coe_toHom, Structure.FG.countable_hom, Hom.homClass, Hom.eqOn_closure, Substructure.mem_map_of_mem, Hom.comp_codRestrict, Substructure.mem_map, Substructure.mem_comap, Structure.FG.instCountable_hom, Hom.codRestrict_toFun_coe, Substructure.closure_image, Substructure.apply_coe_mem_map

FreeSimplexQuiver

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

Frm

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

GrpCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

HeytAlg

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

HomologicalComplex

Definitions

Name	Category	Theorems
Hom 📖	CompData	1 math math: hom_f_injective

HopfAlgCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	1 math math: Hom.toBialgHom_injective

Lat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

LieRinehartAlgebra

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

LinOrd

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

MagmaCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

ModuleCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	3 math math: hom_surjective, hom_bijective, hom_injective

MonCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

PartOrd

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

PartOrdEmb

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

Pointed

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

Preord

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

PresheafOfModules

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

ProfiniteAddGrp

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

ProfiniteGrp

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

QuadraticModuleCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	1 math math: Hom.toIsometry_injective

Quiver

Definitions

Name	Category	Theorems
Hom 📖	CompOp	5713 math math: TopologicalSpace.OpenNhds.coe_id, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv, CategoryTheory.ShortComplex.opcyclesMap_smul, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, CategoryTheory.Grp.Hom.hom_div, CategoryTheory.Abelian.SpectralObject.δ_eq_zero_of_isIso₂, CategoryTheory.Limits.Fork.IsLimit.homIso_natural, CategoryTheory.Adjunction.adjunctionOfEquivLeft_counit_app, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, CategoryTheory.Pseudofunctor.mapComp'_naturality_1_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, CategoryTheory.Join.pseudofunctorLeft_mapId_inv_toNatTrans_app, CategoryTheory.ShortComplex.toCycles_comp_homologyπ, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_assoc, CategoryTheory.Functor.functorHomEquiv_apply_app, CategoryTheory.Pseudofunctor.DescentData.isEquivalence_toDescentData_of_sieve_le, CategoryTheory.Bicategory.prod_whiskerLeft_snd, CategoryTheory.Functor.FullyFaithful.homNatIsoMaxRight_inv_app, CategoryTheory.MorphismProperty.exists_isPushout_of_isFiltered, CategoryTheory.Abelian.SpectralObject.H_map_twoδ₂Toδ₁_toCycles_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_skyscraperPresheafHomEquiv_symm, CommRingCat.HomTopology.isEmbedding_precomp_of_surjective, CategoryTheory.Functor.map_homCongr, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, CategoryTheory.ShortComplex.toCycles_comp_homologyπ_assoc, ModuleCat.hom_zero, CategoryTheory.uliftCoyonedaEquiv_apply, CategoryTheory.Limits.eq_zero_of_mono_cokernel, CategoryTheory.Limits.zero_of_from_zero, CategoryTheory.TwoSquare.equivNatTrans_symm_apply, CategoryTheory.ShortComplex.Homotopy.h₀_f_assoc, CommRingCat.HomTopology.isClosedEmbedding_precomp_of_surjective, Bicategory.Opposite.op2_associator, CategoryTheory.Presieve.ofArrows_eq_ofArrows_uncurry, CategoryTheory.Limits.cokernelBiproductιIso_hom, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, CategoryTheory.Types.instIsCorepresentableForgetTypeHom, LightCondensed.free_internallyProjective_iff_tensor_condition, CategoryTheory.Limits.limitConeOfUnique_cone_π, CategoryTheory.StrictPseudofunctorPreCore.map_id, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.Pseudofunctor.DescentData.ofObj_hom, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom, TopModuleCat.hom_zero, SemiNormedGrp.explicitCokernelDesc_norm_le, CategoryTheory.Bicategory.RightExtension.w_assoc, SemimoduleCat.Hom.hom₂_apply, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, CategoryTheory.Functor.natTransEquiv_apply_app, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_inv_app, CategoryTheory.uliftCoyonedaIsoCoyoneda_hom_app_app, CategoryTheory.Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv, CategoryTheory.LaxFunctor.mapComp'_whiskerRight_comp_mapComp', CategoryTheory.coyonedaEquiv_symm_app_apply, CategoryTheory.Presheaf.instIsLocallySurjectiveHomWhiskerRightOppositeForget, CategoryTheory.Oplax.StrongTrans.Modification.vcomp_app, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, CategoryTheory.ComposableArrows.isoMk₁_hom_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_adj, CategoryTheory.ObjectProperty.isoModSerre_zero_iff, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerLeft, TopCat.PrelocalPredicate.res, CategoryTheory.PreGaloisCategory.mulAction_def, CategoryTheory.Pseudofunctor.map₂_associator_assoc, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionRight_unop, CategoryTheory.ShortComplex.SnakeInput.w₀₂_assoc, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm, TopologicalSpace.Opens.id_apply, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι, CategoryTheory.preadditiveCoyonedaObj_map, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app, CategoryTheory.Functor.homObjEquiv_apply_app, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three_assoc, CategoryTheory.Limits.Bicone.π_of_isColimit, AlgebraicTopology.DoldKan.PInfty_f_add_QInfty_f, CategoryTheory.CatEnrichedOrdinary.id_hComp_heq, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.Limits.inr_of_isLimit, CategoryTheory.sum_whiskerRight, CategoryTheory.LaxFunctor.map₂_associator_assoc, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.Limits.coprod.inl_snd, CategoryTheory.ShortComplex.Homotopy.refl_h₀, LightProfinite.proj_comp_transitionMap, HomologicalComplex.dFrom_comp_xNextIsoSelf, CategoryTheory.Preadditive.IsIso.comp_left_eq_zero, CochainComplex.HomComplex.Cochain.fromSingleMk_neg, CategoryTheory.Presieve.uncurry_bind, CategoryTheory.LaxFunctor.whiskerLeft_mapComp'_comp_mapComp'_assoc, CategoryTheory.ShortComplex.homologyMap_smul, CategoryTheory.Pseudofunctor.DescentData'.comm, CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT_assoc, CategoryTheory.evaluationLeftAdjoint_map_app, CategoryTheory.opHom_apply, CategoryTheory.NatTrans.prod'_app_snd, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τl, CategoryTheory.ShortComplex.hasHomology_of_zeros, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_assoc, CategoryTheory.Limits.kernelIsoOfEq_trans, CategoryTheory.Arrow.equivSigma_symm_apply_left, CategoryTheory.Preadditive.hasKernel_of_hasEqualizer, CategoryTheory.Lax.LaxTrans.comp_naturality, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_snd, CategoryTheory.NonPreadditiveAbelian.neg_sub', CategoryTheory.conjugateEquiv_iso, CategoryTheory.Cat.Hom₂.comp_app, CategoryTheory.Presieve.shrinkFunctorHomEquiv_apply_coe, CategoryTheory.ShortComplex.Homotopy.comm₁, CategoryTheory.ShortComplex.HomologyData.ofIso_right_p, CategoryTheory.Bicategory.Comonad.comul_assoc_flip, HomotopyCategory.quotient_map_out_comp_out, Mathlib.Tactic.Bicategory.evalWhiskerLeft_nil, CategoryTheory.ShortComplex.Homotopy.comp_h₃, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, CategoryTheory.Join.mapPairId_hom_app, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafAdjunction_homEquiv_symm_apply, CategoryTheory.Sheaf.instIsLocallySurjectiveHomToImage, CategoryTheory.PreGaloisCategory.action_ext_of_isGalois, TopCat.presheafToType_map, CategoryTheory.linearCoyoneda_map_app, CategoryTheory.linearCoyoneda_obj_obj_carrier, CategoryTheory.Lax.OplaxTrans.Modification.id_app, CategoryTheory.Limits.biprod.lift_eq, CategoryTheory.ShortComplex.RightHomologyData.ι_g', SSet.RelativeMorphism.botEquiv_symm_apply_map, CategoryTheory.OplaxFunctor.id_mapComp, DerivedCategory.right_fac, AlgebraicGeometry.Scheme.Cover.LocallyDirected.directed, Rep.MonoidalClosed.linearHomEquiv_symm_hom, CategoryTheory.Pseudofunctor.isEquivalence_toDescentDataAsCoalgebra_iff_isEquivalence_comonadComparison, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_comp, CategoryTheory.Sieve.mem_functorPushforward_iff_of_full, CategoryTheory.Adjunction.comp_map_bijective_iff, CategoryTheory.Iso.eHomCongr_inv_comp_assoc, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_map, CochainComplex.HomComplex.Cocycle.fromSingleMk_add, CategoryTheory.AddMon.hom_injective, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_assoc, CategoryTheory.Join.mapWhiskerLeft_app, CategoryTheory.ObjectProperty.SerreClassLocalization.map_eq_zero_iff, HomologicalComplex.double_d_eq_zero₀, Action.neg_hom, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.ComposableArrows.IsComplex.zero'_assoc, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_one, CategoryTheory.Abelian.SpectralObject.opcyclesMap_threeδ₂Toδ₁_opcyclesToE_assoc, CategoryTheory.Abelian.LeftResolution.karoubi.F_obj_p, CategoryTheory.Linear.instMonoHSMulHomOfInvertible, HomologicalComplex.mapBifunctor₁₂.d_eq, CategoryTheory.Localization.Preadditive.homEquiv_symm_apply, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyData_i, CategoryTheory.Comma.opFunctor_obj, CategoryTheory.ReflQuiv.adj_homEquiv, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, CategoryTheory.Bicategory.eqToHomTransIso_refl_left, AlgebraicTopology.DoldKan.σ_comp_PInfty_assoc, CategoryTheory.StrictlyUnitaryLaxFunctor.id_map₂, SimplicialObject.Splitting.IndexSet.epiComp_fst, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, Bicategory.Opposite.op2_associator_inv, HomologicalComplex.dFrom_eq_zero, CategoryTheory.Limits.zero_of_epi_comp, HomologicalComplex.alternatingConst_iCycles_odd_comp_assoc, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, CategoryTheory.Bicategory.Pith.inclusion_mapComp, LightCondensed.ihomPoints_apply, TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing_types, CategoryTheory.shrinkYonedaEquiv_comp, CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_hom, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection', CategoryTheory.ShortComplex.homologyMap_add, CategoryTheory.Grp.Hom.hom_hom_zpow, AlgebraicTopology.NormalizedMooreComplex.obj_d, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, CategoryTheory.Limits.cokernel.map_zero, CategoryTheory.BicartesianSq.of_is_biproduct₁, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_hom_iso, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀, CategoryTheory.Pseudofunctor.isEquivalence_toDescentData, CategoryTheory.Pseudofunctor.DescentData'.comp_pullHom', CategoryTheory.sum_tensor, CategoryTheory.Bicategory.conjugateEquiv_whiskerRight, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality, Rep.ofHom_sub, HomotopicalAlgebra.CofibrantObject.homRel_equivalence_of_isFibrant_tgt, CategoryTheory.CategoryOfElements.map_snd, CategoryTheory.Bicategory.LeftLift.whiskering_map, Action.sum_hom, CategoryTheory.NonPreadditiveAbelian.diag_σ, CategoryTheory.iterated_mateEquiv_conjugateEquiv, CategoryTheory.Bicategory.leftUnitor_inv_naturality_assoc, CategoryTheory.Limits.monoFactorisationZero_I, CategoryTheory.Limits.terminal.subsingleton_to, CategoryTheory.ShortComplex.leftHomologyMap'_sub, CategoryTheory.Limits.biprod.inl_snd_assoc, SimplicialObject.Splitting.IndexSet.id_fst, CategoryTheory.Pretriangulated.Triangle.coyoneda_exact₂, CategoryTheory.ObjectProperty.exists_epiModSerre_comp_eq_zero_iff, CategoryTheory.Lax.StrongTrans.vComp_naturality_hom, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.Sieve.functor_obj, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_map_left_left, CategoryTheory.Limits.ColimitPresentation.Total.exists_hom_of_hom, PresheafOfModules.add_app, CategoryTheory.prod_Hom, CategoryTheory.IsPushout.of_is_bilimit', starEquivCostar_symm_apply_fst, CategoryTheory.ShortComplex.Homotopy.sub_h₀, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection, CategoryTheory.Bicategory.whiskerLeft_inv_hom, CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_hom, CategoryTheory.FreeBicategory.lift_mapId, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, TopCat.Presheaf.coveringOfPresieve.iSup_eq_of_mem_grothendieck, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_leftUnitor, SSet.Subcomplex.mem_ofSimplex_obj_iff, CategoryTheory.ShortComplex.homologyMap_zero, CategoryTheory.Bicategory.Adj.associator_inv_τr, CategoryTheory.Bicategory.Prod.sectL_mapId_inv, CategoryTheory.Abelian.SpectralObject.zero₂_assoc, CategoryTheory.Limits.HasColimitOfHasCoproductsOfHasCoequalizers.buildColimit_pt, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, CategoryTheory.ExponentiableMorphism.homEquiv_symm_apply_eq, groupHomology.map₁_one, CochainComplex.HomComplex.Cocycle.equivHom_symm_apply, CategoryTheory.Functor.coe_mapLinearMap, AddCommGrpCat.hom_add, CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_app_app, CategoryTheory.Functor.eqvGen_colimitTypeRel_iff_of_isFiltered, groupCohomology.d₀₁_comp_d₁₂, CategoryTheory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.Functor.map_mul, CategoryTheory.isCoseparator_iff_mono, prevD_comp_left, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hg', ModuleCat.freeHomEquiv_apply, CategoryTheory.ObjectProperty.exists_comp_isoModSerre_eq_zero_iff, CategoryTheory.Idempotents.neg_def, CategoryTheory.Bicategory.whiskerRight_comp_assoc, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃_assoc, CategoryTheory.Bicategory.Prod.snd_map, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_assoc, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv_symm, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom, CategoryTheory.Limits.Multicofork.ofπ_ι_app, CategoryTheory.Pseudofunctor.DescentData'.pullHom'_eq_pullHom_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.neg_φH, CategoryTheory.Bicategory.InducedBicategory.bicategory_associator_inv_hom, CategoryTheory.Abelian.Pseudoelement.pseudoZero_def, CategoryTheory.Bicategory.LeftExtension.w_assoc, TopCat.coe_of_of, CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, CategoryTheory.ShortComplex.mono_homologyMap_iff_up_to_refinements, CategoryTheory.instHasFunctorialSurjectiveInjectiveFactorizationTypeHom, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, CategoryTheory.CatEnriched.id_hComp, CategoryTheory.Pseudofunctor.DescentData'.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpPullbackHom, CategoryTheory.AddMonObj.ofRepresentableBy_add, CategoryTheory.OplaxFunctor.map₂_associator, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight_assoc, CategoryTheory.Bicategory.Adj.rIso_inv, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, CategoryTheory.Bicategory.mateEquiv_comp_id_right, CategoryTheory.CatCenter.app_sub, CategoryTheory.Pseudofunctor.StrongTrans.homCategory_comp_as_app, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π_assoc, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.Bicategory.inv_hom_whiskerRight_assoc, CategoryTheory.Bicategory.whisker_exchange, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_inv, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_eq_iff', CategoryTheory.Bicategory.inv_hom_whiskerRight, TopModuleCat.hom_zero_apply, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_left_symm, HomologicalComplex.extend.d_comp_eq_zero_iff, CategoryTheory.finrank_hom_simple_simple_le_one, CategoryTheory.Functor.hom_map, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, CategoryTheory.Functor.uliftCoyonedaCoreprXIso_hom_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hg, CategoryTheory.eHomEquiv_id, CategoryTheory.Cat.associator_hom_app, CategoryTheory.Quiv.homEquivOfIso_symm_apply, CategoryTheory.Limits.kernelBiprodSndIso_hom, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_obj, CochainComplex.mappingCone.inr_f_fst_v, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.counit, CategoryTheory.ShortComplex.Homotopy.smul_h₁, CategoryTheory.Bicategory.pentagon_inv, CategoryTheory.ShortComplex.zero_assoc, CategoryTheory.Limits.colimit_ι_zero_cokernel_desc_assoc, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, AddMonCat.zeroHom_apply, CategoryTheory.MorphismProperty.LeftFraction₂.map_add, groupHomology.mapShortComplexH1_zero, CategoryTheory.Bicategory.associatorNatIsoLeftCat_hom_toNatTrans_app, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_inverse_obj_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app_assoc, CategoryTheory.ShortComplex.RightHomologyData.wp, Mathlib.Tactic.Bicategory.StructuralOfExpr_bicategoricalComp, CategoryTheory.Limits.coneUnopOfCoconeEquiv_counitIso, SimplicialObject.Splitting.IndexSet.fac_pull_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Bicategory.Adjunction.homEquiv₂_symm_apply, CategoryTheory.ObjectProperty.prop_of_isLimit_kernelFork, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π, CategoryTheory.Sieve.pushforward_apply, CategoryTheory.Bicategory.InducedBicategory.Hom.category_id_hom, CategoryTheory.LaxFunctor.comp_mapId, CategoryTheory.ShiftedHom.mk₀_zero, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_assoc, CategoryTheory.down_comp_assoc, CategoryTheory.Pseudofunctor.map₂_left_unitor_assoc, HomologicalComplex.homotopyCofiber.inrX_fstX_assoc, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_φ, CategoryTheory.GrothendieckTopology.Cover.Arrow.ext_iff, CategoryTheory.ShortComplex.leftHomologyMap_sub, CategoryTheory.Bicategory.Pith.comp_of, CochainComplex.HomComplex.Cochain.fromSingleEquiv_fromSingleMk, CategoryTheory.Adjunction.homEquiv_naturality_left_square, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, LightCondensed.ihomPoints_symm_comp, CategoryTheory.Lax.LaxTrans.whiskerLeft_as_app, CategoryTheory.NonPreadditiveAbelian.add_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.yoneda_map_app, CategoryTheory.OplaxFunctor.map₂_associator_app, CategoryTheory.Oplax.LaxTrans.vComp_naturality_id, CategoryTheory.ShortComplex.RightHomologyData.wp_assoc, groupHomology.mapShortComplexH2_zero, CategoryTheory.StrictPseudofunctorCore.map₂_left_unitor, CategoryTheory.Bicategory.Lan.existsUnique, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_id_fiber, AlgebraicGeometry.Spec.map_surjective, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_whiskerRight_as_app, CategoryTheory.Oplax.OplaxTrans.Modification.vcomp_app, CategoryTheory.Bicategory.eqToHomTransIso_refl_refl, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀', CategoryTheory.Limits.biproduct.ι_π_assoc, CategoryTheory.curryingIso_hom_toFunctor_obj_map, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition', CategoryTheory.FreeBicategory.mk_left_unitor_inv, AlgebraicGeometry.Scheme.SpecToEquivOfField_eq_iff, CategoryTheory.Limits.Cone.equiv_inv_pt, CategoryTheory.Preregular.exists_fac, CategoryTheory.MorphismProperty.exists_hom_of_isFinitelyPresentable, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_assoc, SSet.OneTruncation₂.nerveHomEquiv_id, CategoryTheory.Functor.Monoidal.RepresentableBy.tensorObj_homEquiv, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_left_assoc, AlgebraicGeometry.isCompact_iff_exists, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.Bicategory.RightLift.w_assoc, CategoryTheory.MorphismProperty.RightFraction.cases, CategoryTheory.Comon.uniqueHomToTrivial_default_hom, CategoryTheory.Bicategory.mateEquiv_vcomp, CategoryTheory.Pseudofunctor.StrongTrans.comp_app, CategoryTheory.InducedCategory.homLinearEquiv_apply, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom_assoc, CategoryTheory.yonedaCommGrpGrpObj_map, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.ShrinkHoms.id_def, CategoryTheory.ShortComplex.LeftHomologyData.ofZeros_f', AlgebraicGeometry.pointsPi_surjective_of_isAffine, CategoryTheory.Pseudofunctor.mapComp'_hom_comp_whiskerLeft_mapComp'_hom, CategoryTheory.conjugateEquiv_symm_id, Homotopy.mkInductiveAux₃, CategoryTheory.Subgroupoid.id_mem_of_tgt, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id_symm, AlgebraicTopology.DoldKan.PInfty_comp_QInfty, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_pullbackObjUnitToUnit, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_assoc, CochainComplex.IsKInjective.nonempty_homotopy_zero, CategoryTheory.nerve.functorOfNerveMap_map, CategoryTheory.Mon.hom_injective, CategoryTheory.Lax.LaxTrans.LaxFunctor.bicategory_rightUnitor_inv_as_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.Functor.prod'_μ_fst, homOfEq_heq, CategoryTheory.yonedaAddMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.Bicategory.Adj.comp_τl_assoc, CategoryTheory.StrictPseudofunctor.mk'_obj, CategoryTheory.ShortComplex.exact_iff_iCycles_pOpcycles_zero, CategoryTheory.Oplax.LaxTrans.homCategory_comp_as_app, CategoryTheory.Abelian.LeftResolution.chainComplexMap_zero, CategoryTheory.Oplax.OplaxTrans.StrongCore.naturality_hom, CategoryTheory.Bicategory.Adj.forget₁_mapId, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inl, CochainComplex.Lifting.comp_coe_cocyle₁'_v_eq_zero, CategoryTheory.Subobject.isPullback_aux, CategoryTheory.ShortComplex.exact_iff_kernel_ι_comp_cokernel_π_zero, CategoryTheory.Localization.liftNatTrans_add, CategoryTheory.Subgroupoid.mul_mem_cancel_right, CategoryTheory.Abelian.Ext.mk₀_addEquiv₀_apply, CategoryTheory.MonoidalCategory.externalProductBifunctor_map_app, CategoryTheory.Adjunction.adjunctionOfEquivRight_counit_app, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_obj_π, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id, SimplicialObject.Splitting.PInfty_comp_πSummand_id, CategoryTheory.Bicategory.postcomp₂_app_toFunctor_obj, LightCondSet.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Limits.IsZero.unique_to, CategoryTheory.ShortComplex.liftCycles_comp_homologyπ_eq_iff_up_to_refinements, CategoryTheory.SingleObj.id_as_one, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_assoc, SSet.horn₃₁.exists_desc, CategoryTheory.Functor.PreservesHomology.preservesKernels, CategoryTheory.LocallyDiscrete.id_as, CategoryTheory.Abelian.SpectralObject.δToCycles_πE, SSet.Subcomplex.range_eq_ofSimplex, CategoryTheory.shrinkYonedaMonObjObjEquiv_symm_comp, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.rightHomologyData_Q, CategoryTheory.Functor.FullyFaithful.homNatIsoMaxRight_hom_app_down, CategoryTheory.Oplax.OplaxTrans.homCategory_id_as_app, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, HomologicalComplex.dTo_eq_zero, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_f, CategoryTheory.ShortComplex.opcyclesMap_sub, CategoryTheory.NonPreadditiveAbelian.add_def, CategoryTheory.AddMonObj.add_eq_add, CategoryTheory.Bicategory.right_triangle_of_left_triangle, CategoryTheory.Lax.OplaxTrans.rightUnitor_inv_as_app, Opens.mayerVietorisSquare_X₃, AddMonCat.hom_zero, CategoryTheory.BicategoricalCoherence.left'_iso, DerivedCategory.HomologySequence.comp_δ, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_associator, CategoryTheory.ULiftHom.down_map, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_inv, CategoryTheory.ShortComplex.opcyclesMap'_sub, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, CategoryTheory.ShortComplex.RightHomologyMapData.neg_φQ, CategoryTheory.Functor.RepresentableBy.homEquiv_eq, CategoryTheory.Bicategory.LeftExtension.ofCompId_right, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_id, CategoryTheory.linearYoneda_obj_map, Path.length_ne_zero_iff_eq_comp, CategoryTheory.CostructuredArrow.IsUniversal.existsUnique, CategoryTheory.CountableCategory.countableHom, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_inv_app, PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.kf_w, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_hom, CommRingCat.HomTopology.instCompactSpaceHomOfIsTopologicalRingOfT1SpaceOfCarrier, CategoryTheory.OplaxFunctor.mapComp_naturality_right_assoc, CategoryTheory.prodOpEquiv_inverse_map, HomotopyCategory.isZero_quotient_obj_iff, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_apply, CategoryTheory.MorphismProperty.Comma.mapLeftEq_inv_app_right, CategoryTheory.Oplax.LaxTrans.naturality_naturality_assoc, CategoryTheory.CategoryOfElements.map_map_coe, SemiNormedGrp.hom_sub, CategoryTheory.Linear.comp_apply, CategoryTheory.ShortComplex.HasLeftHomology.of_zeros, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.DifferentialObject.d_squared_apply, CategoryTheory.Biproduct.column_nonzero_of_iso', CategoryTheory.Functor.homologySequence_comp_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom, RingHom.EssFiniteType.exists_eq_comp_ι_app_of_isColimit, CategoryTheory.CostructuredArrow.w_prod_fst, CategoryTheory.StrictPseudofunctor.id_mapComp_hom, AlgebraicGeometry.Spec.map_injective, CategoryTheory.Presheaf.functorToRepresentables_map, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, CategoryTheory.Linear.smulOfRingMorphism_smul_eq', CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, ModuleCat.Iso.homCongr_eq_arrowCongr, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm_assoc, CategoryTheory.Subobject.factorThru_eq_zero, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, TopologicalSpace.OpenNhds.comp_apply, CategoryTheory.finrank_hom_simple_simple_eq_one_iff, CochainComplex.homologyMap_homologyδOfTriangle_assoc, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_μ, CategoryTheory.Limits.MulticospanIndex.multicospan_map, CategoryTheory.Functor.FullyFaithful.homMulEquiv_apply, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_inv_hom, CategoryTheory.Subgroupoid.full_arrow_eq_iff, CategoryTheory.ShortComplex.leftHomologyMap'_neg, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Cat.Hom₂.eqToHom_toNatTrans, CategoryTheory.prodFunctorToFunctorProd_map, CategoryTheory.Cat.Hom₂.id_app, CategoryTheory.Adjunction.comp_homEquiv, CategoryTheory.Quotient.Linear.smul_eq, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app_assoc, CategoryTheory.coyonedaEvaluation_map_down, CategoryTheory.nerve.homEquiv_edgeMk_map_nerveMap, FunctorToFintypeCat.naturality, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_assoc, HomologicalComplex.mapBifunctor₂₃.d₂_eq, CochainComplex.HomComplex.Cocycle.fromSingleMk_surjective, CategoryTheory.Pseudofunctor.DescentData.pullFunctor_map_hom, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_map_base, CategoryTheory.prod_id_fst, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂, CategoryTheory.SimplicialThickening.compFunctor_obj, CategoryTheory.Limits.prod.inl_snd, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_neg_f, HomotopicalAlgebra.LeftHomotopyClass.whitehead, CategoryTheory.WithTerminal.map₂_app, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_inv_as_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, SimplexCategory.instFiniteHom, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_whiskerLeft_as_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_obj_str, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Limits.KernelFork.condition_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv, CategoryTheory.Functor.FullyFaithful.homEquiv_apply, CategoryTheory.Preadditive.sub_comp_assoc, CategoryTheory.Limits.zero_of_source_iso_zero, CategoryTheory.preadditiveYonedaObj_obj_carrier, LightCondensed.finYoneda_map, CategoryTheory.Limits.reflexivePair.mkNatIso_hom_app, CategoryTheory.Monad.algebraPreadditive_homGroup_sub_f, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_id, CategoryTheory.tensorRightHomEquiv_symm_naturality, AddCommGrpCat.hom_zero, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit'_π_apply, CategoryTheory.evaluationRightAdjoint_obj_map, CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_inv, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, CategoryTheory.ShortComplex.LeftHomologyData.f'_π_assoc, Rep.add_hom, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Types.instReflectsLimitsOfSizeForgetTypeHom, CategoryTheory.ShortComplex.RightHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork_φH, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, CategoryTheory.Cat.Hom.isoMk_hom, CochainComplex.IsKProjective.homotopyZero_def, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom_assoc, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, SSet.horn.yonedaEquiv_ι, AlgebraicGeometry.pointsPi_injective, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_naturality, HomologicalComplex.biprod_inl_snd_f_assoc, CategoryTheory.Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str, CategoryTheory.Join.isoMkFunctor_hom_app, CategoryTheory.Pseudofunctor.mapId'_inv_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂_homEquiv, CategoryTheory.conjugateEquiv_symm_comp_assoc, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, CategoryTheory.AddMonObj.zero_comp, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τr, CategoryTheory.Subfunctor.ofSection_eq_range, Homotopy.nullHomotopicMap_f_eq_zero, SemimoduleCat.Iso.homCongr_eq_arrowCongr, TopologicalSpace.Opens.comp_apply, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CategoryTheory.Bicategory.LeftLift.w_assoc, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_succ, HomologicalComplex.eq_liftCycles_homologyπ_up_to_refinements, HomologicalComplex₂.totalAux.d₂_eq, CategoryTheory.ShortComplex.cyclesMap_neg, CategoryTheory.Cat.Hom.toNatIso_hom, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_eq, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ_assoc, CategoryTheory.Abelian.LeftResolution.karoubi.F'_map_f, CochainComplex.mappingCone.d_snd_v, CategoryTheory.Preadditive.isColimitCoforkOfCokernelCofork_desc, CategoryTheory.Bicategory.whiskerRightIso_hom, CategoryTheory.Abelian.SpectralObject.δ_δ_assoc, CategoryTheory.Bicategory.associatorNatIsoLeft_inv_app, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_map, CategoryTheory.Functor.IsPreFibered.exists_isCartesian', CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, CategoryTheory.IsCofiltered.bowtie, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, CategoryTheory.ForgetEnrichment.equivFunctor_map, TopologicalSpace.OpenNhds.val_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, CategoryTheory.Limits.IsColimit.existsUnique, CategoryTheory.Equalizer.firstObjEqFamily_inv, CategoryTheory.Limits.prod.inr_fst_assoc, CategoryTheory.ObjectProperty.prop_of_isColimit_cokernelCofork, SheafOfModules.unitHomEquiv_symm_comp, CategoryTheory.MonoidalPreadditive.whiskerLeft_add, CategoryTheory.yonedaEquiv_apply, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, CategoryTheory.Lax.LaxTrans.associator_inv_as_app, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp, CategoryTheory.Bicategory.rightUnitor_inv_naturality, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app_assoc, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.Limits.biprod.inlCokernelCofork_π, CategoryTheory.ForgetEnrichment.equivInverse_map, CategoryTheory.Abelian.SpectralObject.Ψ_opcyclesMap, HomologicalComplex₂.d_f_comp_d_f, CategoryTheory.Limits.kernelForkBiproductToSubtype_cone, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_ε_unmop_unmop, CategoryTheory.MonoidalCategory.whiskerLeft_dite, CategoryTheory.Pseudofunctor.CoGrothendieck.instIsEquivalenceαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, SSet.yonedaEquiv_symm_zero, HomologicalComplex.add_f_apply, AlgebraicGeometry.isPullback_fiberToSpecResidueField_of_isPullback, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity, CategoryTheory.Functor.equivCatHom_symm_apply, HomotopicalAlgebra.bijective_leftHomotopyClassToHom_iff_bijective_rightHomotopyClassToHom, CategoryTheory.CatEnriched.id_hComp_id, CategoryTheory.Limits.kernel.zeroKernelFork_ι, HomologicalComplex.biprod_total_f, CategoryTheory.Adjunction.leftAdjointOplaxMonoidal_η, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_apply, CategoryTheory.InducedCategory.homEquiv_apply, CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str, CategoryTheory.Limits.KernelFork.IsLimit.isZero_of_mono, CategoryTheory.Bicategory.Adjunction.homEquiv₁_apply, CategoryTheory.StrictPseudofunctorCore.map₂_associator, Profinite.exists_lift_of_finite_of_mono_of_epi, CategoryTheory.Bicategory.Prod.swap_map₂, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_hom_app, AlgebraicGeometry.Scheme.exists_hom_isAffine_of_isLocalAtSource, AlgebraicGeometry.Scheme.Modules.Hom.zero_app, AlgebraicGeometry.tilde.map_sub, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.WithInitial.opEquiv_functor_map, CategoryTheory.LocallyDiscrete.comp_as, SemimoduleCat.hom_zsmul, CategoryTheory.tensorRightHomEquiv_whiskerLeft_comp_evaluation, CategoryTheory.Pseudofunctor.DescentData.isoMk_inv_hom, HomologicalComplex₂.d₁_eq_zero', CategoryTheory.Types.mem_jointlySurjectivePrecoverage_iff, Mathlib.Tactic.Bicategory.naturality_rightUnitor, CategoryTheory.Bicategory.Pith.whiskerRight_iso_inv, HomologicalComplex₂.D₁_D₁_assoc, TopologicalSpace.Opens.infLELeft_apply_mk, CategoryTheory.Cat.Hom₂.comp_app_assoc, CategoryTheory.Subgroupoid.le_iff, CategoryTheory.Functor.homologySequence_comp, CategoryTheory.prod.rightUnitor_map, CategoryTheory.congrArg_cast_hom_right, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.InjectiveResolution.of_def, FintypeCat.instFiniteHom, SemimoduleCat.hom_nsmul, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁, CategoryTheory.ComposableArrows.mk₅_surjective, CategoryTheory.Coyoneda.objOpOp_inv_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, SheafOfModules.freeHomEquiv_freeMap, CategoryTheory.Functor.prod'_δ_snd, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, Path.exists_mem_notMem_hom_path_path_of_notMem_mem, CategoryTheory.Iso.homCongr_trans, CategoryTheory.Bicategory.rightUnitor_inv_congr, CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists, CategoryTheory.Lax.LaxTrans.Modification.id_app, CategoryTheory.MorphismProperty.pullbackMap, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.GradedObject.zero_apply, CategoryTheory.IsPushout.zero_top, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_isColimit, CategoryTheory.Pseudofunctor.map₂_left_unitor, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_base, CategoryTheory.Bicategory.unitors_inv_equal, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, CategoryTheory.Bicategory.Pith.leftUnitor_inv_iso_hom, CategoryTheory.nonempty_hom_of_preconnected_groupoid, CochainComplex.HomComplex.Cochain.toSingleMk_neg, CategoryTheory.Presieve.shrinkFunctorHomEquiv_symm_apply_app, CategoryTheory.Bicategory.leftZigzagIso_symm, CategoryTheory.ShortComplex.homologyMap'_zero, CategoryTheory.CommSq.instHasLift, CategoryTheory.Preadditive.IsIso.comp_right_eq_zero, CategoryTheory.StrictPseudofunctor.mk''_mapId, CategoryTheory.Bicategory.associator_inv_naturality_middle, CategoryTheory.Limits.Sigma.ι_π_assoc, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyData_K, CategoryTheory.Bicategory.associator_naturality_right_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.Pseudofunctor.DescentData'.pullHom'_self', CategoryTheory.Presheaf.freeYonedaHomEquiv_comp, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight_assoc, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_mono₂, CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_isIso, CategoryTheory.Groupoid.vertexGroup.inv_eq_inv, CategoryTheory.Bicategory.prod_id_fst, CategoryTheory.Bicategory.triangle_assoc_comp_left, CategoryTheory.Limits.IsColimit.homIso_hom, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.Limits.kernel.condition_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, CategoryTheory.Limits.equalizer_as_kernel, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃_assoc, CategoryTheory.Pseudofunctor.toDescentDataAsCoalgebraCompCoalgebraEquivalenceFunctorIso_inv_app_f, HomologicalComplex.mapBifunctor₂₃.d₃_eq, CategoryTheory.Bicategory.associator_inv_naturality_right, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_symm_apply, CategoryTheory.Lax.OplaxTrans.rightUnitor_hom_as_app, HomologicalComplex.comp_pOpcycles_eq_zero_iff_up_to_refinements, CategoryTheory.GrpObj.comp_zpow, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, HomologicalComplex.extend.d_none_eq_zero', CategoryTheory.ShortComplex.HomologyMapData.add_left, groupCohomology.congr, CategoryTheory.Functor.IsStronglyCocartesian.universal_property', CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIso_hom, CategoryTheory.has_weakly_initial_of_weakly_initial_set_and_hasProducts, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃, HomologicalComplex₂.D₁_D₁, PresheafOfModules.freeYonedaEquiv_symm_app, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_inv_homologyι_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_hom, CategoryTheory.Limits.biproduct.matrixEquiv_symm_apply, CategoryTheory.zero_map, CategoryTheory.Sheaf.isLocallySurjective_iff_epi, CategoryTheory.InjectiveResolution.complex_d_comp, CategoryTheory.leftDistributor_hom, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_hom, CategoryTheory.FreeBicategory.mk_right_unitor_inv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_l, CategoryTheory.Limits.PreservesCokernel.of_iso_comparison, CategoryTheory.Bicategory.whiskerLeft_comp, CategoryTheory.Limits.imageSubobject_arrow_comp_eq_zero, HomologicalComplex.single_obj_d, CategoryTheory.CategoryOfElements.homMk_coe, CategoryTheory.tensorLeftHomEquiv_naturality, CategoryTheory.Subgroupoid.mul, HomologicalComplex₂.D₂_D₁_assoc, CochainComplex.IsKInjective.Qh_map_bijective, CategoryTheory.FinCategory.categoryAsType_comp, CategoryTheory.eqToHom_heq_id_cod, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_symm_apply, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, CategoryTheory.Pseudofunctor.ObjectProperty.ι_app_toFunctor, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.Bicategory.conjugateEquiv_symm_id, CategoryTheory.Discrete.sumEquiv_inverse_map, AlgebraicGeometry.Scheme.exists_hom_comp_eq_comp_of_locallyOfFiniteType, CategoryTheory.uliftYonedaEquiv_symm_comp, CategoryTheory.ShortComplex.ShortExact.comp_δ, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv, CategoryTheory.Limits.kernelBiprodFstIso_hom, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality, CategoryTheory.LaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Bicategory.conjugateEquiv_apply, CategoryTheory.Bicategory.prod_whiskerRight_fst, CategoryTheory.ShortComplex.RightHomologyMapData.compatibilityOfZerosOfIsLimitKernelFork_φH, CategoryTheory.Limits.monoFactorisationZero_e, CategoryTheory.Functor.FullyFaithful.map_bijective, CategoryTheory.Adjunction.eq_homEquiv_apply, CategoryTheory.Pseudofunctor.DescentData.comp_hom, CategoryTheory.Bicategory.whiskerRight_comp_symm, CategoryTheory.Triangulated.AbelianSubcategory.exists_distinguished_triangle_of_epi, CategoryTheory.ThinSkeleton.fromThinSkeleton_map, CategoryTheory.Endofunctor.Algebra.ext_iff, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τl, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv, SimplicialObject.Splitting.cofan_inj_eq, CategoryTheory.Bicategory.Pith.comp₂_iso_hom_assoc, SSet.Homotopy.h₁_assoc, DerivedCategory.subsingleton_hom_of_isStrictlyLE_of_isStrictlyGE, CategoryTheory.MonObj.ofRepresentableBy_one, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallySurjectiveHomYonedaGluedToSheafOfIsLocallySurjectiveZariskiTopologyDescFunctorOppositeType, starEquivCostar_apply_fst, Path.exists_notMem_mem_hom_path_path_of_notMem_mem, CategoryTheory.ShortComplex.cyclesMap_sub, CategoryTheory.IsPullback.inr_fst, HomologicalComplex₂.D₂_D₂, CategoryTheory.Cat.leftUnitor_hom_app, CategoryTheory.Functor.curry₃_obj_obj_map_app, CategoryTheory.Bicategory.associator_eqToHom_hom_assoc, CategoryTheory.LocallyDiscrete.subsingleton2Hom, CategoryTheory.ShortComplex.Homotopy.g_h₃_assoc, CategoryTheory.evaluationAdjunctionLeft_unit_app_app, CategoryTheory.CostructuredArrow.prodFunctor_map, CategoryTheory.FintypeCat.instFiberFunctorActionFintypeCatForget₂HomSubtypeHomObjFiniteV, CategoryTheory.FinCategory.asTypeToObjAsType_map, CategoryTheory.Bicategory.whiskerRight_id, Homotopy.prevD_succ_cochainComplex, SSet.exists_nonDegenerate, CategoryTheory.AddMon.Hom.hom_add, HomotopicalAlgebra.FibrantObject.HoCat.exists_resolution_map, HomologicalComplex.d_toCycles_assoc, CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory_rightUnitor_hom_as_app, CategoryTheory.kernel_zero_of_nonzero_from_simple, ContinuousMap.Homotopy.heq_path_of_eq_image, CategoryTheory.ProjectiveResolution.sub_extMk, CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.exists_of_fiberMk_eq_fiberMk, CategoryTheory.ShortComplex.Splitting.id, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, CategoryTheory.StructuredArrow.prodInverse_map, CategoryTheory.Iso.homFromEquiv_symm_apply, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, CategoryTheory.MonObj.comp_mul_assoc, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_apply, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans, HomologicalComplex.xPrevIsoSelf_comp_dTo, CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map, SheafOfModules.unitHomEquiv_symm_freeHomEquiv_apply, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality, CategoryTheory.Functor.RepresentableBy.coyoneda_homEquiv, CategoryTheory.TwoSquare.equivNatTrans_apply, CategoryTheory.ShortComplex.Homotopy.add_h₁, CochainComplex.HomComplex.Cochain.toSingleMk_add, CategoryTheory.coyonedaEquiv_comp, CategoryTheory.uliftYonedaEquiv_symm_apply_app, CategoryTheory.IsRegularEpi.exists_of_isKernelPair, groupHomology.d₃₂_comp_d₂₁_assoc, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom, CategoryTheory.Abelian.Ext.mk₀_neg, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂, CategoryTheory.Limits.isoZeroOfEpiZero_hom, CategoryTheory.Pretriangulated.Triangle.yoneda_exact₂, CategoryTheory.Oplax.LaxTrans.naturality_comp_assoc, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimit'_π_apply, CategoryTheory.WithInitial.liftFromUnderComp_inv_app, CategoryTheory.conjugateEquiv_symm_apply_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_hom_app_unmop_app, CategoryTheory.Limits.WalkingParallelPair.inclusionWalkingReflexivePair_map, CategoryTheory.MorphismProperty.Comma.mapLeftEq_inv_app_left, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, FGModuleCat.instFiniteHomModuleCatObjIsFG, CategoryTheory.Limits.PullbackCone.mk_π_app, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_app, CategoryTheory.Triangulated.AbelianSubcategory.ιK_mor₁_assoc, CategoryTheory.MonoidalPreadditive.add_whiskerRight, CategoryTheory.LaxFunctor.id_mapId, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, CategoryTheory.Limits.CokernelCofork.IsColimit.comp_π_eq_zero_iff_up_to_refinements, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_map, CategoryTheory.nerve.homEquiv_apply, CategoryTheory.isIso_iff_coyoneda_map_bijective, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_naturality_inv_toNatTrans_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.Limits.Types.binaryCoproductCocone_ι_app, CategoryTheory.ComposableArrows.mk₁_surjective, CategoryTheory.conjugateEquiv_apply_app, CategoryTheory.StrictPseudofunctor.id_obj, CategoryTheory.Limits.biproductBiproductIso_hom, CochainComplex.HomComplex.δ_v, CategoryTheory.InjectiveResolution.comp_descHomotopyZeroSucc_assoc, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id, CategoryTheory.Groupoid.isThin_iff, CategoryTheory.Limits.kernelBiproductπIso_hom, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp, Rep.FiniteCyclicGroup.chainComplexFunctor_obj, CategoryTheory.Abelian.tfae_epi, AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subset, CategoryTheory.Oplax.StrongTrans.homCategory_id_as_app, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, CategoryTheory.Idempotents.add_def, HomologicalComplex.d_comp_d_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_naturality, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, CategoryTheory.MonoidalOpposite.unmopEquiv_inverse_map_unmop, CategoryTheory.AddMonObj.add_comp, CategoryTheory.Triangulated.AbelianSubcategory.exists_lift_ιK, CategoryTheory.MorphismProperty.LeftFraction.cases, CategoryTheory.ShortComplex.HomologyMapData.neg_left, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv_assoc, AlgebraicGeometry.AffineSpace.homOverEquiv_symm_apply_coe, CategoryTheory.Limits.BinaryBicone.sndKernelFork_ι, CategoryTheory.Bicategory.InducedBicategory.eqToHom_hom, CochainComplex.fromSingle₀Equiv_apply_coe, CategoryTheory.Functor.FullyFaithful.nonempty_iff_map_bijective, SimplexCategory.σ_injective, CategoryTheory.CategoryOfElements.to_comma_map_right, CategoryTheory.Pseudofunctor.Grothendieck.ext_iff, CategoryTheory.Functor.prod'_ε_fst, CategoryTheory.evaluationRightAdjoint_map_app, CategoryTheory.Functor.imageSieve_eq_imageSieve, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.frobeniusMorphism_mate, CategoryTheory.Subgroupoid.IsWide.eqToHom_mem, HomologicalComplex.dgoToHomologicalComplex_obj_d, CategoryTheory.Bicategory.lanLiftUnit_desc_assoc, CategoryTheory.Localization.liftNatTrans_zero, CategoryTheory.ShortComplex.homologyMap'_nullHomotopic, CategoryTheory.Limits.BinaryFan.IsLimit.lift'_coe, CategoryTheory.tensorRightHomEquiv_whiskerRight_comp_evaluation, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, CategoryTheory.Cat.Hom.isoMk_inv, CategoryTheory.ShortComplex.Homotopy.smul_h₂, CategoryTheory.Bicategory.whiskerLeft_hom_inv, HomotopyCategory.quotient_map_eq_zero_iff, CategoryTheory.Abelian.SpectralObject.δ_δ, CategoryTheory.Abelian.Pseudoelement.zero_eq_zero', CategoryTheory.Lax.LaxTrans.id_app, CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatHomObjFiniteAutFunctorFunctorToContActionOfFiberFunctor, CategoryTheory.instSmallHomOfLocallySmall, CategoryTheory.Subobject.factors_add, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.StrictlyUnitaryLaxFunctor.id_obj, CochainComplex.HomComplex.Cochain.neg_v, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, CategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork_π, CategoryTheory.Limits.KernelFork.ι_ofι, CochainComplex.HomComplex.Cochain.sub_v, CategoryTheory.Linear.units_smul_comp, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.f', CategoryTheory.Bicategory.mateEquiv_id_comp_right, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv, CategoryTheory.Linear.leftComp_apply, CategoryTheory.Bicategory.leftUnitor_comp_inv, CochainComplex.mappingCone.liftCochain_v_descCochain_v, CategoryTheory.Limits.cokernel.zeroCokernelCofork_π, CategoryTheory.Functor.Linear.map_smul, Homotopy.nullHomotopicMap'_f_eq_zero, CategoryTheory.Presheaf.restrictedULiftYoneda_obj_map, CategoryTheory.Pseudofunctor.mapComp_id_left, CategoryTheory.Iso.unop2_inv, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage_ι, CategoryTheory.Limits.IsBilimit.total, CategoryTheory.Sieve.mem_ofObjects_iff, CategoryTheory.SemiadditiveOfBinaryBiproducts.comp_add, SheafOfModules.GeneratingSections.epi, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand_assoc, CategoryTheory.Bicategory.postcomp_obj, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, CategoryTheory.Limits.FormalCoproduct.Hom.fromIncl_asSigma, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φH, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Comma.opFunctor_map, HomologicalComplex₂.d₂_eq_zero, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app, CategoryTheory.Triangulated.AbelianSubcategory.mor₁_πQ, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_right, HomologicalComplex.mapBifunctorMapHomotopy.comm₁, CategoryTheory.StrictPseudofunctor.comp_mapComp_hom, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hf', CategoryTheory.Biprod.unipotentLower_inv, Action.smul_hom, CategoryTheory.ShortComplex.cyclesMap'_sub, CategoryTheory.Bicategory.leftZigzagIso_hom, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapComp, CategoryTheory.ShortComplex.homologyMap'_sub, CategoryTheory.Sieve.equalizer_apply, CategoryTheory.ShortComplex.Splitting.rightHomologyData_ι, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inl, CategoryTheory.Equalizer.firstObjEqFamily_hom, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t_assoc, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range', CategoryTheory.Functor.toOplaxFunctor'_obj, Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom, CategoryTheory.ShortComplex.hasHomology_of_hasCokernel, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, Bicategory.Opposite.bicategory_associator_hom_unop2, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_hom, CategoryTheory.OplaxFunctor.PseudoCore.mapCompIso_hom, CategoryTheory.StrictPseudofunctor.comp_mapId_hom, CategoryTheory.Idempotents.Karoubi.hom_eq_zero_iff, CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT_app_assoc, CochainComplex.Lifting.exists_hom, CategoryTheory.Oplax.LaxTrans.comp_app, CategoryTheory.Limits.biprod.inr_fst, AlgebraicGeometry.RingedSpace.exists_res_eq_zero_of_germ_eq_zero, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, CategoryTheory.ShortComplex.Homotopy.sub_h₁, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_mul, CategoryTheory.Limits.IsBilimit.binary_total, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_φ, CochainComplex.mappingCone.inr_triangleδ, Bicategory.Opposite.unop2_id_bop, CategoryTheory.kernelCokernelCompSequence.ι_φ, CategoryTheory.LaxFunctor.mapComp_assoc_right_app, CategoryTheory.Oplax.LaxTrans.rightUnitor_hom_as_app, CategoryTheory.Bicategory.LeftExtension.ofCompId_left_as, CategoryTheory.Oplax.OplaxTrans.associator_hom_as_app, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_inv, MonCat.oneHom_apply, CategoryTheory.Idempotents.Karoubi.inclusionHom_apply, CategoryTheory.End.smul_left, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom, CategoryTheory.Preadditive.isSeparator_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id, HomologicalComplex.fromOpcycles_d_assoc, CategoryTheory.Pseudofunctor.toOplax_mapComp, Bicategory.Opposite.unopFunctor_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_μ_unmop_app, CategoryTheory.Functor.FullyFaithful.homNatIso_inv_app_down, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, CategoryTheory.Grp.Hom.hom_zpow, CategoryTheory.Limits.spanHomMk_app, CategoryTheory.BicategoricalCoherence.tensorRight_iso, CategoryTheory.IsPullback.zero_top, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight, CategoryTheory.Abelian.SpectralObject.fromOpcycles_H_map_twoδ₁Toδ₀, CategoryTheory.Functor.IsStronglyCartesian.map_self, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃_assoc, CategoryTheory.isPullback_of_cofan_isVanKampen, CategoryTheory.Functor.CorepresentableBy.ofIsoObj_homEquiv, CategoryTheory.Bicategory.Prod.sectR_mapComp_inv, CategoryTheory.Bicategory.Prod.fst_mapComp_hom, CategoryTheory.MonoidalCategory.prodMonoidal_whiskerRight, CategoryTheory.GrpObj.lift_conj_eq_mul_mul_inv, SemimoduleCat.ofHom₂_hom_apply_hom, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv_assoc, CategoryTheory.IsFiltered.crown₄, CategoryTheory.HomOrthogonal.matrixDecomposition_id, CategoryTheory.ShortComplex.Homotopy.ofNullHomotopic_h₀, CochainComplex.mappingCone.id_X, CategoryTheory.Functor.Full.map_surjective, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.uliftCoyonedaEquiv_symm_apply_app, CategoryTheory.Bicategory.id_whiskerLeft_symm, CategoryTheory.Pseudofunctor.mapComp'_naturality_1, CategoryTheory.Functor.representableByUliftFunctorEquiv_symm_apply_homEquiv, CommRingCat.HomTopology.continuous_precomp, Hom.op_inj, CategoryTheory.ShortComplex.Homotopy.refl_h₃, CochainComplex.HomComplex.Cochain.single_zero, CategoryTheory.ShortComplex.homologyMap'_add, CategoryTheory.actionAsFunctor_map, CategoryTheory.ShortComplex.SnakeInput.δ_L₃_f, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_sub_f, AddCommGrpCat.asHom_injective, CategoryTheory.Pseudofunctor.toDescentDataAsCoalgebra_obj_obj, CategoryTheory.Pseudofunctor.isStackFor_ofArrows_iff, CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff, CategoryTheory.Pseudofunctor.mkOfLax'_mapComp_hom, CategoryTheory.Limits.coker.condition_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₁₃_eq_conjugateEquiv_symm, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, CategoryTheory.Preadditive.nsmul_comp, SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι_app, CategoryTheory.Localization.Preadditive.add'_map, SimplicialObject.Splitting.IndexSet.ext', CategoryTheory.PreGaloisCategory.connected_component_unique, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_of, CategoryTheory.Limits.BinaryBicone.inl_snd_assoc, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.Bicategory.LeftLift.IsKan.fac_assoc, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr, CategoryTheory.linearYoneda_obj_obj_carrier, CategoryTheory.Preadditive.isSeparating_iff, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_unitIso_inv_app_hom, CategoryTheory.Pretriangulated.Triangle.smul_hom₂, CategoryTheory.Limits.Cotrident.IsColimit.homIso_natural, CategoryTheory.Bicategory.postcomposing_obj, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app, CategoryTheory.Triangulated.TStructure.truncLTι_comp_truncGEπ_assoc, CategoryTheory.Triangulated.TStructure.isIso_truncLT_map_iff, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app_assoc, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τl, CategoryTheory.Coyoneda.objOpOp_hom_app, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_symm_τr, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, CategoryTheory.ShortComplex.iCycles_g, CategoryTheory.FreeBicategory.mk_vcomp, sSetTopAdj_homEquiv_stdSimplex_zero, CategoryTheory.Functor.CoconeTypes.descColimitType_injective_iff_of_isFiltered', CategoryTheory.SubobjectRepresentableBy.homEquiv_eq, CategoryTheory.LaxFunctor.PseudoCore.mapCompIso_inv, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, SSet.Subcomplex.ofSimplexProd_eq_range, CategoryTheory.nerve.homEquiv_edgeMk, DerivedCategory.HomologySequence.mono_homologyMap_mor₁_iff, CategoryTheory.Join.pseudofunctorLeft_mapId_hom_toNatTrans_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app_assoc, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_mapId, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff, CochainComplex.homologyδOfTriangle_homologyMap_assoc, ModuleCat.homLinearEquiv_symm_apply, HomologicalComplex.truncGE'.d_comp_d, CategoryTheory.AddMonObj.comp_nsmul, ModuleCat.hom_smul, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CategoryTheory.Limits.cokernel.π_zero_isIso, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_zero_f, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.Cat.rightUnitor_hom_toNatTrans, CategoryTheory.Bicategory.precomposingCat_map, CategoryTheory.Functor.homObjEquiv_symm_apply_app, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, CategoryTheory.Bicategory.Prod.snd_map₂, Path.hom_heq_of_cons_eq_cons, CategoryTheory.Abelian.Preradical.ι_π_assoc, CategoryTheory.Functor.map_inv', CategoryTheory.PreGaloisCategory.instFullContActionFintypeCatHomObjFiniteAutFunctorFunctorToContAction, CategoryTheory.HasSplitEqualizer.splittable, Path.length_ne_zero_iff_eq_cons, Rep.MonoidalClosed.linearHomEquivComm_hom, CategoryTheory.Preadditive.cokernelCoforkOfCofork_ofπ, CategoryTheory.Lax.OplaxTrans.naturality_comp, HomologicalComplex.extend.d_none_eq_zero, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, SemimoduleCat.homLinearEquiv_apply, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight_assoc, CategoryTheory.Functor.RepresentableBy.comp_homEquiv_symm, CategoryTheory.Bicategory.whiskerRight_comp_symm_assoc, CategoryTheory.Pseudofunctor.DescentData.iso_hom, CategoryTheory.Functor.equivCatHom_apply, HomologicalComplex.cylinder.πCompι₀Homotopy.nullHomotopicMap_eq, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.ShortComplex.Homotopy.neg_h₁, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, HomologicalComplex.mapBifunctor₂₃.ιOrZero_eq_zero, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_naturality_assoc, CochainComplex.ConnectData.d_comp_d, CategoryTheory.NatTrans.app_nsmul, HomologicalComplex.sub_f_apply, CategoryTheory.Abelian.SpectralObject.map_fourδ₁Toδ₀_d, CochainComplex.mappingCone.d_snd_v'_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_mapId, CategoryTheory.whiskerLeft_def, CategoryTheory.NatTrans.prod_app_fst, HomologicalComplex.homotopyCofiber.descSigma_ext_iff, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.homologyπ_isoHomology_inv_assoc, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_mapComp_inv_toNatTrans_app, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_inv, AlgebraicGeometry.IsLocalIso.le_of_isZariskiLocalAtSource, TopCat.Presheaf.IsSheaf.isSheafUniqueGluing_types, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τr, CategoryTheory.Iso.eHomCongr_comp_assoc, CategoryTheory.Adjunction.homEquiv_unit, Hom.mop_inj, CategoryTheory.Join.opEquiv_inverse_map_inclRight_op, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_hom, HomologicalComplex.d_pOpcycles, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_inv, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality, CategoryTheory.Pseudofunctor.mapComp_id_right, CategoryTheory.Preadditive.comp_neg, CategoryTheory.conjugateEquiv_leftUnitor_hom, CategoryTheory.Sum.functorEquiv_inverse_map, CategoryTheory.shrinkYonedaEquiv_symm_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Functor.map_comp_heq, Mathlib.Tactic.Bicategory.naturality_whiskerRight, TopCat.Hom.equivContinuousMap_apply, CategoryTheory.Limits.isIsoZero_iff_source_target_isZero, CategoryTheory.Bicategory.LeftExtension.whiskering_map, CategoryTheory.Bicategory.comp_whiskerRight, CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_H, CategoryTheory.BicategoricalCoherence.left_iso, CategoryTheory.Limits.Pi.ι_π_of_ne, CategoryTheory.Presheaf.isLocallySurjective_toSheafify, CategoryTheory.ShortComplex.add_τ₃, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality, CategoryTheory.Limits.limitCompCoyonedaIsoCone_hom_app, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality_assoc, Bicategory.Opposite.bicategory_leftUnitor_hom_unop2, CategoryTheory.Adjunction.homEquiv_ofNatIsoRight_apply, CategoryTheory.uliftYonedaEquiv_apply, CategoryTheory.Limits.WidePullbackShape.mkCone_π_app, HomotopicalAlgebra.Cylinder.LeftHomotopy.covering_homotopy, CategoryTheory.Iso.homCongr_comp, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Bicategory.comp_whiskerLeft_symm, CategoryTheory.Bicategory.inv_whiskerRight, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_inv, CategoryTheory.Bicategory.Pith.id₂_iso_inv, CategoryTheory.StructuredArrow.prodFunctor_map, CategoryTheory.IsCardinalPresentable.exists_eq_of_isColimit, CategoryTheory.ShortComplex.Homotopy.refl_h₂, CategoryTheory.Arrow.equivSigma_apply_snd_snd, CategoryTheory.bijection_natural, HomologicalComplex.fromOpcycles_eq_zero, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f_assoc, ChainComplex.toSingle₀Equiv_apply_coe, HomologicalComplex.homologyι_opcyclesToCycles_assoc, CategoryTheory.Limits.Fork.IsLimit.existsUnique, CategoryTheory.Lax.LaxTrans.vComp_app, CategoryTheory.Functor.FullyFaithful.homEquiv_symm_apply, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_obj_obj, CategoryTheory.Monad.algebraPreadditive_homGroup_add_f, PresheafOfModules.zsmul_app, Condensed.finYoneda_map, FDRep.instFiniteDimensionalHom, CategoryTheory.ObjectProperty.exists_isoModSerre_comp_eq_zero_iff, CategoryTheory.NormalEpi.w, CategoryTheory.Limits.coequalizer_as_cokernel, CategoryTheory.Localization.small_of_hasSmallLocalizedHom, CategoryTheory.CartesianClosed.homEquiv_apply_eq, SimplexCategory.instSubsingletonHomMkOfNatNat, CategoryTheory.Bicategory.mateEquiv_symm_apply', SSet.Subcomplex.instSubsingletonHomToSSetBot, CategoryTheory.Oplax.LaxTrans.naturality_naturality, CategoryTheory.Limits.PullbackCone.combine_π_app, CategoryTheory.Abelian.SpectralObject.SpectralSequence.pageD_pageD, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_apply_app, CategoryTheory.Pseudofunctor.mapComp'_comp_id, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.Oplax.StrongTrans.naturality_comp, MonObj.mopEquiv_functor_obj_mon_one_unmop, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coassoc_assoc, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_mapId_hom_toNatTrans_app, CategoryTheory.Grp.Hom.hom_hom_div, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_hom, CategoryTheory.OplaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_apply, CategoryTheory.Oplax.OplaxTrans.associator_inv_as_app, CategoryTheory.IsPushout.inl_snd', CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois_finite_family, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Pseudofunctor.presheafHom_obj, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_δ_assoc, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃, CategoryTheory.Bicategory.Adjunction.homEquiv₂_apply, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, CategoryTheory.Limits.Pi.ι_π, CategoryTheory.Abelian.SpectralObject.fromOpcycles_H_map_twoδ₁Toδ₀_assoc, CategoryTheory.Pseudofunctor.mkOfLax'_mapId_inv, CategoryTheory.PreGaloisCategory.toAut_hom_app_apply, CategoryTheory.Limits.CokernelCofork.IsColimit.isIso_π, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_assoc, SimplicialObject.Splitting.IndexSet.mk_snd_coe, CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists, CategoryTheory.AddMonObj.add_comp_assoc, CategoryTheory.Congruence.equivalence, CategoryTheory.Preadditive.smul_iso_hom, CategoryTheory.Oplax.StrongTrans.naturality_id_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.mapComp_naturality_right, CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, FintypeCat.toProfinite_map_hom_hom_apply, CategoryTheory.Oplax.LaxTrans.Modification.id_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.Oplax.LaxTrans.naturality_id, CategoryTheory.ObjectProperty.homMk_zero, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_inv, CategoryTheory.BicartesianSq.of_has_biproduct₂, Rep.coindVEquiv_symm_apply_coe, CategoryTheory.whiskerRight_def, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_left_unitor, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom, HomologicalComplex₂.d_f_comp_d_f_assoc, CategoryTheory.Pseudofunctor.toLax_mapComp, CategoryTheory.ObjectProperty.isStrongGenerator_iff_exists_extremalEpi, CategoryTheory.Pseudofunctor.DescentData'.comp_hom, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_hom, HomologicalComplex.homotopyCofiber.inlX_sndX_assoc, CategoryTheory.Pseudofunctor.isoMapOfCommSq_horiz_id, CategoryTheory.Types.instFullForgetTypeHom, CategoryTheory.Oplax.OplaxTrans.naturality_comp, CategoryTheory.CommSq.shortComplex_f, CategoryTheory.CatEnriched.id_hComp_heq, CategoryTheory.MonObj.comp_one, CochainComplex.of_d_ne, CategoryTheory.Abelian.SpectralObject.d_d, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.Limits.FintypeCat.productEquiv_apply, CategoryTheory.Lax.OplaxTrans.whiskerRight_as_app, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left, CategoryTheory.Discrete.instSubsingletonDiscreteHom, CategoryTheory.uliftYonedaEquiv_symm_map, CategoryTheory.Functor.prod_ε_snd, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π, HomologicalComplex.homologyι_comp_fromOpcycles, CategoryTheory.Functor.cones_obj, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_neg_f, CategoryTheory.Pseudofunctor.DescentData'.isoMk_inv_hom, Rep.ofHom_add, CategoryTheory.NonPreadditiveAbelian.sub_sub_sub, CategoryTheory.Lax.LaxTrans.naturality_comp, CategoryTheory.Presieve.preZeroHypercover_I₀, CochainComplex.homologyδOfTriangle_homologyMap, CondensedMod.isDiscrete_iff_isDiscrete_forget, CochainComplex.HomComplex.Cochain.toSingleMk_v_eq_zero, FintypeCat.comp_apply, CategoryTheory.Limits.zero_of_target_iso_zero', CategoryTheory.Pseudofunctor.DescentData.iso_inv, CategoryTheory.Adjunction.map_comp_bijective_iff, CategoryTheory.InjectiveResolution.extMk_surjective, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.Limits.biprod.fstKernelFork_ι, CategoryTheory.Limits.biproduct.matrix_desc_assoc, FintypeCat.uSwitchEquiv_naturality, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_hom, AlgebraicTopology.DoldKan.QInfty_f_0, HomologicalComplex.homologyMap_neg, CategoryTheory.ShortComplex.RightHomologyData.wι_assoc, CategoryTheory.Presieve.isSheafFor_iff_bijective_shrinkFunctor_ι_comp, CategoryTheory.Oplax.StrongTrans.id_naturality_inv, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app, CategoryTheory.InjectiveResolution.ι_f_succ, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CategoryTheory.Lax.OplaxTrans.vComp_naturality_comp, CategoryTheory.MonObj.one_comp_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_assoc, FintypeCat.equivEquivIso_symm_apply_symm_apply, CategoryTheory.presheafHom_obj, CategoryTheory.FinCategory.categoryAsType_id, CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnected, prevD_eq_toPrev_dTo, CategoryTheory.Limits.IsColimit.homEquiv_apply, CategoryTheory.Limits.comp_zero, CategoryTheory.Limits.monoFactorisationZero_m, CategoryTheory.Preadditive.neg_iso_hom, CategoryTheory.Groupoid.vertexGroup_inv, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_assoc, CategoryTheory.Oplax.LaxTrans.id_app, CategoryTheory.NatTrans.app_add, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_inv_as_app, AlgebraicTopology.DoldKan.Γ₂_obj_p_app, SimplexCategory.eq_σ_comp_of_not_injective, symmetrify_reverse, CategoryTheory.Functor.whiskerLeft_obj_map_bijective_of_isCoverDense, CategoryTheory.Pseudofunctor.map₂_right_unitor_assoc, CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.ext_iff, CategoryTheory.Bicategory.associatorNatIsoRightCat_inv_toNatTrans_app, CategoryTheory.GrpObj.inv_comp_assoc, CategoryTheory.Bicategory.Prod.sectL_mapComp_hom, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, CategoryTheory.Limits.preservesKernel_zero, CategoryTheory.Abelian.Ext.mk₀_smul, CategoryTheory.prod_id', CategoryTheory.Bicategory.associator_inv_naturality_left, CategoryTheory.Functor.map_zero, CategoryTheory.Abelian.image_ι_comp_eq_zero, CategoryTheory.opEquiv_apply, CategoryTheory.Pseudofunctor.CoGrothendieck.instFullαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, SSet.yonedaEquiv_symm_comp, SemiNormedGrp.zero_apply, CategoryTheory.Abelian.SpectralObject.zero₃, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_comp_mapComp'_inv, CategoryTheory.Functor.map_add', CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Oplax.LaxTrans.leftUnitor_hom_as_app, CategoryTheory.Functor.prod_η_snd, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero_assoc, AlgebraicTopology.AlternatingFaceMapComplex.d_squared, CategoryTheory.Limits.inr_pushoutZeroZeroIso_hom, CategoryTheory.Bicategory.leftUnitor_inv_naturality, CochainComplex.homologyMap_comp_eq_zero_of_distTriang, CategoryTheory.Quiv.homEquivOfIso_apply, CategoryTheory.ShortComplex.opcyclesMap_add, CategoryTheory.WithTerminal.lift_map, CategoryTheory.ShortComplex.Exact.comp_eq_zero, CategoryTheory.StructuredArrow.IsUniversal.existsUnique, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom, CategoryTheory.Limits.biprod.decomp_hom_to, CategoryTheory.Pseudofunctor.DescentData.nonempty_fullyFaithful_toDescentData_iff_of_sieve_eq, CategoryTheory.Biprod.inr_ofComponents, CategoryTheory.Equivalence.inverseFunctor_map, TopCat.presheafToTop_obj, CategoryTheory.Bicategory.unitors_equal, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.Biprod.ofComponents_snd, CategoryTheory.Arrow.mk_injective, CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatHomObjFiniteAutFunctorFunctorToContAction, CategoryTheory.Cat.associator_inv_app, CategoryTheory.Abelian.SpectralObject.cyclesMap_Ψ_assoc, CategoryTheory.Bicategory.associator_naturality_right, CategoryTheory.Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.Bicategory.whiskerRightIso_inv, CategoryTheory.NonPreadditiveAbelian.sub_add, CategoryTheory.Bicategory.precomposing_map_app, FundamentalGroupoid.instSubsingletonHomPUnit, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, CategoryTheory.Limits.biproduct.lift_matrix_assoc, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, Rep.tensorHomEquiv_apply, CategoryTheory.Bicategory.Prod.sectL_obj, CategoryTheory.Limits.biproduct.lift_desc_assoc, CochainComplex.HomComplex.Cocycle.toSingleMk_surjective, CochainComplex.mappingCocone.id_X, CategoryTheory.Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, CategoryTheory.SingleObj.inv_as_inv, HomologicalComplex.mapBifunctorMapHomotopy.zero₁, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit_under, CategoryTheory.Subgroupoid.coe_comp_coe, CategoryTheory.Preadditive.epi_iff_cancel_zero, Homotopy.dNext_zero_chainComplex, HomologicalComplex.mapBifunctor₂₃.d₃_eq_zero, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.MonoidalOpposite.tensorIso_hom_app_unmop, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left, Mathlib.Tactic.Bicategory.structuralIsoOfExpr_whiskerLeft, CategoryTheory.Limits.biproduct.matrixEquiv_apply, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d_assoc, HomotopyCategory.Pretriangulated.complete_distinguished_triangle_morphism, FintypeCat.hom_ext_iff, DerivedCategory.to_singleFunctor_obj_eq_zero_of_injective, CategoryTheory.SubobjectRepresentableBy.pullback_homEquiv_symm_obj_Ω₀, CategoryTheory.Cat.rightUnitor_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, CategoryTheory.DifferentialObject.ext_iff, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eq, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, CategoryTheory.Linear.smulOfRingMorphism_smul_eq, CategoryTheory.Preadditive.comp_sum_assoc, HomologicalComplex₂.d₁_eq, DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE, CategoryTheory.Oplax.LaxTrans.id_naturality, CategoryTheory.Abelian.SpectralObject.map_fourδ₁Toδ₀_d_assoc, CategoryTheory.Comon.ComonToMonOpOp_map, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_hom_app, MonCat.hom_one, CategoryTheory.StructuredArrow.mk_surjective, CategoryTheory.Pseudofunctor.ObjectProperty.ι_naturality, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id, LightCondensed.internallyProjective_iff_tensor_condition, CategoryTheory.Limits.kernelBiprodFstIso_inv, CategoryTheory.LocalizerMorphism.LeftResolution.mk_surjective, CategoryTheory.Adjunction.homEquiv_ofNatIsoLeft_apply, CategoryTheory.ShortComplex.Homotopy.smul_h₀, CochainComplex.HomComplex.Cochain.ofHom_neg, CategoryTheory.Pseudofunctor.mapComp_id_right_hom, CategoryTheory.yonedaMonObj_map, Homotopy.prevD_chainComplex, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_mono₃, CategoryTheory.Bicategory.conjugateEquiv_symm_of_iso, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp, CategoryTheory.Oplax.StrongTrans.Modification.naturality_assoc, CategoryTheory.ShortComplex.Homotopy.smul_h₃, CategoryTheory.LaxFunctor.mapComp_naturality_right_app_assoc, CochainComplex.HomComplex.Cocycle.toSingleMk_add, CategoryTheory.Limits.kernelBiproductToSubtypeIso_hom, CategoryTheory.shrinkYonedaObjObjEquiv_map_app, CategoryTheory.ObjectProperty.hasLimit_parallelPair_comp_ι, CategoryTheory.Subgroupoid.mem_discrete_iff, CategoryTheory.Subfunctor.ofSection_obj, CategoryTheory.uliftYonedaEquiv_naturality, Rep.coindFunctorIso_inv_app_hom_toFun_coe, CategoryTheory.ShortComplex.cyclesMap_smul, SSet.stdSimplex.δ_objEquiv_symm_apply, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_hom_as_app, CategoryTheory.Functor.curry₃_obj_map_app_app, CategoryTheory.Grothendieck.map_map, CategoryTheory.Lax.LaxTrans.vComp_naturality_naturality, CategoryTheory.Bicategory.prod_whiskerRight_snd, CategoryTheory.OrthogonalReflection.toSucc_surjectivity, CategoryTheory.CatEnrichedOrdinary.hComp_id, CategoryTheory.CatCenter.app_add, CategoryTheory.Limits.CokernelCofork.condition, AlgebraicGeometry.QuasiCompactCover.exists_hom, CategoryTheory.conjugateEquiv_counit_symm, CochainComplex.HomComplex.Cochain.zero_v, SimplicialObject.Splitting.IndexSet.eqId_iff_mono, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_map₂, CategoryTheory.Limits.cokernel.condition, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τr, CategoryTheory.StrictPseudofunctor.comp_mapId_inv, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_assoc, CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork_Q, TopCat.Sheaf.extend_hom_app, CategoryTheory.Functor.map_add, CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst_eq, CategoryTheory.CatEnrichedOrdinary.hComp_comp, CategoryTheory.conj_eqToHom_iff_heq', CategoryTheory.NonPreadditiveAbelian.sub_zero, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.g, CategoryTheory.Bicategory.Adj.id_τl, CategoryTheory.Limits.IsLimit.pushout_zero_ext, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inr, CategoryTheory.Bicategory.Adj.comp_τl, CategoryTheory.isCardinalFiltered_iff_aux₂, CategoryTheory.ShortComplex.leftHomologyMap_add, ModuleCat.homAddEquiv_symm_apply_hom, CategoryTheory.IsPushout.zero_bot, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inr, CategoryTheory.InjectiveResolution.add_extMk, CategoryTheory.Abelian.LeftResolution.karoubi.F_map_f, CategoryTheory.evaluationAdjunctionRight_counit_app_app, CategoryTheory.Preadditive.smul_iso_inv, CategoryTheory.IsPushout.zero_left, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, CategoryTheory.AddMonObj.comp_add, CategoryTheory.MorphismProperty.Comma.mapRightEq_hom_app_left, CategoryTheory.PrelaxFunctor.mkOfHomFunctors_toPrelaxFunctorStruct, CategoryTheory.Bicategory.Comonad.comul_assoc_flip_assoc, CategoryTheory.Limits.Fork.IsLimit.homIso_symm_apply, HomotopicalAlgebra.RightHomotopyClass.mk_surjective, HomologicalComplex.mapBifunctor₁₂.d₂_eq_zero, CategoryTheory.Biprod.unipotentUpper_hom, CategoryTheory.Functor.natTransEquiv_symm_apply_app, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, Prefunctor.star_fst, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_symm_apply, CategoryTheory.Limits.cokernel.zeroCokernelCofork_pt, CategoryTheory.OplaxFunctor.map₂_associator_app_assoc, CategoryTheory.StrictPseudofunctor.mk'_mapComp, CategoryTheory.Monad.adj_counit, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp, CommRingCat.HomTopology.precompHomeomorph_apply, CategoryTheory.ShortComplex.Homotopy.ofEq_h₂, CategoryTheory.AddMonObj.nsmul_comp_assoc, FintypeCat.id_apply, CategoryTheory.Presieve.preZeroHypercover_X, CategoryTheory.LaxFunctor.map₂_associator_app_assoc, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, CategoryTheory.SingleObj.comp_as_mul, CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_apply, CategoryTheory.Subobject.bot_factors_iff_zero, CategoryTheory.Functor.uncurry_map_app, CategoryTheory.MonoidalPreadditive.whiskerLeft_zero, SimplexCategory.toMk₁Equiv_apply, CategoryTheory.MonoidalOpposite.mopMopEquivalence_inverse_map_unmop_unmop, CategoryTheory.PreGaloisCategory.functorToContAction_map, CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork_H, CategoryTheory.ShortComplex.Homotopy.ofNullHomotopic_h₁, CategoryTheory.ActionCategory.uncurry_map, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans, CategoryTheory.Lax.LaxTrans.id_naturality, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp_assoc, HomologicalComplex.iCycles_d, SSet.hoFunctor.unitHomEquiv_eq, HomologicalComplex.mapBifunctor₁₂.ιOrZero_eq_zero, CategoryTheory.ShortComplex.Homotopy.comm₃, CategoryTheory.NonPreadditiveAbelian.sub_comp, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_assoc, prevD_nat, CategoryTheory.Limits.pullbackZeroZeroIso_inv_fst, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_right_assoc, CategoryTheory.InjectiveResolution.extMk_zero, CategoryTheory.Idempotents.idem_of_id_sub_idem, ChainComplex.mk_congr_succ_X₃, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.ShortComplex.homologyMap'_neg, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_associator, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, CategoryTheory.Functor.map_zsmul, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂_assoc, CategoryTheory.CostructuredArrow.prodInverse_obj, CategoryTheory.nerve.homEquiv_comp, CategoryTheory.Limits.pullbackZeroZeroIso_hom_snd, FGModuleCat.instFiniteHom, CategoryTheory.Pretriangulated.Triangle.rotate_mor₃, groupCohomology.cochainsMap_zero, CategoryTheory.pseudofunctorOfIsLocallyDiscrete_obj, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles_assoc, HomologicalComplex.dTo_comp_dFrom, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f, CategoryTheory.FreeBicategory.mk_id, CategoryTheory.nerve.mk₁_homEquiv_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.neg_φH, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_neg_f, CategoryTheory.Preadditive.neg_comp_neg_assoc, CategoryTheory.Preadditive.kernelForkOfFork_ofι, CategoryTheory.Functor.toOplaxFunctor_obj, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, CategoryTheory.Bicategory.instIsIsoHomLeftZigzagHom, CategoryTheory.Limits.colimitYonedaHomIsoLimit_π_apply, CategoryTheory.Limits.FintypeCat.productEquiv_symm_comp_π_apply, CategoryTheory.PreGaloisCategory.monoInducesIsoOnDirectSummand, AlgebraicGeometry.Scheme.Cover.exists_lift_trans_eq, CategoryTheory.Bicategory.Prod.fst_map₂, HomologicalComplex₂.D₁_shape, CategoryTheory.Lax.OplaxTrans.homCategory_id_as_app, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, CategoryTheory.heq_comp_eqToHom_iff, CategoryTheory.WithTerminal.liftToTerminal_map, CategoryTheory.Precoverage.mem_finite_iff, AlgebraicGeometry.Scheme.Cover.exists_of_f_eq_f, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app, CategoryTheory.Bicategory.Equivalence.right_triangle, CategoryTheory.prodFunctor_map, CategoryTheory.Preadditive.neg_comp_neg, CategoryTheory.Limits.coconeUnopOfConeEquiv_counitIso, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_obj, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_app, CategoryTheory.Bicategory.InducedBicategory.forget_map, CategoryTheory.Triangulated.Localization.complete_distinguished_triangle_morphism, CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer', CategoryTheory.Pretriangulated.Triangle.sub_hom₁, CategoryTheory.Pseudofunctor.DescentData.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpHom, CategoryTheory.Triangulated.TStructure.exists_triangle, CategoryTheory.Bicategory.associator_eqToHom_inv, CategoryTheory.Bicategory.Equivalence.left_triangle, CategoryTheory.Localization.Preadditive.homEquiv_apply, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, SSet.S.le_iff, AddCommGrpCat.homAddEquiv_symm_apply_hom, CochainComplex.HomComplex.Cocycle.toSingleMk_mem_coboundaries_iff, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, CategoryTheory.Arrow.equivSigma_apply_fst, CategoryTheory.InducedCategory.homEquiv_symm_apply_hom, CategoryTheory.OplaxFunctor.mapId'_eq_mapId, CategoryTheory.Under.mapPushoutAdj_unit_app, CategoryTheory.Pseudofunctor.toDescentDataAsCoalgebra_map_hom, CategoryTheory.Limits.cokernelBiprodInlIso_inv, CategoryTheory.yonedaAddMonObjIsoOfRepresentableBy_inv_app_hom_apply, CategoryTheory.DifferentialObject.d_squared, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, AddCommGrpCat.hom_sub, AddGrpCat.zero_apply, CategoryTheory.Presieve.uncurry_singleton, CategoryTheory.Join.mapWhiskerRight_app, CategoryTheory.PrelaxFunctor.map₂_eqToHom, Mathlib.Tactic.Bicategory.naturality_associator, CategoryTheory.ProjectiveResolution.extMk_hom, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIso_inv, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom, CategoryTheory.PrelaxFunctorStruct.mkOfHomPrefunctors_map₂, CategoryTheory.Presheaf.isLocallyInjective_toSheafify, HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff', CategoryTheory.regularTopology.mem_sieves_iff_hasEffectiveEpi, CategoryTheory.Bicategory.LanLift.existsUnique, CategoryTheory.Bicategory.postcomposing₂_map_as_app_toNatTrans_app, CategoryTheory.conjugateEquiv_symm_iso, CategoryTheory.ComposableArrows.IsComplex.zero_assoc, CategoryTheory.ObjectProperty.monoModSerre_zero_iff, CategoryTheory.Limits.kernel.map_zero, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_naturality, CategoryTheory.ShortComplex.RightHomologyMapData.zero_φH, CategoryTheory.Iso.op2_hom_unop2, CategoryTheory.Equivalence.symmEquivFunctor_map, CochainComplex.HomComplex.Cochain.fromSingleMk_add, CategoryTheory.Limits.Cofork.IsColimit.homIso_apply_coe, CategoryTheory.finrank_endomorphism_eq_one, AlgebraicGeometry.etale_le_weaklyEtale, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.exists_d_comp_eq_d, Bicategory.Opposite.bicategory_leftUnitor_inv_unop2, CategoryTheory.CatEnriched.hComp_id_heq, CategoryTheory.Bicategory.Prod.sectR_mapId_inv, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp, CategoryTheory.Limits.image.ι_zero, CategoryTheory.Abelian.SpectralObject.ιE_δFromOpcycles_assoc, CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext, CategoryTheory.Limits.kernel.ι_of_mono, CategoryTheory.Limits.inl_of_isLimit, CategoryTheory.Functor.toPseudofunctor_obj, CategoryTheory.Pretriangulated.contractibleTriangle_mor₂, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app, CategoryTheory.shrinkYonedaObjObjEquiv_map_app_assoc, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom, CategoryTheory.Monad.adj_unit, CategoryTheory.Subfunctor.ofSection_eq_range', CategoryTheory.MonObj.mul_comp, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero, groupCohomology.map₁_one, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, CategoryTheory.PrelaxFunctor.map₂_hom_inv, CategoryTheory.Limits.coneOfIsSplitMono_π_app, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hf, CategoryTheory.Functor.partialRightAdjointHomEquiv_map, CategoryTheory.StrictlyUnitaryLaxFunctor.id_mapComp, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app, CategoryTheory.Lax.LaxTrans.Modification.vcomp_app, CategoryTheory.linearYoneda_map_app, CategoryTheory.Join.isoMkFunctor_inv_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_base, TopModuleCat.hom_add, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.Lax.OplaxTrans.comp_app, CategoryTheory.Lax.LaxTrans.LaxFunctor.bicategory_whiskerRight_as_app, CategoryTheory.Functor.CorepresentableBy.homEquiv_eq, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_fst_apply, CommRingCat.moduleCatRestrictScalarsPseudofunctor_map, CategoryTheory.ShortComplex.Splitting.g_s, CategoryTheory.Abelian.LeftResolution.karoubi.F'_obj_p, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, CategoryTheory.Hom.mul_def, CochainComplex.IsKInjective.homotopyZero_def, CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_i, CategoryTheory.Pseudofunctor.DescentData'.comp_pullHom'', CategoryTheory.ShortComplex.Homotopy.ofEq_h₀, CategoryTheory.ShortComplex.liftCycles_comp_homologyπ_eq_zero_iff_up_to_refinements, CategoryTheory.ShortComplex.HomologyMapData.zero_left, CategoryTheory.Bicategory.postcomposing₂_obj_naturality_hom_toNatTrans_app, CategoryTheory.Grp.Hom.hom_hom_inv, HomologicalComplex.opcyclesToCycles_homologyπ, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, CategoryTheory.MonoidalCategory.dite_whiskerRight, CategoryTheory.Limits.idZeroEquivIsoZero_apply_inv, CommRingCat.HomTopology.isEmbedding_pushout, Mathlib.Tactic.Bicategory.eval_bicategoricalComp, CategoryTheory.Presieve.preZeroHypercover_f, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_inv, Mathlib.Tactic.Bicategory.naturality_whiskerLeft, CategoryTheory.Localization.SmallHom.equiv_mkInv, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv, AlgebraicGeometry.IsLocalIso.le_of_isLocalAtSource, CategoryTheory.ObjectProperty.SerreClassLocalization.mono_iff, CategoryTheory.Subgroupoid.mem_map_iff, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, CategoryTheory.GrpObj.lift_conj_eq_mul_mul_inv_assoc, CategoryTheory.Adjunction.homAddEquiv_sub, CategoryTheory.tensorLeftHomEquiv_tensor, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_epi₁, CategoryTheory.Presheaf.restrictedULiftYoneda_map_app, CategoryTheory.Pseudofunctor.StrongTrans.homCategory_id_as_app, SSet.Subcomplex.yonedaEquiv_coe, CategoryTheory.Pseudofunctor.isPrestackFor_ofArrows_iff, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_assoc, CategoryTheory.Limits.biprod.sndKernelFork_ι, ComplexShape.Embedding.AreComplementary.hom_ext, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, CategoryTheory.Preadditive.forkOfKernelFork_pt, CategoryTheory.FreeBicategory.mk_left_unitor_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, SimplicialObject.Splitting.IndexSet.mk_fst, AddCommGrpCat.hom_nsmul, HomotopyCategory.quot_mk_eq_quotient_map, CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, CategoryTheory.eqToHom_comp_heq_iff, CochainComplex.HomComplex.Cocycle.toSingleMk_zero, HomologicalComplex.units_smul_f_apply, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, CategoryTheory.Limits.reflexivePair.compRightIso_hom_app, CategoryTheory.Preadditive.sum_comp, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_assoc, AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.comm, CategoryTheory.CatEnrichedOrdinary.Hom.mk_comp, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_fst, CategoryTheory.Pseudofunctor.CoGrothendieck.map_obj_fiber, imageToKernel_epi_comp, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map, CategoryTheory.Limits.ker.condition, HomologicalComplex.homotopyCofiber.inrX_fstX, CochainComplex.HomComplex.Cochain.leftUnshift_v, CategoryTheory.Presieve.map_iff, CategoryTheory.Oplax.LaxTrans.OplaxFunctor.bicategory_rightUnitor_inv_as_app, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_symm_apply, CategoryTheory.Limits.BinaryBicone.inr_fst_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three, SimplexCategoryGenRel.exists_P_σ_P_δ_factorization, DerivedCategory.HomologySequence.comp_δ_assoc, CategoryTheory.Comma.equivProd_inverse_map_left, CategoryTheory.Over.mk_surjective, Mathlib.Tactic.Bicategory.evalWhiskerRight_cons_whisker, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_inv, SheafOfModules.freeHomEquiv_symm_comp, CategoryTheory.WithTerminal.map_map, CategoryTheory.oplaxFunctorOfIsLocallyDiscrete_map, CategoryTheory.CosimplicialObject.cechConerveEquiv_symm_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', CategoryTheory.Pseudofunctor.whiskerLeftIso_mapId, CategoryTheory.Limits.biprod.decomp_hom_from, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_hom_right, CategoryTheory.Functor.map_smul, CategoryTheory.Iso.homCongr_refl, CategoryTheory.Bicategory.Prod.swap_map, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_inv_homologyι, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app, CategoryTheory.Limits.zero_of_comp_mono, CategoryTheory.InitiallySmall.exists_small_weakly_initial_set, CategoryTheory.Bicategory.Pith.rightUnitor_hom_iso, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id_assoc, CochainComplex.ConnectData.map_f, CategoryTheory.Functor.Additive.map_add, CategoryTheory.NatTrans.toCatHom₂_id, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois, CategoryTheory.Abelian.Preradical.toColon_hom_left_colonπ_assoc, CategoryTheory.Bicategory.Comonad.counit_comul_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left, Mathlib.Tactic.Bicategory.evalComp_cons, CategoryTheory.Join.opEquiv_functor_map_op_edge, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁, Bicategory.Opposite.op2_rightUnitor_inv, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.Pseudofunctor.id_mapId, CategoryTheory.yonedaMonObj_obj_coe, CategoryTheory.Functor.map_eq_zero_iff, CategoryTheory.Discrete.productEquiv_counitIso_hom_app, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₁_iff, SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero, CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_left, CategoryTheory.typeEquiv_counitIso_hom_app_hom_app, CategoryTheory.Pseudofunctor.DescentData.Hom.comm_assoc, SemiNormedGrp.hom_add, CategoryTheory.Triangulated.TStructure.eTruncGEπ_top, SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero, CategoryTheory.Biprod.unipotentLower_hom, CategoryTheory.BicategoricalCoherence.right'_iso, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.Lax.LaxTrans.naturality_comp_assoc, CategoryTheory.Join.mapIsoWhiskerRight_hom_app, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_K, CategoryTheory.Limits.zero_of_to_zero, Action.FintypeCat.toEndHom_apply, CategoryTheory.Bicategory.pentagon_assoc, CategoryTheory.Limits.Fork.ofι_π_app, CategoryTheory.TwoSquare.StructuredArrowRightwards.mk_surjective, CategoryTheory.MorphismProperty.map_eq_iff_postcomp, CategoryTheory.Ind.exists_nonempty_arrow_mk_iso_ind_lim, CategoryTheory.Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, CategoryTheory.WithInitial.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.Presieve.regular.single_epi, CategoryTheory.yoneda_obj_obj, CategoryTheory.Join.opEquiv_functor_map_op_inclRight, CategoryTheory.uliftYonedaEquiv_comp, CategoryTheory.Limits.biprod.desc_eq, SSet.stdSimplex.face_obj, CategoryTheory.Limits.coconeOpEquiv_inverse_map, CategoryTheory.Bicategory.Adj.id_τr, CategoryTheory.Functor.sectionsEquivHom_naturality, Homotopy.nullHomotopicMap_f, CategoryTheory.Subgroupoid.IsWide.wide, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, CategoryTheory.Limits.snd_of_isColimit, CategoryTheory.Oplax.StrongTrans.Modification.id_app, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁, CategoryTheory.Bicategory.prod_rightUnitor_inv_fst, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_epi₂, CategoryTheory.IsCofiltered.wideCospan, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHom_unop, CategoryTheory.Subgroupoid.isThin_iff, HomologicalComplex.alternatingConst_iCycles_even_comp_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_inv_app_unmop_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.Limits.biproduct.lift_desc, SSet.stdSimplex.map_apply, HomologicalComplex.d_toCycles, CategoryTheory.LaxFunctor.mapComp'_eq_mapComp, CategoryTheory.Lax.LaxTrans.leftUnitor_hom_as_app, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq, CategoryTheory.Bicategory.Adj.iso₂Mk_inv_τl, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CochainComplex.HomComplex.Cochain.ofHom_sub, CategoryTheory.conjugateEquiv_whiskerRight, CategoryTheory.IsPullback.exists_lift, CategoryTheory.Abelian.Preradical.ι_π, CategoryTheory.Oplax.LaxTrans.naturality_comp, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τl, CategoryTheory.WithInitial.prelaxfunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.bijection_symm_apply_id, CategoryTheory.MonoidalPreadditive.add_tensor, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, TopModuleCat.hom_zsmul, CategoryTheory.ShortComplex.opcyclesMap_neg, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, CategoryTheory.Limits.id_zero, CategoryTheory.Free.single_comp_single, CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq, CategoryTheory.Limits.cokernelBiprodInrIso_inv, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂'_homEquiv, CategoryTheory.IsPushout.inr_fst, CategoryTheory.Pretriangulated.contractible_distinguished₂, CategoryTheory.isCommAddMonObj_iff_isAddCommutative, Rep.resIndAdjunction_homEquiv_symm_apply, CategoryTheory.ShortComplex.Homotopy.ofNullHomotopic_h₂, CategoryTheory.Functor.isRepresentedBy_iff, CategoryTheory.ShortComplex.homologyι_descOpcycles_eq_zero_of_boundary, CategoryTheory.Localization.homEquiv_comp, CategoryTheory.ShortComplex.Homotopy.symm_h₀, CategoryTheory.rightDistributor_inv, SSet.Homotopy.h₀, CategoryTheory.Bicategory.whiskerLeft_isIso, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp, Action.hom_injective, CategoryTheory.ShortComplex.Homotopy.equivSubZero_symm_apply, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, CategoryTheory.Oplax.StrongTrans.isoMk_hom_as_app, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp, CategoryTheory.Functor.homologySequenceδ_comp_assoc, CategoryTheory.Hom.addEquivCongrRight_symm_apply, Action.nsmul_hom, HomologicalComplex.d_pOpcycles_assoc, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_inv, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_leftAdd, CategoryTheory.CostructuredArrow.w_prod_snd, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_functor_map, CategoryTheory.isCardinalFiltered_iff_aux₁, CategoryTheory.ShortComplex.nullHomotopic_τ₁, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, CategoryTheory.IsPullback.inl_snd, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom_isIso, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality_assoc, CategoryTheory.ProjectiveResolution.of_def, CommRingCat.HomTopology.instT2SpaceHomOfCarrier, CategoryTheory.Pseudofunctor.mapComp'_naturality_2_assoc, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_id_fiber, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition', CategoryTheory.ShortComplex.comp_pOpcycles_eq_zero_iff_up_to_refinements, HomologicalComplex₂.totalAux.d₂_eq', CategoryTheory.IsCofiltered.inf_objs_exists, CategoryTheory.Bicategory.eqToHomTransIso_refl_right, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitUnop_π_apply, CategoryTheory.Pseudofunctor.ObjectProperty.map_map_hom, HomotopicalAlgebra.CofibrantObject.exists_bifibrant_map, CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_apply_homEquiv, CategoryTheory.ShortComplex.leftHomologyMap_nullHomotopic, TopologicalSpace.OpenNhds.id_apply, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_assoc, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₁_iff, Homotopy.zero, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.Quotient.instSubsingletonHom, CategoryTheory.Limits.imageSubobject_zero_arrow, CategoryTheory.PreGaloisCategory.exists_lift_of_mono_of_isConnected, CategoryTheory.Functor.map_sub, CategoryTheory.Bicategory.postcomposingCat_obj, CategoryTheory.Localization.Construction.lift_map, CategoryTheory.ProjectiveResolution.π_f_succ, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles_assoc, HomologicalComplex₂.totalAux.d₁_eq, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans, CategoryTheory.CatEnriched.hComp_assoc, CategoryTheory.Lax.OplaxTrans.Modification.naturality, CategoryTheory.yonedaEquiv_yoneda_map, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, Preorder.subsingleton_hom, CategoryTheory.PreZeroHypercover.empty_f, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv, SSet.RelativeMorphism.botEquiv_apply, CategoryTheory.PrelaxFunctor.map₂_inv_hom_isIso_assoc, CategoryTheory.Abelian.SpectralObject.H_map_twoδ₂Toδ₁_toCycles, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst_assoc, CategoryTheory.Pseudofunctor.mkOfLax'_mapId_hom, CategoryTheory.IsPushout.of_hasBinaryCoproduct, CategoryTheory.Idempotents.zero_def, CategoryTheory.Subgroupoid.IsNormal.generatedNormal_le, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, CategoryTheory.Lax.LaxTrans.rightUnitor_hom_as_app, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.congr, CategoryTheory.Limits.pullback.exists_lift, CategoryTheory.Abelian.Ext.mk₀_add, CategoryTheory.IsPullback.of_hasBinaryProduct, CategoryTheory.Quotient.functor_homRel_eq_compClosure_eqvGen, CategoryTheory.Limits.imageSubobject_zero, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_inv, CategoryTheory.ShortComplex.rightHomologyι_descOpcycles_π_eq_zero_of_boundary, CategoryTheory.unit_conjugateEquiv_symm, CategoryTheory.CategoryOfElements.comp_val, CategoryTheory.IsPushout.exists_desc, HomologicalComplex.liftCycles_homologyπ_eq_zero_of_boundary, CategoryTheory.CatEnrichedOrdinary.Hom.id_eq, Homotopy.extend.hom_eq_zero₁, CategoryTheory.PreGaloisCategory.evaluation_aut_bijective_of_isGalois, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply, CategoryTheory.Lax.LaxTrans.naturality_id_assoc, CategoryTheory.Groupoid.vertexGroup_one, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, CategoryTheory.LaxFunctor.mapComp_naturality_right_assoc, CategoryTheory.Limits.BinaryFan.rightUnitor_inv, prevD_eq, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, CategoryTheory.Preadditive.comp_neg_assoc, CategoryTheory.FreeBicategory.preinclusion_map₂, CategoryTheory.OplaxFunctor.mapComp'_comp_mapComp'_whiskerRight, CategoryTheory.AddMonObj.zero_eq_zero, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_inv, HomologicalComplex.mapBifunctor.d₂_eq, CategoryTheory.Bicategory.prod_whiskerLeft_fst, CategoryTheory.Oplax.OplaxTrans.rightUnitor_hom_as_app, CommRingCat.HomTopology.precompHomeomorph_symm_apply, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, CategoryTheory.unit_conjugateEquiv, SSet.stdSimplex.yonedaEquiv_symm_app_objEquiv_symm, CategoryTheory.OplaxFunctor.map₂_associator_assoc, CategoryTheory.Bicategory.precomp_obj, DerivedCategory.left_fac_of_isStrictlyLE_of_isStrictlyGE, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, AlgebraicTopology.AlternatingCofaceMapComplex.d_squared, CategoryTheory.Free.embedding_map, CategoryTheory.Limits.biprod.total, CategoryTheory.Limits.cokernel.π_of_zero, CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_map_coe, CategoryTheory.Limits.coconeUnopOfConeEquiv_inverse_map, Symmetrify.of_map, CategoryTheory.Pseudofunctor.map₂_whisker_left, CategoryTheory.Abelian.SpectralObject.δToCycles_πE_assoc, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_pt, CategoryTheory.uliftYoneda_obj_map, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, CategoryTheory.Quiv.adj_homEquiv, CategoryTheory.Triangulated.TStructure.zero, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀, CategoryTheory.Groupoid.isoEquivHom_apply, CategoryTheory.Enriched.FunctorCategory.homEquiv_id, AlgebraicGeometry.exists_map_preimage_eq_map_preimage, HomologicalComplex.ι_mapBifunctorFlipIso_inv_assoc, CategoryTheory.Groupoid.isoEquivHom_symm_apply_hom, HomologicalComplex.extend_single_d, CategoryTheory.LaxFunctor.mapComp'_whiskerRight_comp_mapComp'_assoc, CategoryTheory.projective_iff_llp_epimorphisms_zero, CategoryTheory.Lax.OplaxTrans.Modification.vcomp_app, SSet.horn₃₂.exists_desc, CategoryTheory.ShortComplex.liftCycles_leftHomologyπ_eq_zero_of_boundary_assoc, CategoryTheory.ProjectiveResolution.add_extMk, HomologicalComplex.mapBifunctor.d₁_eq_zero, CategoryTheory.Limits.HasLimitOfHasProductsOfHasEqualizers.buildLimit_pt, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', CategoryTheory.Pretriangulated.Triangle.coyoneda_exact₃, CategoryTheory.Pseudofunctor.StrongTrans.isoMk_hom_as_app, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_φ, CategoryTheory.Bicategory.adjointifyCounit_left_triangle, CategoryTheory.Oplax.LaxTrans.OplaxFunctor.bicategory_leftUnitor_hom_as_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_assoc, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_id, CategoryTheory.PreGaloisCategory.instFiniteHomOfIsConnected, CategoryTheory.Localization.homEquiv_symm_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, CategoryTheory.rightUnitor_def, CategoryTheory.Functor.curry₃_obj_obj_obj_map, CategoryTheory.ShortComplex.rightHomologyMap'_add, CategoryTheory.Groupoid.invEquiv_apply, HomologicalComplex₂.d₁_eq_zero, CategoryTheory.Lax.StrongTrans.toLax_naturality, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_hom_app, CommRingCat.HomTopology.isClosedEmbedding_hom, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Subobject.factorThru_add_sub_factorThru_right, CategoryTheory.Abelian.AbelianStruct.imageι_π_assoc, HomologicalComplex.zsmul_f_apply, groupCohomology.mapCocycles₁_one, CategoryTheory.ObjectProperty.epiModSerre_zero_iff, CategoryTheory.Subgroupoid.hom.faithful, CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists, SSet.Truncated.HomotopyCategory₂.homMk_surjective, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_symm_apply, CategoryTheory.unitCompPartialBijective_natural, CategoryTheory.SimplicialThickening.functor_map, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id, CategoryTheory.WithTerminal.ofCommaMorphism_app, CochainComplex.singleFunctor_obj_d, CategoryTheory.uliftYoneda_obj_obj, CategoryTheory.Pseudofunctor.toOplax_mapId, CategoryTheory.dite_comp, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_zsmul_f, CategoryTheory.ShortComplex.LeftHomologyData.f'_π, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_hom, CategoryTheory.FinCategory.objAsTypeToAsType_map, SimplexCategory.eq_comp_δ_of_not_surjective', CategoryTheory.Subobject.mk_eq_bot_iff_zero, CategoryTheory.Localization.SmallHom.equiv_mk, CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_right, AlgebraicGeometry.Scheme.IsLocallyDirected.fst_inv_eq_snd_inv, CategoryTheory.eqToHom_comp_heq, CategoryTheory.Preadditive.instMonoNegHom, CategoryTheory.Lax.LaxTrans.LaxFunctor.bicategory_whiskerLeft_as_app, CategoryTheory.Bicategory.prod_associator_inv_fst, HomologicalComplex.homologyMap_add, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv, CategoryTheory.PrelaxFunctor.map₂_hom_inv_assoc, Mathlib.Tactic.Bicategory.evalWhiskerLeft_of_cons, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerLeft, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_hom, HomotopicalAlgebra.LeftHomotopyClass.mk_surjective, CategoryTheory.Pretriangulated.Triangle.neg_hom₁, CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_eq_eqToHom, SheafOfModules.freeHomEquiv_comp_apply, ContinuousCohomology.MultiInd.d_comp_d_assoc, CategoryTheory.yonedaMon_map_app, CategoryTheory.Abelian.SpectralObject.zero₂, SemiNormedGrp.hom_neg, CategoryTheory.shrinkYonedaEquiv_naturality, Hom.opEquiv_apply, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly_assoc, CategoryTheory.Lax.LaxTrans.LaxFunctor.bicategory_rightUnitor_hom_as_app, CategoryTheory.Limits.KernelFork.IsLimit.isIso_ι, HomologicalComplex.extend_d_to_eq_zero, CategoryTheory.yonedaEquiv_naturality', CategoryTheory.Bicategory.InducedBicategory.bicategory_Hom, CategoryTheory.StrictlyUnitaryLaxFunctor.map_id, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality, Action.sub_hom, Rep.smul_hom, FintypeCat.toLightProfinite_map_hom_hom_apply, CategoryTheory.BicategoricalCoherence.tensorRight'_iso, CategoryTheory.Pseudofunctor.DescentData'.comp_hom_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_obj, CategoryTheory.Subgroupoid.mem_ker_iff, CategoryTheory.oplaxFunctorOfIsLocallyDiscrete_obj, CategoryTheory.Types.instPreservesLimitsOfSizeForgetTypeHom, CategoryTheory.Lax.OplaxTrans.associator_hom_as_app, PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, CategoryTheory.Bicategory.prod_Hom, CategoryTheory.Bicategory.Pith.whiskerRight_iso_hom, CategoryTheory.Functor.mapZeroObject_inv, CategoryTheory.Bicategory.comp_whiskerRight_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv, CategoryTheory.Functor.cocones_obj, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, CategoryTheory.tensorHom_def, CategoryTheory.Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app, CategoryTheory.Limits.coker.condition, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply', HomologicalComplex.nsmul_f_apply, CategoryTheory.Types.instIsEquivalenceForgetTypeHom, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.rightHomologyData_p, CategoryTheory.NatTrans.mapElements_map_coe, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv, CategoryTheory.comp_eqToHom_heq_iff, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight, Rep.FiniteCyclicGroup.chainComplexFunctor_map_f, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_inv, CategoryTheory.Bicategory.LeftExtension.whiskerIdCancel_right, CategoryTheory.Bicategory.prod_rightUnitor_inv_snd, CategoryTheory.Pretriangulated.Triangle.neg_hom₃, Rep.smul_comp, CategoryTheory.NatTrans.app_zero, CategoryTheory.NatTrans.prod'_app_fst, CategoryTheory.Linear.comp_units_smul, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, CategoryTheory.ShortComplex.Homotopy.refl_h₁, AlgebraicGeometry.IsImmersion.isImmersion_iff_exists, CategoryTheory.Over.toOverSectionsAdj_unit_app, CategoryTheory.ShortComplex.Exact.shortExact, CategoryTheory.Functor.toPreimages_map, CategoryTheory.Pseudofunctor.toDescentDataAsCoalgebra_obj_hom, CategoryTheory.Bicategory.Pith.associator_hom_iso, CategoryTheory.Limits.KernelFork.condition, CategoryTheory.TransportEnrichment.forgetEnrichmentEquivInverse_map, CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.familyOfElements_apply, CategoryTheory.Limits.biproduct.fromSubtype_π, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_assoc, CategoryTheory.uliftYonedaEquiv_uliftYoneda_map, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_app_toFunctor_map, CategoryTheory.Limits.kernel.ι_of_zero, prevD_eq_zero, CategoryTheory.finrank_hom_simple_simple_eq_zero_iff, CategoryTheory.MonObj.one_comp, CategoryTheory.Quotient.compClosure.congruence, CategoryTheory.Lax.LaxTrans.naturality_id, CategoryTheory.ShortComplex.exact_and_epi_g_iff_g_is_cokernel, CategoryTheory.Functor.IsCartesian.universal_property, CategoryTheory.InjectiveResolution.extMk_eq_zero_iff, CategoryTheory.Pseudofunctor.DescentData.ofObj_obj, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_map_f, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, CategoryTheory.Lax.StrongTrans.naturality_comp_assoc, CategoryTheory.Bicategory.associator_naturality_left_assoc, CategoryTheory.finrank_hom_simple_simple_eq_zero_of_not_iso, CategoryTheory.StrictPseudofunctorCore.map₂_right_unitor, Condensed.epi_iff_locallySurjective_on_compHaus, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_inv_as_app, groupCohomology.mapShortComplexH2_zero, CategoryTheory.Bicategory.prod_leftUnitor_inv_fst, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app_assoc, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_map, CategoryTheory.NonPreadditiveAbelian.add_zero, CategoryTheory.Limits.Fork.IsLimit.homIso_apply_coe, CategoryTheory.Adjunction.instMonoCoeEquivHomObjHomEquivOfReflectsMonomorphisms, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂, CategoryTheory.Bicategory.hom_inv_whiskerRight, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, CategoryTheory.InducedCategory.homAddEquiv_symm_apply_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Bicategory.prod_rightUnitor_hom_fst, CategoryTheory.Bicategory.Adjunction.left_triangle, CategoryTheory.Functor.toPseudofunctor_mapId, CategoryTheory.Limits.cokernel.desc_zero, DerivedCategory.HomologySequence.epi_homologyMap_mor₁_iff, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_hom_app, FreeGroupoid.congr_comp_reverse, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', Rep.resIndAdjunction_homEquiv_apply, CommRingCat.HomTopology.mvPolynomialHomeomorph_symm_apply_hom, CategoryTheory.coyonedaEquiv_naturality, CategoryTheory.Oplax.LaxTrans.Modification.vcomp_app, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_snd, Opens.mayerVietorisSquare_X₂, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, CategoryTheory.Pseudofunctor.CoGrothendieck.ext_iff, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_comp, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_apply, CategoryTheory.Limits.PushoutCocone.mk_ι_app, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_left_symm_assoc, CategoryTheory.coyonedaEquiv_apply, Mathlib.Tactic.Bicategory.naturality_inv, CategoryTheory.Lax.OplaxTrans.naturality_naturality, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, SemimoduleCat.homAddEquiv_apply, CategoryTheory.IsCoreflexivePair.common_retraction, AddGrpCat.ofHom_injective, CategoryTheory.PreZeroHypercover.shrink_X, CategoryTheory.Functor.PreservesHomology.preservesCokernels, groupHomology.d₁₀_comp_coinvariantsMk, AlgebraicGeometry.LocallyRingedSpace.Hom.ext_iff, CategoryTheory.ShortComplex.HasLeftHomology.of_hasCokernel, CategoryTheory.Preadditive.cokernelCoforkOfCofork_π, CategoryTheory.LaxFunctor.whiskerLeft_mapComp'_comp_mapComp', CategoryTheory.Limits.biproduct.toSubtype_fromSubtype, CategoryTheory.Bicategory.Prod.fst_mapId_hom, CategoryTheory.Quiv.homOfEq_map_homOfEq, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv, CategoryTheory.shrinkYonedaMon_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Bicategory.associator_naturality_middle, CategoryTheory.Functor.IsStronglyCartesian.universal_property', CategoryTheory.MonObj.comp_pow, CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_connected, CategoryTheory.Bicategory.prod_id_snd, AlgebraicGeometry.exists_appTop_map_eq_zero_of_isAffine_of_isLimit, CategoryTheory.Presheaf.isLocallyInjective_forget_iff, CategoryTheory.Functor.comp_homologySequenceδ, CategoryTheory.regularTopology.isLocallySurjective_iff, CategoryTheory.Pseudofunctor.DescentData.hom_comp_assoc, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, DerivedCategory.HomologySequence.mono_homologyMap_mor₂_iff, CategoryTheory.Limits.cokernelBiprodInrIso_hom, CategoryTheory.Limits.kernel.condition, HomologicalComplex.homotopyCofiber.inlX_desc_f_assoc, CategoryTheory.MonoOver.bot_arrow_eq_zero, CategoryTheory.ShortComplex.LeftHomologyData.wπ_assoc, CategoryTheory.WithInitial.equivComma_inverse_map_app, CategoryTheory.Biprod.column_nonzero_of_iso, CategoryTheory.Pseudofunctor.mkOfOplax'_mapId_hom, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty, CategoryTheory.Pseudofunctor.Grothendieck.map_obj_fiber, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.g', CategoryTheory.ShortComplex.smul_τ₃, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, CochainComplex.HomComplex.Cochain.fromSingleMk_zero, CategoryTheory.Oplax.LaxTrans.vComp_naturality_comp, CategoryTheory.Functor.CorepresentableBy.id_homEquiv_symm_apply, CategoryTheory.ShortComplex.homologyMap_neg, CategoryTheory.Pseudofunctor.mkOfOplax'_mapComp_hom, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp, CochainComplex.mappingCone.decomp_from, Representation.linHom.invariantsEquivRepHom_apply, CategoryTheory.Pretriangulated.distinguished_cocone_triangle₂, CategoryTheory.Subgroupoid.IsWide.id_mem, CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc, AlgebraicTopology.DoldKan.P_succ, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, CategoryTheory.ShortComplex.nullHomotopic_τ₂, CategoryTheory.MorphismProperty.Comma.mapRightEq_inv_app_right, CategoryTheory.Bicategory.prod_leftUnitor_inv_snd, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app_assoc, HomologicalComplex.homotopyCofiber.d_fstX, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, CategoryTheory.unop_neg, CategoryTheory.StrictPseudofunctor.comp_map, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τl, HomotopicalAlgebra.FibrantObject.HoCat.exists_resolution, FGModuleCat.ihom_obj, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Bicategory.LeftExtension.IsKan.fac_assoc, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id, HomotopyCategory.Pretriangulated.distinguished_cocone_triangle, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_pt, CategoryTheory.CategoryOfElements.ext_iff, AlgebraicGeometry.RingedSpace.isUnit_res_of_isUnit_germ, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, CategoryTheory.Limits.biprod.inl_snd, CategoryTheory.Bicategory.leftUnitorNatIso_hom_app, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_Q, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_obj_fiber, CategoryTheory.Iso.unop2_op_inv, CochainComplex.mappingCone.inr_triangleδ_assoc, Rep.resCoindHomEquiv_symm_apply, CategoryTheory.PrelaxFunctor.map₂_inv, CategoryTheory.Biprod.ofComponents_comp, CategoryTheory.StrictPseudofunctorPreCore.map_comp, CategoryTheory.ShortComplex.HomologyMapData.zero_right, CategoryTheory.heq_comp, CategoryTheory.Limits.limit.existsUnique, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τl, CochainComplex.mappingCone.inl_v_snd_v_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomLeft_op, CategoryTheory.ShortComplex.Homotopy.symm_h₃, CategoryTheory.regularTopology.parallelPair_pullback_initial, CategoryTheory.Under.homMk_surjective, CategoryTheory.StrictPseudofunctor.mk''_map, HomologicalComplex.cylinder.inlX_π, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_inverse_map, CategoryTheory.Oplax.StrongTrans.naturality_naturality_assoc, CategoryTheory.Comonad.adj_counit, CategoryTheory.Lax.OplaxTrans.homCategory_comp_as_app, CategoryTheory.ShortComplex.SnakeInput.w₁₃_assoc, CategoryTheory.Pseudofunctor.isStackFor_iff, CategoryTheory.Adjunction.homAddEquiv_add, CategoryTheory.ShortComplex.comp_homologyπ_eq_iff_up_to_refinements, Bicategory.Opposite.opFunctor_obj, CategoryTheory.endomorphism_simple_eq_smul_id, CategoryTheory.Bicategory.Prod.sectL_mapId_hom, CategoryTheory.Limits.Sigma.ι_π, CategoryTheory.Triangulated.TStructure.liftTruncLT_aux, TopologicalSpace.Opens.coe_id, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_hom, CategoryTheory.CatCenter.smul_eq', CategoryTheory.ShortComplex.LeftHomologyMapData.add_φH, TopCat.presheafToTypes_map, CommRingCat.HomTopology.isEmbedding_hom, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_hom_hom, CategoryTheory.Adjunction.adjunctionOfEquivRight_unit_app, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.Pseudofunctor.isoMapOfCommSq_vert_id, CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_hom_right, HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff, CommRingCat.moduleCatExtendScalarsPseudofunctor_map, CategoryTheory.Grp.Hom.hom_pow, CategoryTheory.Functor.prod'_δ_fst, CategoryTheory.Functor.prod'_μ_snd, CategoryTheory.Bicategory.conjugateEquiv_symm_comm, CategoryTheory.surjective_up_to_refinements_of_epi, HomologicalComplex.biprod_inr_fst_f, CategoryTheory.Bicategory.Pith.whiskerLeft_iso_hom, AddCommGrpCat.zero_apply, CategoryTheory.Pseudofunctor.bijective_toDescentData_map_iff, AlgebraicGeometry.Scheme.stalkMap_congr_hom, CategoryTheory.Groupoid.CategoryTheory.Functor.mapVertexGroup_apply, CategoryTheory.Bicategory.mateEquiv_symm_apply, CategoryTheory.Functor.Elements.initialOfCorepresentableBy_snd, CategoryTheory.Pseudofunctor.map₂_whisker_left_assoc, CategoryTheory.Limits.cokernel.condition_assoc, CategoryTheory.ObjectProperty.SerreClassLocalization.map_comp_eq_zero_iff_of_epi_mono, ModuleCat.ExtendRestrictScalarsAdj.homEquiv_symm_apply, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv, CategoryTheory.Lax.LaxTrans.whiskerRight_as_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, PresheafOfModules.homEquivOfIsLocallyBijective_apply, TopModuleCat.comp_cokerπ, CategoryTheory.Limits.kernelSubobject_arrow_comp_apply, CategoryTheory.Bicategory.Strict.rightUnitor_eqToIso, CategoryTheory.Bicategory.leftUnitor_whiskerRight, CategoryTheory.Limits.IsZero.unique_from, Bicategory.Opposite.homCategory_comp_unop2, CategoryTheory.Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, CategoryTheory.Abelian.Preradical.toColon_hom_left_colonπ, HomologicalComplex.homotopyCofiber.eq_desc, PresheafOfModules.unitHomEquiv_apply_coe, Rep.zsmul_hom, CategoryTheory.Join.pseudofunctorRight_mapId_hom_toNatTrans_app, CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork_p, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_d, Rep.coindResAdjunction_homEquiv_apply, CochainComplex.mappingCone.inr_f_triangle_mor₃_f, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, groupCohomology.inhomogeneousCochains.d_comp_d, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, CategoryTheory.PreGaloisCategory.exists_autMap, CategoryTheory.conjugateEquiv_symm_comp, CategoryTheory.StrictPseudofunctor.toFunctor_obj, CategoryTheory.Sieve.functorInclusion_app, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_snd, Opens.coe_mayerVietorisSquare_X₁, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, CategoryTheory.Oplax.StrongTrans.naturality_id, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_assoc, CategoryTheory.Bicategory.associator_eqToHom_inv_assoc, AlgebraicTopology.DoldKan.Hσ_eq_zero, CochainComplex.ConnectData.d₀_comp, CategoryTheory.Oplax.LaxTrans.OplaxFunctor.bicategory_leftUnitor_inv_as_app, CategoryTheory.StrictPseudofunctor.map_comp, CategoryTheory.Limits.Trident.IsLimit.homIso_apply_coe, CategoryTheory.associator_def, CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_fiber_nonempty, CategoryTheory.Functor.toOplaxFunctor'_map, AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq, HomologicalComplex.tensor_unit_d₂, CategoryTheory.Bicategory.HasLeftKanLift.hasInitial, CategoryTheory.Functor.FullyFaithful.homAddEquiv_symm_apply, CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm, SSet.stdSimplex.σ_objEquiv_symm_apply, CategoryTheory.Join.opEquiv_inverse_map_inclLeft_op, CategoryTheory.Bicategory.prod_leftUnitor_hom_snd, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, CategoryTheory.ShortComplex.RightHomologyData.ι_descQ_eq_zero_of_boundary_assoc, ChainComplex.mk'_congr_succ'_d, CategoryTheory.tensorRightHomEquiv_naturality, CategoryTheory.Limits.coneOpEquiv_counitIso, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, CategoryTheory.IsReflexivePair.common_section, CategoryTheory.Limits.cokernelBiproductιIso_inv, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.Functor.complete_distinguished_essImageDistTriang_morphism, CochainComplex.IsKProjective.nonempty_homotopy_zero, CategoryTheory.Pseudofunctor.DescentData'.pullHom'₁₃_eq_pullHom_of_chosenPullback₃_assoc, CategoryTheory.ShortComplex.Exact.desc', CategoryTheory.Limits.piPiIso_hom, CategoryTheory.Subgroupoid.Map.arrows_iff, SimplicialObject.Splitting.IndexSet.fac_pull, CategoryTheory.Groupoid.vertexGroupIsomOfMap_apply, CategoryTheory.StrictlyUnitaryPseudofunctor.mapId_eq_eqToIso, SimplicialObject.Split.cofan_inj_naturality_symm_assoc, CategoryTheory.MorphismProperty.Comma.ext_iff, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.id_obj, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight_assoc, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_symm_apply, CategoryTheory.Pseudofunctor.StrongTrans.isoMk_inv_as_app, CategoryTheory.Bicategory.whisker_exchange_assoc, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, CategoryTheory.AsSmall.up_map_down, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_fst, Hom.opEquiv_symm_apply, CategoryTheory.tensorRightHomEquiv_tensor, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, CategoryTheory.MonObj.mul_comp_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_hom_as_app, CategoryTheory.Bicategory.yoneda_mapId_inv_as_app_toNatTrans_app, CategoryTheory.Limits.kernelBiproductπIso_inv, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₁, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_f_coe, CategoryTheory.Limits.IsColimit.pullback_zero_ext, HomologicalComplex.homologyι_comp_fromOpcycles_assoc, CategoryTheory.Subfunctor.range_eq_ofSection', CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_hom, AlgebraicTopology.DoldKan.QInfty_comp_PInfty, CategoryTheory.unop_add, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_inv_hom, CochainComplex.HomComplex.Cochain.fromSingleMk_surjective, CategoryTheory.Functor.FullyFaithful.homNatIso'_hom_app_down, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv, CategoryTheory.Limits.parallelPairHomMk_app, Rep.nsmul_hom, CategoryTheory.Preadditive.kernelForkOfFork_ι, CategoryTheory.Bicategory.pentagon, CategoryTheory.CatEnrichedOrdinary.Hom.base_comp, CategoryTheory.ShortComplex.Homotopy.comp_h₁, CategoryTheory.ULiftHom.up_map_down, CategoryTheory.Over.homMk_surjective, CategoryTheory.Oplax.OplaxTrans.homCategory_comp_as_app, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMap_app, CategoryTheory.Pretriangulated.Triangle.zero_hom₁, CategoryTheory.Bicategory.Prod.snd_obj, HomologicalComplex.cylinder.inlX_π_assoc, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.Functor.zero_of_map_zero, CategoryTheory.Limits.pushout.exists_desc, CategoryTheory.Types.instPreservesColimitsOfSizeForgetTypeHom, TopCat.Presheaf.covering_presieve_eq_self, CategoryTheory.WithTerminal.liftFromOverComp_hom_app, CategoryTheory.Functor.coe_mapAddHom, CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsLimitKernelFork_φH, CategoryTheory.ShortComplex.SnakeInput.L₀_g_δ, CategoryTheory.MorphismProperty.HasRightCalculusOfFractions.ext, CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_symm_apply_homEquiv, HomologicalComplex₂.d₂_eq_zero', CategoryTheory.Functor.RepresentableBy.equivUliftYonedaIso_symm_apply_homEquiv, CategoryTheory.Bicategory.rightUnitor_naturality_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_assoc, Path.eq_toPath_comp_of_length_eq_succ, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom_assoc, CategoryTheory.Oplax.LaxTrans.associator_hom_as_app, CategoryTheory.ShortComplex.Splitting.leftHomologyData_π, Rep.coindVEquiv_apply, CategoryTheory.Bicategory.postcomp₂_naturality_hom_toNatTrans_app, CategoryTheory.Abelian.Ext.mk₀_sum, CategoryTheory.Lax.OplaxTrans.vComp_naturality_naturality, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.Limits.prod.inl_snd_assoc, FintypeCat.equivEquivIso_symm_apply_apply, CategoryTheory.Types.hom_eq_coe, CategoryTheory.Lax.LaxTrans.isoMk_hom_as_app, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, HomologicalComplex.d_comp_d', CategoryTheory.Limits.bicone_ι_π_ne_assoc, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.regularTopology.isLocallySurjective_sheaf_of_types, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, CategoryTheory.Prod.snd_map, imageToKernel_epi_of_zero_of_mono, CategoryTheory.Limits.HasZeroMorphisms.zero_comp, HomologicalComplex.zero_f, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top', CategoryTheory.CatEnrichedOrdinary.id_hComp, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃, CategoryTheory.OplaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom, CategoryTheory.nerve.homEquiv_id, CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.shrinkYonedaObjObjEquiv_obj_map_assoc, CochainComplex.mkHom_f_succ_succ, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_id, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_eq_zero, CategoryTheory.MorphismProperty.PreIndSpreads.exists_isPushout, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_map_hom, CategoryTheory.ConcreteCategory.hom_injective, CategoryTheory.Prod.fac'_assoc, CategoryTheory.Functor.isIso_ranAdjunction_homEquiv_iff, CategoryTheory.Presheaf.isLocallySurjective_iff_whisker_forget, CategoryTheory.LocallyDiscrete.mkPseudofunctor_map, CochainComplex.mappingCone.d_snd_v_assoc, CategoryTheory.Lax.LaxTrans.vComp_naturality_id, CategoryTheory.Lax.OplaxTrans.associator_inv_as_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomLeft_unop, CategoryTheory.Abelian.SpectralObject.iCycles_δ, CategoryTheory.HomOrthogonal.matrixDecomposition_comp, Representation.coind'_apply_apply, CategoryTheory.Functor.map_comp_heq', groupCohomology.d₁₂_comp_d₂₃_assoc, CategoryTheory.ShortComplex.Exact.comp_eq_zero_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.naturality_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, CochainComplex.shiftFunctor_map_f, CategoryTheory.Enriched.Functor.natTransEquiv_symm_app_app_apply, CategoryTheory.Lax.OplaxTrans.id_naturality, CategoryTheory.isCommMonObj_iff_isMulCommutative, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_inv_right, CategoryTheory.ShortComplex.cyclesMap'_zero, CochainComplex.mappingCone.d_snd_v', CochainComplex.HomComplex.Cocycle.equivHomShift_symm_apply, CategoryTheory.ObjectProperty.trW_iff', CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_epi₁, CategoryTheory.Bicategory.Adj.iso₂Mk_hom_τl, CategoryTheory.ShortComplex.zero_τ₃, SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk, CategoryTheory.ShortComplex.HasRightHomology.of_hasCokernel, CategoryTheory.Limits.biproduct.ι_π_ne, CategoryTheory.CoreSmallCategoryOfSet.functor_map, CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₃, CochainComplex.mappingCocone.inl_v_snd_v, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObj_obj, AlgebraicTopology.DoldKan.Γ₀_map_app, CategoryTheory.PrelaxFunctor.mapFunctor_map, CategoryTheory.ObjectProperty.leftOrthogonal.map_bijective_of_isTriangulated, CategoryTheory.ShortComplex.Homotopy.sub_h₃, CategoryTheory.Bicategory.whiskerRight_congr, CategoryTheory.Limits.biproduct.fromSubtype_π_assoc, CategoryTheory.Oplax.StrongTrans.categoryStruct_comp_naturality, LightCondensed.free_internallyProjective_iff_tensor_condition', CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_apply, CategoryTheory.Idempotents.split_imp_of_iso, CategoryTheory.Prod.hom_ext_iff, CategoryTheory.Limits.Cone.equiv_inv_π, CategoryTheory.ShortComplex.Homotopy.trans_h₂, Action.FintypeCat.quotientToEndHom_mk, CategoryTheory.ShortComplex.kernel_ι_comp_cokernel_π_comp_cokernelToAbelianCoimage, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_assoc, CategoryTheory.Bicategory.LeftLift.whisker_unit, CategoryTheory.ShortComplex.nullHomotopic_τ₃, CategoryTheory.ShortComplex.rightHomologyMap'_nullHomotopic, AlgebraicTopology.DoldKan.Q_f_0_eq, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_symm_apply, CategoryTheory.Triangulated.TStructure.zero_of_isLE_of_isGE, CategoryTheory.ShortComplex.RightHomologyData.wι, CategoryTheory.Oplax.OplaxTrans.naturality_id_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero, HomologicalComplex.mapBifunctor.d_eq, CategoryTheory.prod_comp_fst, HomologicalComplex.comp_homologyπ_eq_iff_up_to_refinements, CategoryTheory.IsPullback.zero_left, CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, CategoryTheory.Sheaf.isLocallyInjective_forget, CategoryTheory.ShortComplex.iCycles_g_assoc, CategoryTheory.Bicategory.prod_homCategory_id_fst, SingleObj.toHom_apply, CategoryTheory.OplaxFunctor.map₂_leftUnitor, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Sieve.uliftNatTransOfLe_app_down_coe, CategoryTheory.Bicategory.conjugateEquiv_symm_comp, CategoryTheory.WithInitial.equivComma_inverse_obj_map, CategoryTheory.ShortComplex.Exact.mono_g_iff, ModuleCat.hom_sum, CategoryTheory.ShortComplex.SnakeInput.w₀₂, CategoryTheory.ShortComplex.rightHomologyMap_zero, CategoryTheory.ShortComplex.exact_iff_i_p_zero, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_assoc, CategoryTheory.Limits.Bicone.ofLimitCone_ι, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom_assoc, CategoryTheory.CommSq.right_adjoint_hasLift_iff, CategoryTheory.Limits.reflexivePair.mkNatIso_inv_app, CategoryTheory.Limits.biprod.map_eq, CategoryTheory.Abelian.SpectralObject.d_map_fourδ₄Toδ₃, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, starEquivCostar_apply_snd, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_snd_apply, CategoryTheory.StrictPseudofunctor.mk'_map, CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext', CategoryTheory.Bicategory.mateEquiv_hcomp, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_obj, CategoryTheory.subsingleton_of_unop, CategoryTheory.Iso.homCongr_apply, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.Lax.LaxTrans.naturality_naturality, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τl, CommRingCat.moduleCatExtendScalarsPseudofunctor_obj, Bicategory.Opposite.op2_rightUnitor_hom, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀'_assoc, CategoryTheory.PreGaloisCategory.card_hom_le_card_fiber_of_connected, CategoryTheory.Bicategory.whiskerLeft_eqToHom, Homotopy.ofEq_hom, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp, HomologicalComplex.epi_homologyMap_iff_up_to_refinements, CategoryTheory.Bicategory.Pith.id₂_iso_hom, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_comp, HomologicalComplex₂.D₂_shape, CategoryTheory.Adjunction.homEquiv_naturality_right_square_iff, CategoryTheory.conjugateEquiv_counit, CategoryTheory.Mon.Hom.hom_mul, CategoryTheory.Bicategory.associator_hom_congr, CochainComplex.IsKProjective.Qh_map_bijective, Mathlib.Tactic.Bicategory.naturality_leftUnitor, Bicategory.Opposite.unopFunctor_obj, CochainComplex.mappingCone.d_fst_v_assoc, CategoryTheory.tensor_sum, CategoryTheory.Preadditive.mono_iff_isZero_kernel', CategoryTheory.ShortComplex.LeftHomologyData.wi, Action.zero_hom, CategoryTheory.Hom.inv_def, CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomRight, CategoryTheory.Prod.fac_assoc, ModuleCat.hom_nsmul, CategoryTheory.Functor.prod_map, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inl, SimplicialObject.Splitting.IndexSet.id_snd_coe, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_π, CategoryTheory.unopHom_apply, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv_assoc, CategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork_H, CategoryTheory.Functor.ranges_directed, CategoryTheory.Limits.coconeRightOpOfConeEquiv_inverse_map, CategoryTheory.Limits.isLimitConeOfAdj_lift, CategoryTheory.Functor.toOplaxFunctor_mapComp, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_assoc, CategoryTheory.Preadditive.isCoseparating_iff, CategoryTheory.InducedCategory.homAddEquiv_apply, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, CochainComplex.HomComplex.Cochain.toSingleMk_surjective, CategoryTheory.MonoidalPreadditive.tensor_zero, CategoryTheory.Bicategory.Comonad.comul_assoc, groupCohomology.subtype_comp_d₀₁_assoc, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_functor_obj_a, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, CategoryTheory.Limits.pullback_map_diagonal_isPullback, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map_comp, CategoryTheory.ObjectProperty.hasColimit_parallelPair_comp_ι, CategoryTheory.Bicategory.comp_whiskerLeft, CategoryTheory.Lax.LaxTrans.comp_app, CategoryTheory.ShortComplex.leftHomologyMap'_nullHomotopic, CategoryTheory.Adjunction.homAddEquiv_symm_zero, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, TopCat.Presheaf.presieveOfCovering.indexOfHom_spec, CategoryTheory.ShortComplex.sub_τ₁, CategoryTheory.Functor.RepresentableBy.homEquiv_comp, CategoryTheory.Limits.idZeroEquivIsoZero_apply_hom, CategoryTheory.OplaxFunctor.mapComp_naturality_left, CategoryTheory.conjugateEquiv_rightUnitor_hom, CategoryTheory.Lax.StrongTrans.naturality_id, CategoryTheory.Bicategory.LeftLift.whiskerHom_right, CategoryTheory.Mat_.add_apply, CategoryTheory.ObjectProperty.hasInducedTStructure_iff, AlgebraicGeometry.Scheme.Cover.exists_of_trans_eq_trans, CategoryTheory.Bicategory.postcomp₂_app_toFunctor_map, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_right, CategoryTheory.Bicategory.prod_associator_hom_fst, CategoryTheory.IsCofilteredOrEmpty.cone_objs, CategoryTheory.CategoryOfElements.π_map, CategoryTheory.IsPushout.of_isBilimit, PresheafOfModules.neg_app, CategoryTheory.Bicategory.LeftExtension.ofCompId_hom, CategoryTheory.Functor.prod_ε_fst, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_hom_as_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, HomologicalComplex.alternatingConst_iCycles_odd_comp, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv, CategoryTheory.IsFinitelyPresentable.exists_eq_of_isColimit, CategoryTheory.Bicategory.prod_homCategory_comp_fst, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero, CategoryTheory.instIsMonHomInvHomOfIsCommMonObj, HomologicalComplex.homotopyCofiber.inlX_sndX, CategoryTheory.Functor.RepresentableBy.isRepresentedBy, CategoryTheory.PreOneHypercover.Hom.mapMulticospan_map, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₂, CategoryTheory.Linear.homCongr_apply, CategoryTheory.Pseudofunctor.toLax_mapId', CategoryTheory.GrothendieckTopology.uliftYoneda_obj_obj_map_down, CategoryTheory.Lax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.StrictlyUnitaryLaxFunctor.id_map, CategoryTheory.ShortComplex.Homotopy.add_h₀, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_inverse_map_hom, HomologicalComplex.truncGE'.d_comp_d_assoc, HomotopicalAlgebra.CofibrantObject.homMk_surjective, CategoryTheory.ShortComplex.cyclesMap_zero, CategoryTheory.Limits.asEmptyCocone_ι_app, CategoryTheory.ShortComplex.comp_homologyπ_eq_zero_iff_up_to_refinements, ModuleCat.homEquiv_extendScalarsComp, Total.ext_iff, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_snd, dNext_comp_left, CategoryTheory.Bicategory.precomposingCat_obj, CategoryTheory.CommSq.left_adjoint_hasLift_iff, CategoryTheory.Pseudofunctor.mapComp_id_left_inv, CategoryTheory.ShortComplex.cyclesMap'_smul, CategoryTheory.Idempotents.Karoubi.sum_hom, Rep.zero_hom, SemimoduleCat.hom_zero, CategoryTheory.Triangulated.TStructure.isGE_iff_orthogonal, CategoryTheory.ShortComplex.LeftHomologyMapData.zero_φH, CategoryTheory.WithInitial.pseudofunctor_mapId, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc_comp, CategoryTheory.Sieve.uliftFunctorInclusion_app, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, Homotopy.mkCoinductiveAux₂_add_one, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, CategoryTheory.GrothendieckTopology.pointBotPresheafFiberIso_inv, CategoryTheory.Join.pseudofunctorRight_mapId_inv_toNatTrans_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_left, CategoryTheory.conjugateEquiv_mateEquiv_vcomp, CategoryTheory.Oplax.LaxTrans.OplaxFunctor.bicategory_whiskerRight_as_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_iso, HomologicalComplex.homotopyCofiber.inlX_d, HomologicalComplex.mapBifunctor₂₃.d₁_eq, CategoryTheory.typeEquiv_counitIso_inv_app_hom_app, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, CategoryTheory.GrpObj.div_comp_assoc, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_right_addition, CategoryTheory.ConcreteCategory.hom_bijective, CategoryTheory.Bicategory.Comonad.counit_def, CochainComplex.HomComplex.Cocycle.fromSingleMk_neg, CategoryTheory.NonPreadditiveAbelian.lift_sub_lift, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_counitIso_hom_app_f, RingCat.moduleCatRestrictScalarsPseudofunctor_map, AddCommGrpCat.kernelIsoKer_inv_comp_ι, CategoryTheory.LaxFunctor.map₂_associator, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Functor.exists_map_eq_of_isLocallyDirected, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.Bicategory.associator_inv_naturality_left_assoc, CategoryTheory.Monad.algebraPreadditive_homGroup_zsmul_f, CategoryTheory.ShortComplex.HasRightHomology.of_hasKernel, CategoryTheory.OplaxFunctor.mapComp_id_right_assoc, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_inverse_map, CategoryTheory.CostructuredArrow.prodFunctor_obj, CategoryTheory.IsFiltered.tulip, CategoryTheory.Bicategory.whiskerLeftIso_inv, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapId, CategoryTheory.Oplax.StrongTrans.naturality_comp_assoc, CategoryTheory.yonedaAddMonObj_map, CategoryTheory.Comma.equivProd_inverse_map_right, Rep.ofHom_nsmul, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, CategoryTheory.Limits.kernel.zeroKernelFork_pt, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_hom, CategoryTheory.tensorObj_def, CategoryTheory.GrothendieckTopology.Point.jointly_surjective, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, CategoryTheory.Functor.IsLocallyDirected.cond, CategoryTheory.mateEquiv_conjugateEquiv_vcomp, CategoryTheory.Iso.unop2_hom, CategoryTheory.OplaxFunctor.mapComp_assoc_right, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_hom, CategoryTheory.Bicategory.mateEquiv_eq_iff, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, HomologicalComplex.ιMapBifunctorOrZero_eq_zero, CategoryTheory.Abelian.SpectralObject.d_map_fourδ₄Toδ₃_assoc, CategoryTheory.Arrow.equivSigma_symm_apply_hom, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, CategoryTheory.ObjectProperty.extensionProduct_iff, CategoryTheory.Preadditive.comp_sum, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₃, CategoryTheory.Functor.precomp_map_heq, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_eq_ι_iff, CategoryTheory.Limits.biproduct.fromSubtype_eq_lift, CategoryTheory.Functor.prod_μ_fst, CategoryTheory.Bicategory.LeftLift.ofIdComp_right, CategoryTheory.SmallObject.ιFunctorObj_extension', CategoryTheory.OplaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionRight_op, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty_assoc, CategoryTheory.GrothendieckTopology.dense_covering, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_inv, CategoryTheory.Functor.FullyFaithful.homMulEquiv_symm_apply, CategoryTheory.NatTrans.prod_app_snd, CategoryTheory.Pseudofunctor.ObjectProperty.IsClosedUnderMapObj.map_obj, CategoryTheory.Limits.Cotrident.IsColimit.homIso_symm_apply, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app_assoc, CategoryTheory.Bicategory.postcomposing_map_app, Bicategory.Opposite.op2_comp, CategoryTheory.Bicategory.pentagon_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality, groupCohomology.d₁₂_comp_d₂₃, CategoryTheory.yonedaGrpObj_map, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_assoc, CategoryTheory.Limits.eq_zero_of_epi_kernel, CategoryTheory.Pseudofunctor.StrongTrans.Modification.id_app, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id_assoc, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, CategoryTheory.Bicategory.whiskerRight_comp, CategoryTheory.ObjectProperty.isLocal.homEquiv_apply, CategoryTheory.Limits.IsZero.map, CategoryTheory.CatCenter.smul_eq, CategoryTheory.Bicategory.rightUnitorNatIso_inv_app, CategoryTheory.Functor.RepresentableBy.homEquiv_unop_comp, CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf, CategoryTheory.Pseudofunctor.StrongTrans.associator_inv_as_app, Homotopy.symm_hom, Bicategory.Opposite.op2_leftUnitor_hom, SSet.N.le_iff_exists_mono, AlgebraicGeometry.compactSpace_iff_exists, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_hom, CategoryTheory.Pseudofunctor.DescentData'.isoMk_hom_hom, CategoryTheory.Linear.comp_smul, CategoryTheory.MonoidalClosed.uncurry_injective, CategoryTheory.Bicategory.Comonad.comul_counit_assoc, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHom_unop, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_apply, CategoryTheory.Functor.IsCocartesian.universal_property, CategoryTheory.Bicategory.congr_whiskerLeft, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_inv, CategoryTheory.Mon.uniqueHomFromTrivial_default_hom, CategoryTheory.ComposableArrows.isComplex₂_iff, CategoryTheory.Functor.FullyFaithful.map_surjective, CategoryTheory.Pretriangulated.distinguished_cocone_triangle, CategoryTheory.Preadditive.comp_zsmul, CategoryTheory.Limits.CokernelCofork.isColimitMapBifunctor.exists_desc, CategoryTheory.Hom.add_def, CategoryTheory.Pseudofunctor.toLax_mapId, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_zsmul_f, CategoryTheory.ShiftedHom.mk₀_add, SimplicialObject.Splitting.IndexSet.instEpiSimplexCategoryE, SheafOfModules.Presentation.map_relations_I, HomologicalComplex₂.D₁_totalShift₁XIso_hom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv, CategoryTheory.Functor.hom_obj, CategoryTheory.Functor.shiftMap_zero, HomologicalComplex₂.D₂_totalShift₁XIso_hom, CategoryTheory.Subgroupoid.mem_sInf, MonObj.mopEquiv_functor_map_hom_unmop, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, CategoryTheory.Localization.homEquiv_apply, SheafOfModules.freeHomEquiv_apply, ComplexShape.Embedding.homEquiv_symm_apply, CategoryTheory.Oplax.OplaxTrans.isoMk_hom_as_app, CategoryTheory.Cat.leftUnitor_hom_toNatTrans, CategoryTheory.StructuredArrow.prodFunctor_obj, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom_assoc, CochainComplex.mappingCocone.inr_v_fst_f_assoc, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Bicategory.Adj.comp_τr_assoc, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ, CategoryTheory.Triangulated.TStructure.exists_triangle_zero_one, CategoryTheory.Bicategory.whisker_assoc_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.δ_toBiprod_assoc, CategoryTheory.Preadditive.add_comp, SSet.stdSimplex.objEquiv_symm_mem_nonDegenerate_iff_mono, CategoryTheory.conjugateEquiv_comm, SimplicialObject.Splitting.cofan_inj_comp_app, CategoryTheory.Abelian.SpectralObject.zero₁, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three, PresheafOfModules.sub_app, CategoryTheory.GrpObj.comp_div, AlgebraicTopology.NormalizedMooreComplex.d_squared, HomologicalComplex.homologyMap_sub, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.Limits.kernelSubobject_factors_iff, CategoryTheory.Functor.isIso_lanAdjunction_homEquiv_symm_iff, CategoryTheory.Preadditive.add_comp_assoc, TopCat.subpresheafToTypes_map_coe, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_obj_obj, CategoryTheory.ProjectiveResolution.complex_d_succ_comp, CategoryTheory.Prod.fac, CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory_whiskerLeft_as_app, CategoryTheory.MorphismProperty.isLocal_iff, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom, CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions.ext, CategoryTheory.Bicategory.associator_eqToHom_hom, CategoryTheory.Oplax.LaxTrans.Modification.naturality_assoc, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_fst, AlgebraicTopology.DoldKan.Γ₀.map_app, CategoryTheory.Bicategory.whisker_assoc_symm, ComplexShape.Embedding.homEquiv_apply_coe, CategoryTheory.extendCofan_ι_app, CategoryTheory.LocallySmall.hom_small, CategoryTheory.Functor.ιColimitType_eq_iff_of_isFiltered, Homotopy.dNext_succ_chainComplex, CategoryTheory.Lax.StrongTrans.naturality_naturality_assoc, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_map, HomologicalComplex.homotopyCofiber.shape, Homotopy.mkCoinductiveAux₂_zero, CategoryTheory.CommSq.right_adjoint, CategoryTheory.Bicategory.Prod.sectL_mapComp_inv, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism₂, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.Functor.sectionsEquivHom_naturality_symm, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_sub_f, AlgebraicGeometry.Scheme.Modules.pseudofunctor_obj_obj, groupHomology.d₂₁_comp_d₁₀, HomotopicalAlgebra.FibrantObject.homRel_equivalence_of_isCofibrant_src, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.δ_toBiprod, HomotopicalAlgebra.BifibrantObject.homMk_surjective, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φH, CategoryTheory.Equivalence.congrLeftFunctor_map, CategoryTheory.Bicategory.id_whiskerLeft_assoc, CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinements, CategoryTheory.ShortComplex.LeftHomologyData.wπ, HomologicalComplex.cylinder.πCompι₀Homotopy.inrX_nullHomotopy_f, CategoryTheory.CatEnriched.hComp_assoc_heq, CategoryTheory.Bicategory.LeftLift.IsKan.fac, CategoryTheory.Adjunction.homAddEquiv_symm_neg, CategoryTheory.Projective.factors, CategoryTheory.Abelian.Ext.mk₀_zero, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_nsmul_f, CategoryTheory.Bicategory.Pith.id_of, CategoryTheory.IsCofiltered.cospan, CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne_comp_assoc, CategoryTheory.MonoidalCategory.prodMonoidal_whiskerLeft, SheafOfModules.Presentation.mapRelations_mapGenerators, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_inv, ModuleCat.hom_add, CategoryTheory.shrinkYonedaGrp_obj_map_shrinkYonedaGrpObjObjEquiv_symm, Bicategory.Opposite.op2_id, CommRingCat.HomTopology.continuous_apply, CategoryTheory.IsPushout.inr_fst', HomotopicalAlgebra.CofibrantObject.HoCat.exists_resolution_map, CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory_leftUnitor_hom_as_app, CategoryTheory.Bicategory.yoneda₀_mapId_hom_toNatTrans_app, CategoryTheory.CostructuredArrow.mk_surjective, CategoryTheory.Pseudofunctor.IsStack.essSurj_of_sieve, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃_assoc, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero_assoc, CategoryTheory.GrpObj.comp_zpow_assoc, CategoryTheory.Bicategory.toNatTrans_mateEquiv, CategoryTheory.Limits.KernelFork.app_one, CategoryTheory.finrank_hom_simple_simple, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_hom, CategoryTheory.Iso.unop2_op_hom, CategoryTheory.ObjectProperty.exists_comp_monoModSerre_eq_zero_iff, CategoryTheory.OplaxFunctor.map₂_rightUnitor, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, CategoryTheory.Functor.Final.exists_coeq, CategoryTheory.uliftYoneda_map_app, CategoryTheory.Functor.prod'_η_snd, CategoryTheory.ShortComplex.RightHomologyData.ι_g'_assoc, CategoryTheory.Functor.toPseudofunctor'_map, CategoryTheory.Localization.SmallHom.equiv_chgUniv, CategoryTheory.Functor.whiskerRight_zero, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_assoc, CategoryTheory.Functor.uliftYonedaReprXIso_hom_app, CategoryTheory.ObjectProperty.SerreClassLocalization.epi_iff, CategoryTheory.ShortComplex.epi_homologyMap_iff_up_to_refinements, CategoryTheory.ShortComplex.Exact.exact_up_to_refinements, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, CategoryTheory.ShortComplex.add_liftCycles, CategoryTheory.Limits.kernel.ι_zero_isIso, CategoryTheory.Hom.addEquivCongrRight_apply, CategoryTheory.equivYoneda_hom_app, CochainComplex.HomComplex.δ_zero_cochain_v, CochainComplex.HomComplex.Cochain.units_smul_v, CategoryTheory.NonPreadditiveAbelian.neg_add_cancel, CategoryTheory.GrpObj.inv_eq_inv, HomologicalComplex.smul_f_apply, CategoryTheory.StrictlyUnitaryLaxFunctorCore.mapComp_naturality_left, CategoryTheory.Cat.associator_inv_toNatTrans, CategoryTheory.Limits.isKernelCompMono_lift, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_hom_app, CategoryTheory.WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_map₂, SheafOfModules.relationsOfIsCokernelFree_I, Rep.sub_hom, CategoryTheory.Bicategory.Adj.iso₂Mk_hom_τr, CategoryTheory.Iso.homToEquiv_apply, CochainComplex.HomComplex.CohomologyClass.toHom_bijective, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, CategoryTheory.Hom.zero_def, CategoryTheory.ShortComplex.LeftHomologyMapData.zero_φK, Compactum.continuous_of_hom, CategoryTheory.ObjectProperty.preservesCokernels_ι, CategoryTheory.Functor.curryingEquiv_apply_map, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂, CategoryTheory.ShortComplex.HomologyMapData.add_right, CompHausLike.pullback.cone_π, CategoryTheory.NatTrans.app_sum, Mathlib.Tactic.Bicategory.naturality_id, CategoryTheory.Cat.leftUnitor_inv_toNatTrans, CategoryTheory.isSeparator_iff_epi, CategoryTheory.CostructuredArrow.prodInverse_map, CategoryTheory.Functor.initial_iff_of_isCofiltered, CategoryTheory.Join.mapPairId_inv_app, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, CategoryTheory.Oplax.LaxTrans.OplaxFunctor.bicategory_associator_hom_as_app, CategoryTheory.Pseudofunctor.mapId'_eq_mapId, CategoryTheory.Limits.biproduct.total, CategoryTheory.Functor.CorepresentableBy.equivUliftCoyonedaIso_symm_apply_homEquiv, CategoryTheory.Bicategory.associator_inv_naturality_right_assoc, CategoryTheory.Preadditive.coforkOfCokernelCofork_π, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁_assoc, CategoryTheory.FunctorToTypes.functorHomEquiv_apply_app, CategoryTheory.GrpObj.zpow_comp, CategoryTheory.Limits.biprod.inrCokernelCofork_π, CategoryTheory.Limits.IsTerminal.subsingleton_to, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp, CategoryTheory.ShortComplex.rightHomologyMap_sub, CategoryTheory.IsPushout.IsVanKampen.exists_cube_filling, CategoryTheory.StrictPseudofunctor.toFunctor_map, CategoryTheory.Bicategory.Prod.snd_mapId_hom, CategoryTheory.Bicategory.hom_inv_whiskerRight_assoc, CategoryTheory.MonObj.pow_comp_assoc, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app_assoc, CategoryTheory.Bicategory.triangle, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_hom_as_app, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.Limits.Pi.ι_π_assoc, CategoryTheory.Comma.fromProd_map_right, CategoryTheory.Bimon.trivialTo_hom, CategoryTheory.Localization.Preadditive.add_eq, CategoryTheory.Pretriangulated.distinguished_cocone_triangle₁, CategoryTheory.Limits.isoZeroOfMonoZero_inv, CategoryTheory.ShortComplex.ShortExact.δ_comp_assoc, CategoryTheory.Adjunction.homEquiv_ofNatIsoRight_symm_apply, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm, SSet.yonedaEquiv_const, CategoryTheory.Pseudofunctor.toDescentDataAsCoalgebraCompCoalgebraEquivalenceFunctorIso_hom_app_f, CategoryTheory.Functor.map_units_smul, CategoryTheory.MonoidalOpposite.tensorRightIso_hom_app_unmop, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_f, CategoryTheory.CatEnrichedOrdinary.Hom.comp_eq, SSet.prodStdSimplex.nonDegenerateEquiv₁_fst, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_hom, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun, CategoryTheory.Limits.WidePushoutShape.mkCocone_ι_app, CochainComplex.HomComplex.Cocycle.fromSingleMk_zero, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_hom_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_assoc, HomologicalComplex.zero_f_apply, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CategoryTheory.Bicategory.Prod.sectR_map₂, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_inv_app, CategoryTheory.PreGaloisCategory.fiber_in_connected_component, CategoryTheory.instSmallHomDerivedCategoryObjSingleFunctorOfHasExt, CategoryTheory.congrArg_mpr_hom_left, CategoryTheory.Preadditive.hasCokernel_of_hasCoequalizer, CategoryTheory.Limits.biprod.add_eq_lift_desc_id, CategoryTheory.FreeMonoidalCategory.instSubsingletonHomCompDiscreteNormalMonoidalObject, CategoryTheory.ShortComplex.Splitting.g_s_assoc, CategoryTheory.WithInitial.map_map, SSet.stdSimplex.objEquiv_symm_comp, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, CategoryTheory.StrictPseudofunctorPreCore.map₂_whisker_right, CategoryTheory.ProjectiveResolution.extMk_zero, HomologicalComplex.alternatingConst_iCycles_even_comp, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_inv, CategoryTheory.PrelaxFunctor.id_toPrelaxFunctorStruct, CategoryTheory.ShortComplex.Homotopy.equivSubZero_apply, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_symm_apply, CategoryTheory.shrinkYoneda_obj_map_shrinkYonedaObjObjEquiv_symm, Action.add_hom, CategoryTheory.FreeBicategory.normalize_naturality, CategoryTheory.Bicategory.Adj.rIso_hom, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom, CategoryTheory.StrictPseudofunctor.id_map₂, CategoryTheory.Sheaf.ΓObjEquivHom_naturality, CategoryTheory.Limits.sigmaSigmaIso_inv, SimplexCategory.δ_injective, CategoryTheory.HomOrthogonal.matrixDecomposition_apply, CategoryTheory.Bicategory.Prod.sectL_map, CategoryTheory.NatTrans.appHom_apply, HomologicalComplex.toCycles_eq_zero, CategoryTheory.End.smul_right, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_symm, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, CategoryTheory.LocallyDiscrete.mkPseudofunctor_mapComp, CategoryTheory.Functor.IsRepresentedBy.uliftYonedaIso_hom, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_hom, CategoryTheory.NonPreadditiveAbelian.neg_add, Mathlib.Tactic.Bicategory.eval_comp, CategoryTheory.Monad.algebraPreadditive_homGroup_zero_f, CategoryTheory.Bicategory.id_whiskerRight, SheafOfModules.pushforwardCongr_symm, CategoryTheory.Triangulated.TStructure.isIso_truncGT_map_iff, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_hom, CochainComplex.mappingCone.inr_f_fst_v_assoc, CategoryTheory.Pseudofunctor.mapComp'_inv_comp_mapComp'_hom, CategoryTheory.Triangulated.AbelianSubcategory.exists_desc_πQ, CategoryTheory.Iso.op2_unop_inv_unop2, CategoryTheory.Limits.biproduct.matrix_desc, CategoryTheory.IsPullback.of_hasBinaryBiproduct, CategoryTheory.MonObj.ofRepresentableBy_mul, Homotopy.add_hom, CategoryTheory.Limits.Cofork.IsColimit.homIso_natural, CategoryTheory.Bicategory.Pith.hom₂_ext_iff, CategoryTheory.evaluationRightAdjoint_obj_obj, CategoryTheory.Localization.homEquiv_refl, groupHomology.congr, CategoryTheory.IsPushout.inl_snd, CategoryTheory.Bicategory.yoneda₀_mapId_inv_toNatTrans_app, CategoryTheory.Lax.StrongTrans.naturality_id_assoc, CategoryTheory.Abelian.AbelianStruct.ι_imageπ_assoc, homOfEq_heq_right_iff, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, FintypeCat.instFullForgetHomObjFinite, CategoryTheory.Limits.FintypeCat.instPreservesFiniteLimitsFintypeCatForgetHomObjFinite, CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory_whiskerRight_as_app, CochainComplex.mappingCone.inl_v_d_assoc, CategoryTheory.Lax.LaxTrans.isoMk_inv_as_app, CategoryTheory.Localization.homEquiv_trans, CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v, CategoryTheory.Limits.equalizer.existsUnique, Hom.unop_inj, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_mapComp_hom_toNatTrans_app, SimplicialObject.Splitting.PInfty_comp_πSummand_id_assoc, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', CategoryTheory.IsPullback.of_is_bilimit', CategoryTheory.PreGaloisCategory.fiberPullbackEquiv_symm_fst_apply, CategoryTheory.Bicategory.yoneda₀_mapComp_inv_toNatTrans_app, CategoryTheory.AddMon.Hom.hom_zero, ChainComplex.mk'_d, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, CategoryTheory.MonoidalOpposite.tensorRightIso_inv_app_unmop, CategoryTheory.Limits.asEmptyCone_π_app, CategoryTheory.Quotient.inv_mk, CategoryTheory.Comma.fromProd_map_left, CategoryTheory.SimplicialObject.cechNerveEquiv_symm_apply, SheafOfModules.add_val, CategoryTheory.IsFiltered.crown₃, CategoryTheory.ShortComplex.HasLeftHomology.of_hasKernel, CategoryTheory.AddMonObj.comp_nsmul_assoc, AlgebraicGeometry.Scheme.Modules.Hom.sub_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_assoc, Rep.homEquiv_apply, CategoryTheory.Abelian.SpectralObject.δ_pOpcycles_assoc, CategoryTheory.InjectiveResolution.sub_extMk, CategoryTheory.Functor.prod_δ_snd, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.conjugateEquiv_comp_assoc, HomologicalComplex.dgoToHomologicalComplex_map_f, CategoryTheory.Limits.BinaryBicone.inrCokernelCofork_π, CategoryTheory.Triangulated.AbelianSubcategory.eq_zero_of_hom_shift_pos, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τr, CategoryTheory.Oplax.OplaxTrans.naturality_id, CategoryTheory.coyonedaEquiv_coyoneda_map, CategoryTheory.Limits.pullbackZeroZeroIso_hom_fst, CategoryTheory.Bicategory.rightUnitor_comp, CategoryTheory.Bicategory.whiskerRight_id_symm, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_apply, CategoryTheory.Cat.Hom.instIsIsoFunctorαCategoryToNatTransInvHom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv, CategoryTheory.Limits.Trident.ofι_π_app, CategoryTheory.Groupoid.vertexGroupIsomOfMap_symm_apply, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_obj, HomologicalComplex.liftCycles_comp_homologyπ_eq_iff_up_to_refinements, CategoryTheory.Limits.coneOfSectionCompYoneda_π, CategoryTheory.ShortComplex.sub_τ₂, CategoryTheory.OplaxFunctor.mapComp_id_right, CategoryTheory.shrinkYonedaObjObjEquiv_symm_comp, CategoryTheory.op_add, CategoryTheory.Bicategory.triangle_assoc_comp_right, CategoryTheory.ShortComplex.Homotopy.trans_h₃, CategoryTheory.MonoidalCategory.tensor_map, CategoryTheory.Pseudofunctor.toDescentData_obj, CategoryTheory.Limits.isIso_kernelSubobject_zero_arrow, CategoryTheory.Presheaf.IsSheaf.existsUnique_amalgamation_ofArrows, CategoryTheory.Oplax.LaxTrans.whiskerRight_as_app, CategoryTheory.Bicategory.comp_whiskerLeft_assoc, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_hom, CategoryTheory.ShortComplex.rightHomologyMap'_sub, CategoryTheory.Pseudofunctor.mapComp_id_right_inv, CategoryTheory.ShortComplex.Homotopy.neg_h₃, CategoryTheory.StrictlyUnitaryPseudofunctor.id_map₂, CategoryTheory.Bicategory.whiskerLeft_inv_hom_assoc, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.f, CategoryTheory.Comma.unopFunctor_map, CategoryTheory.IsCardinalPresentable.exists_eq_of_isColimit', AlgebraicTopology.DoldKan.Q_succ, CategoryTheory.forgetAdjToOver.homEquiv_symm, CategoryTheory.Bicategory.associatorNatIsoMiddle_hom_app, CategoryTheory.ShortComplex.homologyMap_sub, Prefunctor.costar_fst, CategoryTheory.Triangulated.TStructure.truncLTι_comp_truncGEπ_app_assoc, HomologicalComplex.cyclesMap_zero, CondensedSet.isDiscrete_tfae, CategoryTheory.linearCoyoneda_obj_map, Rep.standardComplex.d_comp_ε, CategoryTheory.Bicategory.instHasInitialLeftExtensionOfHasLeftKanExtension, CategoryTheory.IsCardinalFiltered.wideSpan, ChainComplex.fromSingle₀Equiv_symm_apply_f_zero, SSet.Homotopy.h₀_assoc, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_assoc, CategoryTheory.OverPresheafAux.MakesOverArrow.app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, FDRep.simple_iff_end_is_rank_one, CategoryTheory.Limits.unop_zero, CategoryTheory.Grp.Hom.hom_mul, TopologicalSpace.Opens.leSupr_apply_mk, CategoryTheory.Bicategory.mateEquiv_square, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, CategoryTheory.Pretriangulated.binaryBiproductTriangle_mor₃, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_inv, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, CategoryTheory.extendFan_π_app, HomologicalComplex.homologyMap_zero, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality_assoc, CategoryTheory.ShortComplex.Homotopy.trans_h₀, CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_inv_right, CategoryTheory.Lax.LaxTrans.naturality_naturality_assoc, CategoryTheory.ShortComplex.opcyclesMap_zero, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Bicategory.rightUnitor_naturality, CategoryTheory.MonoidalCategory.leftAssocTensor_map, CategoryTheory.CountableCategory.instCountableHomHomAsType, CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_fiber, CategoryTheory.OverPresheafAux.OverArrows.app_val, CategoryTheory.SimplicialObject.Homotopy.ToChainHomotopy.hom_eq_zero, CategoryTheory.StrictlyUnitaryPseudofunctor.id_map, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.id_hom, CategoryTheory.Subobject.bot_arrow, CategoryTheory.Mon.Hom.hom_pow, CategoryTheory.ShortComplex.neg_τ₂, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_δ_unmop_app, CategoryTheory.Bicategory.whiskerLeft_comp_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, CategoryTheory.yonedaCommGrpGrpObj_obj_coe, CategoryTheory.kernelCokernelCompSequence.δ_fac, CategoryTheory.Subfunctor.range_eq_ofSection, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_iso, CategoryTheory.evaluationUncurried_map, CategoryTheory.Limits.IsZero.iff_isSplitEpi_eq_zero, CategoryTheory.Bicategory.Pith.whiskerLeft_iso_inv, CategoryTheory.Discrete.productEquiv_counitIso_inv_app, CategoryTheory.FinallySmall.exists_small_weakly_terminal_set, CategoryTheory.ShortComplex.HomologyData.exact_iff_i_p_zero, CategoryTheory.Bicategory.rightZigzagIso_symm, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, HomologicalComplex.toCycles_comp_homologyπ, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_hom, CochainComplex.ConnectData.d_comp_d_assoc, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_snd, CategoryTheory.Functor.toPseudofunctor'_obj, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_unit_f_aux, CategoryTheory.MonObj.comp_mul, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Pi.sum_obj_map, CategoryTheory.Lax.StrongTrans.naturality_comp, CategoryTheory.Bicategory.rightUnitorNatIsoCat_hom_toNatTrans_app, TopCat.Sheaf.IsFlasque.structured_arrows_elements_sheaf_chains_bounded, CategoryTheory.Bicategory.whiskerLeftIso_hom, CategoryTheory.yonedaPairing_map, CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory_associator_hom_as_app, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_counit, CategoryTheory.Lax.OplaxTrans.naturality_id_assoc, CochainComplex.HomComplex.Cochain.smul_v, Mathlib.Tactic.Bicategory.structuralIso_inv, CategoryTheory.Functor.toOplaxFunctor_map, HomologicalComplex₂.D₂_D₂_assoc, FintypeCat.hom_apply, CategoryTheory.Pretriangulated.Triangle.isZero₂_iff, HomologicalComplex.homotopyCofiber.d_sndX, CategoryTheory.Pseudofunctor.map₂_whisker_right, CategoryTheory.Limits.cokernelIsoOfEq_trans, CategoryTheory.Bicategory.leftUnitorNatIsoCat_inv_toNatTrans_app, CategoryTheory.Bicategory.whiskerRight_id_assoc, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π, CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory_associator_inv_as_app, CategoryTheory.Bicategory.Prod.sectR_obj, HomologicalComplex.extendMap_add, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, CategoryTheory.PreGaloisCategory.fiberPullbackEquiv_symm_snd_apply, CategoryTheory.Lax.LaxTrans.homCategory_comp_as_app, CategoryTheory.IsPullback.inl_snd', CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂_assoc, CategoryTheory.Bicategory.whisker_assoc_symm_assoc, HomologicalComplex.xPrevIsoSelf_comp_dTo_assoc, CategoryTheory.Preadditive.sum_comp_assoc, SSet.Homotopy.h₁, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι_assoc, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_symm_apply, CategoryTheory.MorphismProperty.pullback_map, CategoryTheory.conjugateEquiv_associator_hom, SimplicialObject.Splitting.decomposition_id, CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epi, CategoryTheory.Pseudofunctor.DescentData'.Hom.comm, CategoryTheory.GrpObj.inv_comp, CategoryTheory.Limits.limitConeOfUnique_isLimit_lift, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app, CategoryTheory.Bicategory.conjugateEquiv_apply', CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, HomologicalComplex.mapBifunctor₁₂.d₃_eq_zero, HomologicalComplex.alternatingConst_d, CategoryTheory.Functor.RepresentableBy.ext_iff, CategoryTheory.Bicategory.mateEquiv_conjugateEquiv_vcomp, CochainComplex.HomComplex.Cochain.fromSingleMk_sub, CategoryTheory.ShortComplex.RightHomologyMapData.zero_φQ, CochainComplex.toSingle₀Equiv_symm_apply_f_succ, CategoryTheory.OplaxFunctor.mapComp_assoc_right_assoc, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τr, CategoryTheory.Limits.zero_of_source_iso_zero', CategoryTheory.ShortComplex.homologyMap'_smul, CochainComplex.mappingCone.inl_v_descShortComplex_f_assoc, CategoryTheory.MonObj.comp_one_assoc, Rep.coindResAdjunction_homEquiv_symm_apply, CategoryTheory.Limits.IsZero.eq_zero_of_tgt, CategoryTheory.Pretriangulated.Triangle.neg_hom₂, CategoryTheory.Bicategory.postcomposing₂_obj_app_toFunctor_map, CategoryTheory.Adjunction.homAddEquiv_zero, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_inv_as_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, CategoryTheory.Iso.op2_unop_hom_unop2, DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective, CategoryTheory.FreeBicategory.mk_associator_hom, CategoryTheory.AddMon.uniqueHomFromTrivial_default_hom, CategoryTheory.evaluationLeftAdjoint_obj_obj, CategoryTheory.op_sum, AddCommGrpCat.biprodIsoProd_inv_comp_desc, TopModuleCat.hom_sub, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_epi₂, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIso_hom, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, CategoryTheory.LaxFunctor.map₂_leftUnitor, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_inv, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, CategoryTheory.Biprod.ofComponents_fst, CategoryTheory.ShortComplex.rightHomologyMap_nullHomotopic, CategoryTheory.Biprod.unipotentUpper_inv, CategoryTheory.Functor.prod_η_fst, CategoryTheory.IsPullback.of_has_biproduct, SheafOfModules.unitHomEquiv_comp_apply, CategoryTheory.CategoryOfElements.toCostructuredArrow_obj, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_f, CategoryTheory.Abelian.Preradical.toColon_hom_left_app_colonπ_app_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left_app, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, CategoryTheory.ShiftedHom.opEquiv'_symm_add, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, CategoryTheory.NonPreadditiveAbelian.add_neg, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id, CategoryTheory.Presheaf.imageSieve_cofanIsColimitDesc_shrinkYoneda_map, CategoryTheory.Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_hom_app_app_down, CategoryTheory.Cat.rightUnitor_inv_app, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, AlgebraicGeometry.StructureSheaf.res_apply, SimplexCategory.eq_σ_comp_of_not_injective', CategoryTheory.Pseudofunctor.Grothendieck.Hom.ext_iff, CategoryTheory.Functor.uncurry_obj_map, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallyInjectiveHomYonedaGluedToSheaf, CategoryTheory.Bicategory.Prod.snd_mapId_inv, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, AlgebraicGeometry.Scheme.Modules.Hom.add_app, SSet.stdSimplex.yonedaEquiv_map, CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_hom, CategoryTheory.Limits.Concrete.colimit_rep_eq_zero, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.kernel_ι_d_comp_d, CategoryTheory.CatEnrichedOrdinary.homEquiv_comp, SemiNormedGrp.completion.map_zero, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_as_app, CategoryTheory.Functor.toPseudofunctor'_mapId, empty_arrow, CategoryTheory.Bicategory.InducedBicategory.bicategory_homCategory_comp_hom, CategoryTheory.Limits.PreservesKernel.of_iso_comparison, CategoryTheory.Enriched.Functor.natTransEquiv_symm_whiskerRight_functorHom_app, AlgebraicTopology.DoldKan.P_add_Q, CategoryTheory.ProjectiveResolution.extMk_eq_zero_iff, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv, CategoryTheory.Cat.Hom.toNatTrans_id, AlgebraicTopology.DoldKan.hσ'_eq, HomologicalComplex₂.d₂_eq, CategoryTheory.CommSq.left_adjoint, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, ChainComplex.toSingle₀Equiv_symm_apply_f_zero, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_as_app, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', CategoryTheory.Subobject.mk_surjective, AlgebraicGeometry.exists_map_preimage_le_map_preimage, CategoryTheory.Lax.StrongTrans.naturality_naturality, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, CategoryTheory.Monad.algebraPreadditive_homGroup_nsmul_f, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι_assoc, CategoryTheory.Subobject.factorThru_add_sub_factorThru_left, HomologicalComplex.extend_d_from_eq_zero, HomotopicalAlgebra.RightHomotopyRel.equivalence, CategoryTheory.Bicategory.precomposing_obj, CategoryTheory.NonPreadditiveAbelian.lift_map_assoc, CategoryTheory.Cat.rightUnitor_inv_toNatTrans, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.Subobject.bot_eq_zero, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom_assoc, Homotopy.extend.hom_eq_zero₂, CategoryTheory.Oplax.OplaxTrans.naturality_naturality, CategoryTheory.Bicategory.conjugateEquiv_of_iso, CategoryTheory.ShortComplex.zero, CategoryTheory.Pseudofunctor.isPrestackFor_iff, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionRight_op, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_unitIso_hom_app_hom, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_assoc, CategoryTheory.Presheaf.imageSieve_whisker_forget, CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_pushouts, CategoryTheory.Pretriangulated.Opposite.distinguished_cocone_triangle, CategoryTheory.Subgroupoid.IsNormal.conjugation_bij, TopModuleCat.hom_nsmul, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_ι, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv_assoc, CategoryTheory.ShortComplex.LeftHomologyData.liftK_π_eq_zero_of_boundary, Mathlib.Tactic.Elementwise.forget_hom_Type, CategoryTheory.bicategoricalComp_refl, CategoryTheory.Limits.Cofork.IsColimit.existsUnique, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, CategoryTheory.WithInitial.map₂_app, CategoryTheory.Iso.eHomCongr_comp, CategoryTheory.Bicategory.LeftLift.ofIdComp_hom, CochainComplex.HomComplex.Cocycle.toSingleMk_sub, CategoryTheory.ShortComplex.Homotopy.neg_h₀, CategoryTheory.Classifier.surjective_χ, CategoryTheory.Functor.IsRepresentedBy.map_bijective, CategoryTheory.Bicategory.rightZigzagIso_inv, CategoryTheory.Bicategory.prod_comp_fst, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'_inv, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.Pseudofunctor.StrongTrans.associator_hom_as_app, HomologicalComplex.toCycles_comp_homologyπ_assoc, CategoryTheory.Limits.image.preComp_comp, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, CategoryTheory.Pseudofunctor.map₂_right_unitor, CategoryTheory.ShortComplex.exact_and_mono_f_iff_f_is_kernel, CategoryTheory.Functor.representableByUliftFunctorEquiv_apply_homEquiv, CategoryTheory.Lax.LaxTrans.StrongCore.naturality_hom, CategoryTheory.ShiftedHom.homEquiv_apply, HomologicalComplex₂.D₂_D₁, CategoryTheory.tensorUnit_def, Homotopy.mkCoinductiveAux₃, CategoryTheory.Bicategory.Pith.associator_inv_iso_inv, CategoryTheory.Triangulated.AbelianSubcategory.mor₁_πQ_assoc, CategoryTheory.Bicategory.rightUnitor_comp_inv, LightCondensed.ihomPoints_symm_apply, CategoryTheory.Pretriangulated.Triangle.add_hom₂, CategoryTheory.Pseudofunctor.IsStackFor.isEquivalence, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_inverse_obj_obj, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHom_op, CategoryTheory.Functor.Elements.shrinkYonedaCompWhiskeringLeftObjπCompColimIso_inv_app_apply, CategoryTheory.Abelian.AbelianStruct.imageι_π, CategoryTheory.Adjunction.leftAdjointOfEquiv_map, CategoryTheory.InjectiveResolution.extMk_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, CategoryTheory.Limits.CokernelCofork.condition_assoc, CategoryTheory.Localization.hasSmallLocalizedHom_iff, CategoryTheory.Subgroupoid.coe_inv_coe', CategoryTheory.Bicategory.whiskerLeft_hom_inv_assoc, AlgebraicTopology.DoldKan.hσ'_eq_zero, CategoryTheory.uliftYonedaEquiv_symm_comp_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand, CategoryTheory.Under.mk_surjective, CategoryTheory.ShortComplex.add_τ₂, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_inv, CategoryTheory.NormalMono.w, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_hom_right, AlgebraicGeometry.exists_app_map_eq_map_of_isLimit, CategoryTheory.initiallySmall_iff_exists_small_weakly_initial_set, CategoryTheory.uliftCoyonedaEquiv_naturality, CochainComplex.HomComplex.Cocycle.fromSingleMk_sub, CategoryTheory.Pseudofunctor.CoGrothendieck.instEssSurjαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, CategoryTheory.IsFiltered.bowtie, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_assoc, HomologicalComplex₂.shape_f, CategoryTheory.Limits.eq_zero_of_image_eq_zero, Mathlib.Tactic.Bicategory.evalWhiskerRight_nil, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, CategoryTheory.Pretriangulated.Triangle.zero_hom₃, SemiNormedGrp₁.zero_apply, CategoryTheory.Pretriangulated.Triangle.add_hom₃, CategoryTheory.Pseudofunctor.mapComp'_eq_mapComp, CategoryTheory.Subobject.factorThru_add, RingCat.moduleCatRestrictScalarsPseudofunctor_obj, CategoryTheory.CatCenter.app_neg_one_zpow, CategoryTheory.MonoidalPreadditive.zero_tensor, CategoryTheory.pseudofunctorOfIsLocallyDiscrete_map, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.Functor.map_zero', CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, CondensedSet.LocallyConstant.instFaithfulCondensedTypeDiscrete, SSet.stdSimplex.objEquiv_toOrderHom_apply, Rep.indResHomEquiv_apply, CategoryTheory.Localization.SmallHom.equiv_comp, CategoryTheory.Bicategory.HasLeftKanExtension.hasInitial, CategoryTheory.Limits.fst_of_isColimit, CategoryTheory.IsGrothendieckAbelian.instInjectiveZMonomorphismsRlpMonoMapFactorizationDataRlpOfNatHom, CategoryTheory.ShortComplex.rightHomologyMap_add, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, CategoryTheory.NonPreadditiveAbelian.add_comp, CategoryTheory.Pseudofunctor.Grothendieck.Hom.congr, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_apply, CategoryTheory.Limits.coprod.inr_fst_assoc, CategoryTheory.Lax.LaxTrans.LaxFunctor.bicategory_leftUnitor_hom_as_app, CategoryTheory.PrelaxFunctor.map₂_comp, CategoryTheory.Presieve.uncurry_ofArrows, CategoryTheory.Functor.homEquivOfIsRightKanExtension_symm_apply, Bicategory.Opposite.unop2_comp, CategoryTheory.OplaxFunctor.mapComp_naturality_left_assoc, CategoryTheory.Limits.inr_pushoutZeroZeroIso_inv, CategoryTheory.NatTrans.toCatHom₂_comp, CategoryTheory.Limits.Bicone.ι_π, CategoryTheory.ComposableArrows.isoMk₀_inv_app, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_map₂, CategoryTheory.GrpObj.div_comp, CategoryTheory.Limits.limit.homIso_hom, CategoryTheory.Functor.prod'_ε_snd, CategoryTheory.Limits.biprod.inr_fst_assoc, CategoryTheory.sum.inrCompAssociator_inv_app_down_down, CategoryTheory.Presieve.shrinkFunctor_ι_comp_eq_iff_isAmalgamation, CategoryTheory.Limits.colimit.existsUnique, CategoryTheory.PrelaxFunctor.mapFunctor_obj, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, CategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber, CategoryTheory.uliftYonedaIsoYoneda_hom_app_app, CategoryTheory.Bicategory.leftUnitorNatIsoCat_hom_toNatTrans_app, CategoryTheory.ShortComplex.rightHomologyι_descOpcycles_π_eq_zero_of_boundary_assoc, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_symm_apply, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_iso_hom, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_hom_as_app, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Pseudofunctor.map₂_whisker_left_app_assoc, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.Pseudofunctor.DescentData'.descentDataEquivalence_unitIso, CochainComplex.mappingCone.decomp_to, CategoryTheory.Bicategory.lanUnit_desc, SemiNormedGrp.explicitCokernelDesc_zero, CategoryTheory.eqToHom_down, CategoryTheory.equivYoneda_inv_app, CategoryTheory.CommSq.shortComplex'_g, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, Rep.leftRegularHomEquiv_symm_single, CategoryTheory.PreGaloisCategory.comp_autMap_apply, AlgebraicGeometry.Spec.homEquiv_apply, CategoryTheory.Subgroupoid.IsNormal.vertexSubgroup, CategoryTheory.StrictPseudofunctor.comp_mapComp_inv, CategoryTheory.Bicategory.whiskerLeft_id, inhomogeneousCochains.d_eq, CategoryTheory.Adjunction.homAddEquiv_symm_apply, CategoryTheory.Functor.Faithful.map_injective, CategoryTheory.Presieve.mem_comap_jointlySurjectivePrecoverage_iff, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, HomologicalComplex.extend.comp_d_eq_zero_iff, CategoryTheory.NatTrans.appLinearMap_apply, CategoryTheory.InjectiveResolution.comp_descHomotopyZeroOne_assoc, CategoryTheory.MonoidalClosed.curry_injective, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zsmul_f, CategoryTheory.Localization.Construction.liftToPathCategory_map, CategoryTheory.Limits.Trident.IsLimit.homIso_symm_apply, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv_assoc, CategoryTheory.ActionCategory.comp_val, CategoryTheory.Abelian.Pseudoelement.zero_eq_zero, CategoryTheory.Lax.StrongTrans.vComp_naturality_inv, Mathlib.Tactic.Bicategory.eval_of, CategoryTheory.LaxFunctor.mapComp_assoc_right_assoc, CategoryTheory.shift_zero_eq_zero, CategoryTheory.Functor.Final.zigzag_of_eqvGen_colimitTypeRel, CategoryTheory.ShortComplex.eq_liftCycles_homologyπ_up_to_refinements, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.isCardinalFiltered_aux, CategoryTheory.Limits.BinaryBicone.inlCokernelCofork_π, CategoryTheory.Pseudofunctor.mapComp'_naturality_2, CategoryTheory.Groupoid.invEquiv_symm_apply, CategoryTheory.IsPullback.zero_bot, CategoryTheory.Oplax.StrongTrans.vcomp_naturality_hom, CategoryTheory.ObjectProperty.rightOrthogonal.map_bijective_of_isTriangulated, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_obj_base, CategoryTheory.Functor.CorepresentableBy.homEquiv_comp, CategoryTheory.CatEnrichedOrdinary.hComp_id_heq, HomologicalComplex₂.D₁_D₂_assoc, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafAdjunction_homEquiv_apply, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.Adjunction.homAddEquiv_symm_add, Homotopy.trans_hom, CategoryTheory.Lax.StrongTrans.id_naturality_inv, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, CategoryTheory.Monad.beckAlgebraCofork_ι_app, CategoryTheory.Idempotents.Karoubi.complement_p, CategoryTheory.Sheaf.instIsLocallySurjectiveHomMapTypeSheafComposeForget, CategoryTheory.ite_comp, CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_right_assoc, SemiNormedGrp.comp_explicitCokernelπ, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app_assoc, CategoryTheory.conjugateEquiv_symm_comm, CategoryTheory.Oplax.OplaxTrans.naturality_naturality_assoc, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, CategoryTheory.ShortComplex.RightHomologyData.ofIsLimitKernelFork_ι, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_δ_unmop_unmop, CategoryTheory.Limits.Sigma.ι_π_of_ne_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionRight_unop, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_hom, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_map, CategoryTheory.Bicategory.InducedBicategory.forget_obj, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, CochainComplex.mappingCone.lift_desc_f, CategoryTheory.IsFiltered.crown, SingleObj.toHom_symm_apply, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τl, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, CategoryTheory.Limits.colimit_ι_zero_cokernel_desc, CategoryTheory.Limits.CokernelCofork.map_condition, CategoryTheory.MonoidalOpposite.tensorRightMopIso_inv_app_unmop, CategoryTheory.Limits.biproduct.lift_matrix, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁_assoc, CategoryTheory.MonoidalCategory.dite_tensor, CategoryTheory.Triangulated.TStructure.isIso_truncLE_map_iff, CategoryTheory.MonObj.pow_comp, CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_K, CategoryTheory.StrictPseudofunctor.id_map, CategoryTheory.ProjectiveResolution.extMk_surjective, CategoryTheory.Pseudofunctor.toDescentData_map_hom, CategoryTheory.CountableCategory.instCountableHomObjAsType, CategoryTheory.ShortComplex.HomologyMapData.neg_right, CategoryTheory.Pseudofunctor.map₂_associator, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles, CategoryTheory.Bicategory.conjugateEquiv_associator_hom, CategoryTheory.Bicategory.Prod.swap_obj, CategoryTheory.epi_from_simple_zero_of_not_iso, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀_assoc, CategoryTheory.Free.lift_map_single, DerivedCategory.right_fac_of_isStrictlyLE, CategoryTheory.Idempotents.Karoubi.zsmul_hom, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, CategoryTheory.Abelian.coimage.comp_π_eq_zero, CategoryTheory.Join.opEquiv_inverse_map_edge_op, CategoryTheory.ObjectProperty.homMk_surjective, CategoryTheory.Limits.image_ι_comp_eq_zero, CategoryTheory.PrelaxFunctor.map₂_hom_inv_isIso, CategoryTheory.Triangulated.AbelianSubcategory.ιK_mor₁, CategoryTheory.Functor.curryingFlipEquiv_apply_map, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_assoc, CategoryTheory.Limits.zero_of_target_iso_zero, CategoryTheory.ShortComplex.Homotopy.add_h₂, CategoryTheory.yonedaGrpObj_obj_coe, CategoryTheory.conjugateEquiv_id, CategoryTheory.Functor.mapAddHom_apply, CategoryTheory.Subgroupoid.IsNormal.conj', CategoryTheory.Abelian.Ext.smul_eq_comp_mk₀, Rep.resCoindHomEquiv_apply, CategoryTheory.ShortComplex.Splitting.r_f, CategoryTheory.Bicategory.Pith.inclusion_mapId, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.Pseudofunctor.ObjectProperty.IsClosedUnderIsomorphisms.isClosedUnderIsomorphisms, CategoryTheory.Oplax.LaxTrans.Modification.naturality, CochainComplex.ConnectData.shape, CategoryTheory.Triangulated.TStructure.zero', CategoryTheory.Oplax.LaxTrans.Modification.whiskerLeft_naturality_assoc, CondensedSet.LocallyConstant.instFullCondensedTypeDiscrete, AlgebraicGeometry.tilde.map_add, CategoryTheory.HasSplitCoequalizer.splittable, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_inv, RingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, CategoryTheory.Triangulated.TStructure.descTruncGT_aux, CategoryTheory.Functor.Initial.exists_eq, Action.FintypeCat.quotientToQuotientOfLE_hom_mk, CategoryTheory.IsPullback.zero_right, CochainComplex.HomComplex.Cochain.leftShift_v, CochainComplex.mappingCone.desc_f, CochainComplex.mappingCone.d_fst_v'_assoc, CategoryTheory.StrictPseudofunctor.id_mapId_hom, Bicategory.Opposite.op2_leftUnitor_inv, CochainComplex.mappingCocone.inr_v_fst_f, CategoryTheory.Bicategory.InducedBicategory.Hom.category_comp_hom, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Bicategory.Prod.fst_map, SSet.stdSimplex.ofSimplex_yonedaEquiv_δ, CategoryTheory.Functor.postcomp_map_heq, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, imageToKernel_zero_right, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_τl, CategoryTheory.Pseudofunctor.DescentData'.pullHom'_hom_self, AlgebraicTopology.DoldKan.σ_comp_PInfty, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_iso_inv, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_inv, CategoryTheory.WithTerminal.liftFromOver_obj_map, CochainComplex.HomComplex.Cochain.toSingleMk_zero, CategoryTheory.Bicategory.eqToHom_whiskerRight, CategoryTheory.Bicategory.Adj.associator_inv_τl, CategoryTheory.Bicategory.prod_comp_snd, CategoryTheory.IsFiltered.span, CategoryTheory.Adjunction.homEquiv_symm_unit, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq_assoc, CategoryTheory.Preadditive.comp_add, LightCondensed.ihom_map_val_app, CategoryTheory.Oplax.OplaxTrans.rightUnitor_inv_as_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux, CategoryTheory.Abelian.Ext.addEquiv₀_symm_apply, CategoryTheory.ShortComplex.Homotopy.eq_add_nullHomotopic, CategoryTheory.Limits.kernelZeroIsoSource_hom, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_map_localPreimage, CategoryTheory.Presheaf.isLocallySurjective_toPlus, dNext_eq_dFrom_fromNext, CategoryTheory.Preadditive.sum_comp'_assoc, CochainComplex.mappingCone.inl_v_d, CategoryTheory.Linear.homCongr_symm_apply, CategoryTheory.OplaxFunctor.mapComp'_comp_whiskerLeft_mapComp', CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT, CategoryTheory.Pretriangulated.contractibleTriangle_mor₃, CategoryTheory.ShortComplex.Homotopy.comp_h₀, CategoryTheory.Adjunction.homAddEquiv_neg, MonObj.mopEquiv_functor_obj_mon_mul_unmop, CategoryTheory.Bicategory.Pith.comp₂_iso_hom, CategoryTheory.Limits.biproduct.desc_eq, CategoryTheory.Bicategory.lanLiftUnit_desc, CategoryTheory.Bicategory.leftUnitor_naturality_assoc, CategoryTheory.Lax.LaxTrans.homCategory_id_as_app, CategoryTheory.Bicategory.conjugateEquiv_id, CategoryTheory.Lax.StrongTrans.id_naturality_hom, CategoryTheory.Functor.IsStronglyCartesian.universal_property, CategoryTheory.Adjunction.homEquiv_symm_id, CategoryTheory.isIso_iff_yoneda_map_bijective, TopCat.Hom.equivContinuousMap_symm_apply, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_map, CategoryTheory.Bicategory.whisker_assoc, CategoryTheory.Lax.OplaxTrans.naturality_id, CategoryTheory.comp_ite, CategoryTheory.ShortComplex.ShortExact.δ_comp, CategoryTheory.Subgroupoid.coe_inv_coe, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CategoryTheory.SemiCartesianMonoidalCategory.default_eq_toUnit, CategoryTheory.Pseudofunctor.DescentData'.Hom.comm_assoc, CategoryTheory.StructuredArrow.w_prod_fst_assoc, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_inverse_map, CategoryTheory.ShortComplex.HomologyMapData.smul_right, CategoryTheory.Limits.biprod.lift_desc_assoc, CategoryTheory.Functor.isMittagLeffler_iff_subset_range_comp, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_hom_comp_ι_assoc, CategoryTheory.Preadditive.isLimitForkOfKernelFork_lift, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, CategoryTheory.Preadditive.epi_iff_isZero_cokernel', CategoryTheory.PreOneHypercover.sieve₁_apply, CategoryTheory.Bicategory.postcomposingCat_map, SimplicialObject.Splitting.IndexSet.epiComp_snd_coe, CategoryTheory.Limits.CokernelCofork.map_π, CategoryTheory.Bicategory.Adj.comp_τr, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φK, FintypeCat.inv_hom_id_apply, CategoryTheory.OplaxFunctor.PseudoCore.mapIdIso_hom, CategoryTheory.Adjunction.homEquiv_naturality_left_square_iff, CategoryTheory.ShortComplex.homologyι_descOpcycles_eq_zero_of_boundary_assoc, HomotopicalAlgebra.FibrantObject.homMk_surjective, HomologicalComplex.homologyι_descOpcycles_eq_zero_of_boundary_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, ModuleCat.hom_zsmul, CategoryTheory.Sieve.ofArrows.exists, CategoryTheory.Triangulated.TStructure.triangle_map_exists, CategoryTheory.Preadditive.inv_def, CategoryTheory.Endofunctor.Coalgebra.ext_iff, CategoryTheory.Subobject.Classifier.surjective_χ, CategoryTheory.Abelian.SpectralObject.ιE_δFromOpcycles, HomologicalComplex.mapBifunctorMapHomotopy.comm₁_aux, CategoryTheory.Adjunction.homEquiv_naturality_right_symm, CategoryTheory.Presheaf.instIsLocallySurjectiveHomToRangeSheafify, ChainComplex.linearYonedaObj_d, CategoryTheory.ShortComplex.Homotopy.symm_h₂, Action.zsmul_hom, CategoryTheory.Limits.coconeRightOpOfConeEquiv_counitIso, CategoryTheory.Preadditive.neg_comp, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, CategoryTheory.Bicategory.conjugateEquiv_symm_iso, CategoryTheory.Bicategory.InducedBicategory.isoMk_inv_hom, Compactum.str_hom_commute, Homotopy.smul_hom, Homotopy.prevD_zero_cochainComplex, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_fromBiprod_assoc, HomotopicalAlgebra.RightHomotopyClass.whitehead, CategoryTheory.Bicategory.Prod.sectR_mapComp_hom, SSet.Quasicategory.hornFilling, CategoryTheory.Limits.MonoFactorisation.kernel_ι_comp, CategoryTheory.HomOrthogonal.eq_zero, CategoryTheory.StrictPseudofunctor.mapComp_eq_eqToIso, CategoryTheory.Pretriangulated.Triangle.add_hom₁, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_map, CategoryTheory.PrelaxFunctor.map₂_comp_assoc, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CategoryTheory.Limits.biproduct.toSubtype_eq_desc, CategoryTheory.LaxFunctor.mapComp_naturality_right, CategoryTheory.Triangulated.TStructure.liftTruncLE_aux, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm, CategoryTheory.Abelian.Preradical.ι_π_app, CategoryTheory.Functor.FullyFaithful.homNatIso'_inv_app_down, HomotopicalAlgebra.bijective_rightHomotopyClassToHom, CategoryTheory.Mat.add_apply, CategoryTheory.Bicategory.yoneda_mapId_hom_as_app_toNatTrans_app, CategoryTheory.Preadditive.mul_def, Rep.MonoidalClosed.linearHomEquiv_hom, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_cofanIsColimitDesc_shrinkYoneda_map, CategoryTheory.ShortComplex.Homotopy.sub_h₂, CategoryTheory.Abelian.Ext.mk₀_eq_zero_iff, CategoryTheory.congrArg_cast_hom_left, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_as_app, CategoryTheory.StrictPseudofunctorPreCore.map₂_whisker_left, Rep.invariantsAdjunction_homEquiv_apply_hom, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_left_addition, CategoryTheory.Functor.IsRepresentedBy.iff_isIso_uliftYonedaEquiv, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.comp_hom_assoc, CategoryTheory.Bicategory.associatorNatIsoRight_hom_app, CategoryTheory.Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.Limits.Bicone.ofColimitCocone_π, CategoryTheory.Bicategory.Adj.lIso_inv, CategoryTheory.Bicategory.instIsIsoHomRightZigzagHom, CategoryTheory.yonedaEquiv_naturality, CategoryTheory.Functor.homAddMonoidHom_apply, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty_assoc, CategoryTheory.Adjunction.homEquiv_apply, CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjective, CategoryTheory.MonoidalLinear.smul_whiskerRight, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, CategoryTheory.shrinkYonedaRepresentableBy_homEquiv, CategoryTheory.Subgroupoid.inv_mem_iff, CategoryTheory.Mat_.comp_apply, CategoryTheory.WithTerminal.pseudofunctor_mapId, CategoryTheory.kernelCokernelCompSequence.φ_π, CategoryTheory.PreGaloisCategory.evaluation_aut_surjective_of_isGalois, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom, SimplicialObject.Split.natTransCofanInj_app, CategoryTheory.MonoidalLinear.whiskerLeft_smul, CochainComplex.HomComplex.Cocycle.toSingleMk_neg, CategoryTheory.Bicategory.associator_inv_congr, CategoryTheory.Bicategory.inv_whiskerLeft, CochainComplex.ConnectData.d₀_comp_assoc, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_app, ModuleCat.Hom.hom₂_apply, ChainComplex.fromSingle₀Equiv_apply, CochainComplex.mappingCone.d_fst_v', CategoryTheory.ComposableArrows.mk₃_surjective, CategoryTheory.Pseudofunctor.IsStackFor.essSurj, CategoryTheory.ShortComplex.LeftHomologyMapData.neg_φK, TopModuleCat.hom_smul, CategoryTheory.NonPreadditiveAbelian.add_comm, CondensedMod.epi_iff_locallySurjective_on_compHaus, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_map, CategoryTheory.Pseudofunctor.id_mapComp, CategoryTheory.Limits.isoZeroOfEpiZero_inv, CategoryTheory.StrictPseudofunctor.mk'_map₂, CategoryTheory.IsFilteredOrEmpty.cocone_objs, CategoryTheory.yonedaAddMonObj_obj_coe, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.Lax.LaxTrans.Modification.naturality_assoc, HomologicalComplex.exactAt_iff_exact_up_to_refinements, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, CategoryTheory.WithInitial.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_map, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_symm_apply, SemiNormedGrp.hom_zero, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, CategoryTheory.Iso.op2_inv_unop2, CategoryTheory.Pseudofunctor.DescentData'.pullHom'_hom_comp, CategoryTheory.Limits.kernel.condition_assoc, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_functor_map_f, CategoryTheory.GrpObj.comp_inv_assoc, CategoryTheory.PrelaxFunctor.map₂_isIso, CategoryTheory.types_hom, CategoryTheory.Lax.LaxTrans.LaxFunctor.bicategory_leftUnitor_inv_as_app, CategoryTheory.IsKernelPair.pullback, CategoryTheory.Bicategory.mateEquiv_leftUnitor_hom_rightUnitor_inv, CategoryTheory.Bicategory.LeftExtension.whisker_unit, CategoryTheory.Bicategory.conjugateEquiv_mateEquiv_vcomp, Rep.sum_hom, CategoryTheory.ObjectProperty.HasInducedTStructure.exists_triangle_zero_one, CategoryTheory.LaxFunctor.map₂_rightUnitor_app, CategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernel, CategoryTheory.Idempotents.split_iff_of_iso, Homotopy.comm, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, CategoryTheory.ActionCategory.id_val, CategoryTheory.ShortComplex.Homotopy.trans_h₁, CategoryTheory.Pseudofunctor.mapComp'_id_comp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_assoc, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, HomologicalComplex.mapBifunctor.d₁_eq', CategoryTheory.Limits.cokernelBiprodInlIso_hom, CategoryTheory.Iso.homCongr_symm_apply, CategoryTheory.IsCofilteredOrEmpty.cone_maps, CategoryTheory.yonedaCommGrpGrp_map_app, CategoryTheory.StrictPseudofunctor.comp_map₂, CategoryTheory.Bicategory.prod_homCategory_id_snd, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles, CategoryTheory.ShortComplex.Homotopy.comm₂, CategoryTheory.Limits.biproduct.ι_π, HomologicalComplex.d_comp_d, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp_assoc, CategoryTheory.PreZeroHypercover.sumLift_h₀, CategoryTheory.Abelian.SpectralObject.d_d_assoc, ChainComplex.mk_congr_succ_d₂, CommRingCat.HomTopology.isHomeomorph_precomp, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CategoryTheory.ObjectProperty.zero_hom, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τr, SSet.mem_degenerate_iff, SSet.S.le_iff_nonempty_hom, CategoryTheory.Bicategory.InducedBicategory.forget_map₂, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Abelian.image.ι_comp_eq_zero, TopCat.Presheaf.isGluing_iff_pairwise, CategoryTheory.GrpObj.comp_div_assoc, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, Bicategory.Opposite.bicategory_homCategory_id_unop2, CategoryTheory.IsPushout.of_hasBinaryBiproduct, CategoryTheory.Bicategory.associatorNatIsoLeft_hom_app, HomologicalComplex.mapBifunctor.d₂_eq_zero, CategoryTheory.ShortComplex.Splitting.s_r, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_fst, ChainComplex.chainComplex_d_succ_succ_zero, CategoryTheory.MonoidalCategory.rightAssocTensor_map, CategoryTheory.Subgroupoid.mem_full_iff, CategoryTheory.Bicategory.LeftLift.whiskerIdCancel_right, CategoryTheory.Sieve.shrinkFunctorIsoFunctor_hom_app_coe, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, CategoryTheory.PrelaxFunctor.comp_toPrelaxFunctorStruct, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right, CategoryTheory.GrothendieckTopology.Point.presheafFiber_map_shrinkYoneda_map_shrinkYonedaCompPresheafFiberIso_inv_app, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_app_π_assoc, CategoryTheory.MonoidalClosed.curryHomEquiv'_symm_apply, CategoryTheory.ShortComplex.sub_τ₃, CategoryTheory.PrelaxFunctor.map₂_inv_hom_assoc, CategoryTheory.Limits.Pi.ι_π_of_ne_assoc, CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, SSet.Finite.exists_epi_from_isCardinalPresentable, CategoryTheory.map_yonedaEquiv, Homotopy.comp_hom, CategoryTheory.Oplax.StrongTrans.isoMk_inv_as_app, CategoryTheory.CatEnrichedOrdinary.hComp_assoc, CategoryTheory.Bicategory.Prod.fst_mapComp_inv, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π, dNext_eq, CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer', CategoryTheory.Oplax.StrongTrans.Modification.naturality, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.op_zsmul, CategoryTheory.Sieve.natTransOfLe_app_coe, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, CategoryTheory.eHomEquiv_comp, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapComp, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, CochainComplex.shiftFunctor_obj_d', CategoryTheory.Pretriangulated.Triangle.smul_hom₃, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_comp, CategoryTheory.Hom.one_def, CategoryTheory.Oplax.LaxTrans.isoMk_hom_as_app, CategoryTheory.NonPreadditiveAbelian.neg_sub, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp_assoc, CategoryTheory.Limits.BinaryCofan.IsColimit.desc'_coe, groupCohomology.mapShortComplexH1_zero, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_symm_unitToPushforwardObjUnit, CategoryTheory.WithTerminal.pseudofunctor_mapComp, CategoryTheory.FunctorToTypes.binaryProductCone_π_app, ModuleCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.Limits.image.ι_zero', CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.Oplax.LaxTrans.homCategory_id_as_app, CategoryTheory.NonPreadditiveAbelian.comp_add, CategoryTheory.Limits.coneOpEquiv_inverse_map, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.conjugateIsoEquiv_apply_hom, CategoryTheory.WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.Pseudofunctor.DescentData'.comm_assoc, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_epi₃, CategoryTheory.shrinkYonedaIsoYoneda_inv_app_app, CategoryTheory.Bicategory.Adj.associator_hom_τr, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom, Rep.homEquiv_symm_apply, CategoryTheory.Abelian.SpectralObject.SpectralSequence.pageD_pageD_assoc, Bicategory.Opposite.unop2_id, CategoryTheory.evaluationAdjunctionRight_unit_app, AlgebraicTopology.DoldKan.N₂_obj_X_d, CategoryTheory.Limits.WalkingMultispan.instIsEmptyHomRightLeft, CategoryTheory.BicartesianSq.of_is_biproduct₂, ModuleCat.homLinearEquiv_apply, CategoryTheory.Subgroupoid.mul_mem_cancel_left, CategoryTheory.Abelian.SpectralObject.zero₃_assoc, CategoryTheory.Limits.Multifork.ofι_π_app, CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork_ι, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_hom_right, CategoryTheory.ShortComplex.RightHomologyMapData.add_φH, CochainComplex.HomComplex.Cocycle.equivHom_apply, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f, CategoryTheory.Pi.sum_map_app, CategoryTheory.Localization.structuredArrowEquiv_symm_apply, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app, CategoryTheory.Triangulated.instNonemptyOctahedron, CategoryTheory.Sieve.shrinkFunctor_obj, CategoryTheory.Pretriangulated.Triangle.sub_hom₃, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, CategoryTheory.ShortComplex.rightHomologyMap_neg, CategoryTheory.Bicategory.prod_leftUnitor_hom_fst, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero_assoc, CategoryTheory.Limits.pullbackZeroZeroIso_inv_snd, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_hom, CategoryTheory.CommSq.instHasLift_1, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Lax.OplaxTrans.comp_naturality, Rep.add_comp, CategoryTheory.Limits.biproduct.lift_eq, CategoryTheory.BicartesianSq.of_has_biproduct₁, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, HomotopicalAlgebra.LeftHomotopyRel.equivalence, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, CategoryTheory.Pseudofunctor.DescentData'.pullHom'_self, CategoryTheory.ObjectProperty.preservesKernels_ι, CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_π, GrpCat.ofHom_injective, CategoryTheory.conjugateIsoEquiv_apply_inv, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_zero_f, HomologicalComplex.mapBifunctor₂₃.d_eq, HomotopicalAlgebra.map_surjective_of_isLocalization, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, CategoryTheory.WithInitial.liftFromUnderComp_hom_app, CategoryTheory.shrinkYonedaObjObjEquiv_obj_map, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_comp_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φQ, CategoryTheory.Limits.kernelZeroIsoSource_inv, CategoryTheory.Bicategory.Adjunction.comp_left_triangle_aux, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CategoryTheory.Triangulated.Localization.distinguished_cocone_triangle, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_obj_ι, CategoryTheory.yonedaEvaluation_map_down, CategoryTheory.CartesianClosed.uncurry_injective, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_fst, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByLeft_homEquiv, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_hom, CategoryTheory.Iso.homToEquiv_symm_apply, CategoryTheory.PreGaloisCategory.surjective_of_nonempty_fiber_of_isConnected, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.unitCompPartialBijective_symm_natural, CategoryTheory.NatTrans.app_smul, CategoryTheory.FunctorToTypes.binaryCoproductCocone_ι_app, CategoryTheory.Subgroupoid.mem_iff, CategoryTheory.Functor.sectionsEquivHom_apply_app, CochainComplex.cm5b.I_d, CategoryTheory.InjectiveResolution.comp_descHomotopyZeroOne, CategoryTheory.Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq, AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology, CategoryTheory.ShortComplex.Homotopy.ofEq_h₁, CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_hom_right, CategoryTheory.IsPullback.of_isBilimit, CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer', CategoryTheory.StrictlyUnitaryPseudofunctor.map_id, CategoryTheory.Iso.homFromEquiv_apply, CategoryTheory.Lax.OplaxTrans.leftUnitor_hom_as_app, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, groupHomology.d₁₀_eq_zero_of_isTrivial, CategoryTheory.PreGaloisCategory.mulAction_naturality, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.Lax.LaxTrans.leftUnitor_inv_as_app, CategoryTheory.prodOpEquiv_functor_map, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_hom, Bicategory.Opposite.bicategory_homCategory_comp_unop2, CategoryTheory.Pseudofunctor.mkOfOplax'_mapId_inv, CategoryTheory.GrpObj.comp_inv, HomologicalComplex.homotopyCofiber.inlX_d_assoc, CategoryTheory.Oplax.LaxTrans.OplaxFunctor.bicategory_rightUnitor_hom_as_app, CategoryTheory.Limits.kernelBiprodSndIso_inv, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit_π_apply, groupCohomology.d₀₁_comp_d₁₂_assoc, CategoryTheory.LocallyDiscrete.mkPseudofunctor_obj, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom, CategoryTheory.ShortComplex.homologyMap_nullHomotopic, CategoryTheory.Functor.prod'_η_fst, CategoryTheory.Limits.inl_pushoutZeroZeroIso_inv, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_mono₂, CategoryTheory.MonoidalClosed.homEquiv_apply_eq, CategoryTheory.Limits.coneOfSectionCompCoyoneda_π, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, CategoryTheory.conjugateEquiv_whiskerLeft, CochainComplex.fromSingle₀Equiv_symm_apply_f_zero, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_symm_apply, SSet.OneTruncation₂.reflQuiver_Hom, AlgebraicGeometry.tilde.map_zero, CategoryTheory.Iso.homCongr_symm, CategoryTheory.Lax.LaxTrans.LaxFunctor.bicategory_associator_hom_as_app, HomologicalComplex.homotopyCofiber.desc_f, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimit, CochainComplex.ConnectData.comp_d₀, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom, CategoryTheory.Functor.toPseudofunctor'_mapComp, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down, CategoryTheory.Free.lift_map, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_apply_val, Hom.cast_eq_cast, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly, Opens.mayerVietorisSquare'_toSquare, CategoryTheory.Lax.LaxTrans.vComp_naturality_comp, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, CategoryTheory.WithInitial.liftFromUnder_map_app, HomologicalComplex.ι_mapBifunctorFlipIso_hom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, CategoryTheory.Bicategory.id_whiskerLeft, SimplicialObject.Splitting.comp_PInfty_eq_zero_iff, CategoryTheory.conjugateIsoEquiv_symm_apply_inv, CategoryTheory.ShortComplex.rightHomologyMap'_neg, CategoryTheory.Limits.limitCompYonedaIsoCocone_hom_app, SimplexCategory.toMk₁_surjective, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_snd, CategoryTheory.SimplicialObject.cechNerveEquiv_apply, MonObj.mopMonObj_one_unmop, CategoryTheory.Bicategory.Pith.associator_inv_iso_hom, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight_assoc, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, SimplexCategory.toMk₁_bijective, CategoryTheory.StructuredArrow.projectSubobject_factors, SemiNormedGrp.explicitCokernelDesc_comp_eq_zero, Opens.coe_mayerVietorisSquare_X₄, CategoryTheory.Pseudofunctor.mapComp_id_left_hom, CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf, ContinuousCohomology.MultiInd.d_comp_d, CategoryTheory.AddMonObj.comp_zero_assoc, CategoryTheory.Functor.postcomp_map_heq', CategoryTheory.MonoidalPreadditive.zero_whiskerRight, CategoryTheory.Bicategory.prod_associator_inv_snd, CategoryTheory.Subgroupoid.inv, CategoryTheory.AddMon.uniqueHomToTrivial_default_hom, CategoryTheory.TwoSquare.CostructuredArrowDownwards.mk_surjective, CategoryTheory.Oplax.LaxTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.InjectiveResolution.neg_extMk, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.OplaxFunctor.id_mapId, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom_assoc, CategoryTheory.Functor.map_neg, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_skyscraperPresheafHomEquiv_symm_assoc, CategoryTheory.Idempotents.DoldKan.Γ_map_app, CommGrpCat.one_apply, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_counitIso, CategoryTheory.Oplax.LaxTrans.naturality_id_assoc, CategoryTheory.Functor.homMonoidHom_apply, CategoryTheory.Limits.KernelFork.map_condition, CategoryTheory.Abelian.Ext.mk₀_linearEquiv₀_apply, groupHomology.d₃₂_comp_d₂₁, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, CategoryTheory.Pseudofunctor.map₂_whisker_left_app, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_map_f, HomologicalComplex.alternatingConst_iCycles_odd_comp_apply, CategoryTheory.Adjunction.homEquiv_naturality_left_symm, HomologicalComplex.opcyclesToCycles_homologyπ_assoc, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π_assoc, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.homologyπ_isoHomology_inv, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_rightUnitor, CategoryTheory.Limits.colimitYonedaHomIsoLimitOp_π_apply, CategoryTheory.Pseudofunctor.DescentData.isEquivalence_toDescentData_iff_of_sieve_eq, CategoryTheory.Pseudofunctor.CoGrothendieck.comp_const, Prefunctor.costar_snd, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CategoryTheory.WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_map, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.biprod.add_eq_lift_id_desc, CategoryTheory.PreGaloisCategory.IsNaturalSMul.naturality, CategoryTheory.StrictlyUnitaryLaxFunctor.ext_iff, CategoryTheory.Bicategory.Prod.snd_mapComp_hom, CochainComplex.mappingCone.inl_v_descShortComplex_f, CategoryTheory.Groupoid.isoEquivHom_symm_apply_inv, AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply, SheafOfModules.relationsOfIsCokernelFree_s, CategoryTheory.prodOpEquiv_counitIso_hom_app, RingHom.EssFiniteType.exists_comp_map_eq_of_isColimit, CategoryTheory.Bicategory.leftUnitor_hom_congr, CategoryTheory.Subgroupoid.subset_generated, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.Limits.Sigma.ι_π_of_ne, AddCommGrpCat.kernelIsoKer_hom_comp_subtype, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_obj_str, CategoryTheory.Limits.FintypeCat.jointly_surjective, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, CategoryTheory.ActionCategory.homOfPair.val, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, CategoryTheory.Lax.LaxTrans.LaxFunctor.bicategory_associator_inv_as_app, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_hom, CategoryTheory.ShortComplex.Splitting.r_f_assoc, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, CategoryTheory.Sieve.functor_map_coe, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty, HomologicalComplex.mapBifunctor₁₂.d₁_eq_zero, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_ε, CategoryTheory.Limits.kernelSubobject_arrow_comp_assoc, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp_assoc, CategoryTheory.Functor.Final.exists_coeq_of_locally_small, CategoryTheory.Subgroupoid.mem_im_iff, CategoryTheory.coyonedaPairing_map, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τr, CategoryTheory.IsPushout.zero_right, CategoryTheory.Adjunction.homEquiv_counit, CategoryTheory.leftDistributor_inv, CategoryTheory.Bicategory.whiskerRight_isIso, CochainComplex.HomComplex.Cochain.ofHom_add, CategoryTheory.Limits.ker.condition_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, CategoryTheory.Pretriangulated.Triangle.sub_hom₂, CategoryTheory.Linear.instEpiHSMulHomOfInvertible, SemiNormedGrp.comp_explicitCokernelπ_assoc, CategoryTheory.PrelaxFunctor.map₂_id, CategoryTheory.Bicategory.rightUnitor_inv_naturality_assoc, CategoryTheory.Localization.Preadditive.add'_zero, CategoryTheory.Limits.coprod.inr_fst, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_s, HomologicalComplex.mapBifunctor.d₂_eq_zero', CategoryTheory.Limits.zero_app, CategoryTheory.Functor.map_injective, CategoryTheory.Limits.isoZeroOfMonoZero_hom, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_inv_app, CategoryTheory.Oplax.OplaxTrans.isoMk_inv_as_app, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_map, CategoryTheory.StrictPseudofunctor.mk''_mapComp, AlgebraicGeometry.Scheme.exists_π_app_comp_eq_of_locallyOfFinitePresentation, CochainComplex.mappingCone.map_descShortComplex, CategoryTheory.Abelian.SpectralObject.cyclesMap_Ψ, CategoryTheory.ShiftedHom.opEquiv'_apply, CochainComplex.toSingle₀Equiv_apply, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁_assoc, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.Limits.BinaryBicone.fstKernelFork_ι, CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne_comp, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm, CategoryTheory.Functor.toOplaxFunctor_mapId, CategoryTheory.Prod.fac', CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_hom_app, SSet.stdSimplex.mem_nonDegenerate_iff_mono, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_obj_str, CategoryTheory.ComposableArrows.isoMk₁_inv_app, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero, CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_add_f, CategoryTheory.Grp.Hom.hom_inv, CategoryTheory.IsPushout.hom_eq_add_up_to_refinements, CategoryTheory.BicategoricalCoherence.assoc_iso, groupHomology.chainsMap_zero, CochainComplex.HomComplex.Cochain.single_v_eq_zero', CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Bicategory.Comonad.comul_assoc_assoc, CategoryTheory.tensorLeftHomEquiv_whiskerLeft_comp_evaluation, CategoryTheory.Presheaf.coconeOfRepresentable_ι_app, CategoryTheory.Preadditive.comp_nsmul, HomologicalComplex.homologyι_opcyclesToCycles, CategoryTheory.Bicategory.associatorNatIsoLeftCat_inv_toNatTrans_app, AlgebraicGeometry.exists_map_eq_top, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_epi₃, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, CategoryTheory.PreGaloisCategory.exists_lift_of_mono, CategoryTheory.Preadditive.forkOfKernelFork_ι, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_assoc, CategoryTheory.Mat_.id_apply, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, CategoryTheory.Bicategory.Pith.leftUnitor_hom_iso, CategoryTheory.WithInitial.lift_map, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, CategoryTheory.Bicategory.instHasInitialLeftLiftOfHasLeftKanLift, CochainComplex.HomComplex.Cochain.ofHom_zero, CategoryTheory.Oplax.LaxTrans.associator_inv_as_app, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, HomologicalComplex.mapBifunctor.d₂_eq', CategoryTheory.Arrow.mk_surjective, CochainComplex.mappingCone.inr_f_triangle_mor₃_f_assoc, CategoryTheory.conjugateEquiv_adjunction_id_symm, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, GrpCat.one_apply, Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂, CategoryTheory.hasExt_iff, CategoryTheory.Bicategory.lanUnit_desc_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_assoc, CategoryTheory.Oplax.LaxTrans.vComp_naturality_naturality, CategoryTheory.Bicategory.associator_naturality_left, Rep.comp_smul, CategoryTheory.CategoryOfElements.id_val, CategoryTheory.Oplax.LaxTrans.Modification.whiskerRight_naturality, Mathlib.Tactic.Bicategory.evalWhiskerRight_cons_of_of, Rep.ofHom_sum, TopologicalSpace.Opens.apply_mk, CategoryTheory.PresheafHom.IsSheafFor.exists_app, CochainComplex.cochainComplex_d_succ_succ_zero, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom_assoc, TopologicalSpace.Opens.infLELeft_apply, CategoryTheory.ShrinkHoms.comp_def, CategoryTheory.GrothendieckTopology.instIsIsoFunctorOppositeToPresheafFiberNatTransPointBotCoeEquivHomUnopOpObjTypeShrinkYonedaSymmShrinkYonedaObjObjEquivId, CategoryTheory.Limits.BinaryFan.leftUnitor_inv, CategoryTheory.Abelian.tfae_mono, prevD_comp_right, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_hom, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, CategoryTheory.Bicategory.Pith.comp₂_iso_inv_assoc, CategoryTheory.ShortComplex.Homotopy.g_h₃, CategoryTheory.IsPushout.of_has_biproduct, SSet.yonedaEquiv_comp, CategoryTheory.Functor.Elements.coconeπOpCompShrinkYonedaObj_ι_app, CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff, CategoryTheory.MonoidalOpposite.tensorLeftIso_hom_app_unmop, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_map₂, CategoryTheory.Abelian.Ext.mk₀_bijective, CategoryTheory.Lax.OplaxTrans.whiskerLeft_as_app, CategoryTheory.ShortComplex.RightHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork_φQ, CategoryTheory.Preadditive.isCoseparator_iff, SimplicialObject.Splitting.IndexSet.eqId_iff_eq, CategoryTheory.ObjectProperty.isColocal.homEquiv_apply, CategoryTheory.coherentTopology.isLocallySurjective_π_app_zero_of_isLocallySurjective_map, CategoryTheory.Limits.cospanHomMk_app, CategoryTheory.ObjectProperty.IsStrongGenerator.exists_of_mono_not_isIso, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, CategoryTheory.Limits.Types.Pushout.cocone_ι_app, CategoryTheory.Bicategory.prod_homCategory_comp_snd, CategoryTheory.Functor.prod_μ_snd, HomologicalComplex₂.total_d, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq, CategoryTheory.Limits.KernelFork.map_ι, SSet.Quasicategory.hornFilling', CategoryTheory.MarkovCategory.instSubsingletonHomTensorUnit, CategoryTheory.Oplax.StrongTrans.id_naturality_hom, CategoryTheory.Bicategory.leftUnitor_naturality, CategoryTheory.Limits.zero_comp, CategoryTheory.PreGaloisCategory.functorToContAction_obj_obj, CategoryTheory.Localization.hasSmallLocalizedShiftedHom_iff, CategoryTheory.Bicategory.InducedBicategory.bicategory_homCategory_id_hom, CategoryTheory.CatEnrichedOrdinary.id_hComp_id, CategoryTheory.OverPresheafAux.MakesOverArrow.of_arrow, Rep.indResHomEquiv_symm_apply, CategoryTheory.typeEquiv_functor_obj_obj_obj, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_mapId, CategoryTheory.GrothendieckTopology.instWEqualsLocallyBijectiveTypeHom, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τr, CategoryTheory.Bicategory.associatorNatIsoMiddleCat_hom_toNatTrans_app, SSet.OneTruncation₂.nerveHomEquiv_apply, CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coassoc, FintypeCat.uSwitchEquiv_symm_naturality, CategoryTheory.regularTopology.exists_effectiveEpi_iff_mem_induced, CategoryTheory.MonoOver.initialTo_b_eq_zero, CategoryTheory.Pretriangulated.Triangle.isZero₃_iff, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_hom_app, CochainComplex.homologyMap_homologyδOfTriangle, CategoryTheory.ShrinkHoms.inverse_map, CategoryTheory.Limits.coneUnopOfCoconeEquiv_inverse_map, CategoryTheory.WithTerminal.liftFromOverComp_inv_app, CategoryTheory.Monad.algebraPreadditive_homGroup_neg_f, HomologicalComplex.mapBifunctor.d₁_eq_zero', CategoryTheory.WithInitial.liftToInitial_map, CategoryTheory.ShortComplex.Homotopy.comp_h₂, CategoryTheory.PreGaloisCategory.instIsEquivalenceContActionFintypeCatHomObjFiniteAutFunctorFunctorToContAction, CategoryTheory.ShortComplex.Homotopy.ofEq_h₃, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, CategoryTheory.Limits.reflexivePair.compRightIso_inv_app, AlgebraicGeometry.exists_appTop_map_eq_zero_of_isLimit, CategoryTheory.Bicategory.Comonad.counit_comul, ModuleCat.ofHom₂_hom_apply_hom, CategoryTheory.unop_zsmul, SheafOfModules.conjugateEquiv_pullbackId_hom, CategoryTheory.Sheaf.Hom.add_app, CategoryTheory.Limits.CokernelCofork.π_ofπ, CategoryTheory.PreGaloisCategory.endEquivAutGalois_π, CategoryTheory.ActionCategory.π_map, CategoryTheory.CatEnriched.eqToHom_hComp_eqToHom, CategoryTheory.Oplax.LaxTrans.isoMk_inv_as_app, CategoryTheory.Prod.swap_map, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_hom, CategoryTheory.NatTrans.app_units_zsmul, CategoryTheory.ShortComplex.cyclesMap'_add, CategoryTheory.AddMonObj.comp_zero, CategoryTheory.Presieve.extension_iff_amalgamation, groupCohomology.subtype_comp_d₀₁, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app, CategoryTheory.prod_comp, CategoryTheory.CatEnrichedOrdinary.eqToHom_hComp_eqToHom, CategoryTheory.Subgroupoid.mem_top, CategoryTheory.NonPreadditiveAbelian.diag_σ_assoc, CategoryTheory.Limits.comp_factorThruImage_eq_zero, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_right_unitor, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app, CategoryTheory.Oplax.LaxTrans.Modification.whiskerLeft_naturality, CategoryTheory.Cat.Hom.toNatTrans_comp, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, CategoryTheory.LaxFunctor.mapComp_naturality_right_app, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.Limits.coconeOpEquiv_counitIso, CategoryTheory.MonoidalClosed.curryHomEquiv'_apply, CategoryTheory.LaxFunctor.mapComp_assoc_right, CategoryTheory.Limits.biproduct.ι_toSubtype, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_inv_right, CochainComplex.mappingCone.inl_v_snd_v, CategoryTheory.Discrete.sumEquiv_functor_map, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_mk, CategoryTheory.Oplax.LaxTrans.rightUnitor_inv_as_app, CategoryTheory.Bicategory.mateEquiv_apply, CategoryTheory.whiskerLeft_sum, CategoryTheory.GrothendieckTopology.Point.shrinkYonedaCompPresheafFiberIso_inv_app_toPresheafFiber, CategoryTheory.Bicategory.Adj.associator_hom_τl, CategoryTheory.Types.instReflectsColimitsOfSizeForgetTypeHom, CategoryTheory.Cat.FreeRefl.instSubsingletonHomOfUnique, CategoryTheory.PrelaxFunctorStruct.mkOfHomPrefunctors_toPrefunctor_map, CategoryTheory.Adjunction.leftAdjointOplaxMonoidal_δ, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Bicategory.LeftExtension.whiskerHom_right, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_mapComp, CategoryTheory.Bicategory.InducedBicategory.bicategory_associator_hom_hom, CategoryTheory.eHomEquiv_comp_assoc, AlgebraicGeometry.exists_app_map_eq_zero_of_isLimit, CategoryTheory.Oplax.StrongTrans.naturality_naturality, CategoryTheory.ShortComplex.RightHomologyData.ι_descQ_eq_zero_of_boundary, CategoryTheory.ShortComplex.neg_τ₁, CategoryTheory.MonoidalOpposite.tensorRightMopIso_hom_app_unmop, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.ShortComplex.Homotopy.ofNullHomotopic_h₃, HomologicalComplex.unit_tensor_d₁, CategoryTheory.StructuredArrow.w_prod_snd_assoc, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, CategoryTheory.StructuredArrow.prodInverse_obj, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom, CategoryTheory.Limits.IsZero.eq_zero_of_src, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_rightAdd, CategoryTheory.PrelaxFunctor.map₂Iso_hom, ModuleCat.hom_sub, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_hom, CategoryTheory.ShortComplex.LeftHomologyMapData.add_φK, Homotopy.nullHomotopy_hom, CategoryTheory.Pseudofunctor.mkOfOplax'_mapComp_inv, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition'_assoc, CategoryTheory.NonPreadditiveAbelian.sub_def, CategoryTheory.DifferentialObject.d_squared_assoc, CategoryTheory.conjugateEquiv_adjunction_id, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHom_op, CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_f', CategoryTheory.GrothendieckTopology.Point.map_aux, CategoryTheory.Oplax.OplaxTrans.leftUnitor_hom_as_app, CategoryTheory.Limits.biproduct.ι_toSubtype_assoc, CategoryTheory.Functor.final_iff_of_isFiltered, CategoryTheory.coyonedaEquiv_symm_map, CategoryTheory.Lax.LaxTrans.associator_hom_as_app, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom_assoc, CategoryTheory.ObjectProperty.IsStrongGenerator.exists_of_subobject_ne_top, CategoryTheory.Adjunction.homEquiv_naturality_right_square, CategoryTheory.Abelian.FunctorCategory.functor_category_isIso_coimageImageComparison, CategoryTheory.Oplax.LaxTrans.OplaxFunctor.bicategory_associator_inv_as_app, CategoryTheory.rightDistributor_hom, ModuleCat.ofHom₂_compr₂, CategoryTheory.PrelaxFunctor.map₂Iso_inv, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, starEquivCostar_symm_apply_snd, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, ChainComplex.mk_d, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, HomologicalComplex.comp_homologyπ_eq_zero_iff_up_to_refinements, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_inv, CategoryTheory.ShortComplex.Homotopy.neg_h₂, CategoryTheory.Lax.LaxTrans.rightUnitor_inv_as_app, CategoryTheory.Limits.SequentialProduct.cone_π_app, PresheafOfModules.freeYonedaEquiv_comp, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_hom, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_assoc, CochainComplex.ConnectData.comp_d₀_assoc, CategoryTheory.MonoidalPreadditive.tensor_add, Bicategory.Opposite.bicategory_associator_inv_unop2, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_assoc, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.finrank_endomorphism_simple_eq_one, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f, CategoryTheory.ShortComplex.HasRightHomology.of_zeros, CategoryTheory.Limits.IsZero.iff_id_eq_zero, CategoryTheory.Abelian.SpectralObject.δ_pOpcycles, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, CategoryTheory.Lax.OplaxTrans.naturality_comp_assoc, CategoryTheory.Pseudofunctor.DescentData.id_hom, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, HomologicalComplex₂.d₂_eq', CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.ShortComplex.zero_τ₁, CategoryTheory.IsFiltered.sup_objs_exists, CategoryTheory.LaxFunctor.mapComp_naturality_left_app, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, CategoryTheory.Triangulated.TStructure.descTruncGE_aux, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_p, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv_assoc, CategoryTheory.ShortComplex.smul_τ₁, CategoryTheory.Limits.cokernel.π_of_epi, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_v_eq_zero, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp, CategoryTheory.OplaxFunctor.mapComp_id_left_assoc, CategoryTheory.StrictPseudofunctor.mk'_mapId, FintypeCat.hom_inv_id_apply, CategoryTheory.WithTerminal.liftFromOver_map_app, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_mono₁, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_hom, Mathlib.Tactic.Bicategory.naturality_comp, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism₁, CategoryTheory.Limits.coequalizer.existsUnique, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_fromBiprod, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, Homotopy.dNext_cochainComplex, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, Homotopy.nullHomotopicMap'_f, CategoryTheory.Bicategory.Prod.swap_mapComp_hom, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp_assoc, CategoryTheory.Presieve.uncurry_pullbackArrows, CategoryTheory.Pseudofunctor.StrongTrans.Modification.vcomp_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.MorphismProperty.IsCompatibleWithTriangulation.compatible_with_triangulation, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_counitIso, CategoryTheory.Pseudofunctor.DescentData.isoMk_hom_hom, CategoryTheory.CatEnrichedOrdinary.hComp_assoc_heq, CategoryTheory.shrinkYonedaMon_obj_map_shrinkYonedaMonObjObjEquiv_symm, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_assoc, CategoryTheory.Bicategory.LeftLift.ofIdComp_left_as, CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiberMk_jointly_surjective, CategoryTheory.StrictPseudofunctor.id_mapId_inv, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app, CategoryTheory.Lax.OplaxTrans.leftUnitor_inv_as_app, CategoryTheory.ShortComplex.exact_iff_of_forks, CategoryTheory.Sieve.mem_ofArrows_iff, SingleObj.pathEquivList_cons, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.isoMk_inv_hom, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_inv_right, PresheafOfModules.sheafificationAdjunction_homEquiv_apply, CategoryTheory.Adjunction.representableBy_homEquiv, CategoryTheory.Functor.Elements.initialOfRepresentableBy_snd, CategoryTheory.epi_iff_surjective_up_to_refinements, SemiNormedGrp.explicitCokernelDesc_norm_le_of_norm_le, TopCat.Presheaf.germ_eq, CategoryTheory.Functor.PreservesHomology.preservesCokernel, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_app_toFunctor_obj, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, Prefunctor.IsCovering.map_injective, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.f'_eq, CategoryTheory.Lax.OplaxTrans.Modification.naturality_assoc, CategoryTheory.Functor.CorepresentableBy.ext_iff, CategoryTheory.ShortComplex.smul_τ₂, CategoryTheory.IsCoreflexivePair.common_retraction', CategoryTheory.shrinkYonedaIsoYoneda_hom_app_app, HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff, CategoryTheory.Limits.BinaryBicone.inl_snd, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq, CategoryTheory.Functor.CorepresentableBy.homEquiv_symm_comp, CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_inv, CategoryTheory.Abelian.Ext.linearEquiv₀_symm_apply, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_as_app_toNatTrans_app, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_as, CategoryTheory.FreeBicategory.mk_associator_inv, CochainComplex.isKInjective_of_injective_aux, Rep.comp_add, CategoryTheory.ShiftedHom.mk₀_neg, CategoryTheory.Join.mapIsoWhiskerLeft_inv_app, CategoryTheory.Triangulated.TStructure.truncLTι_comp_truncGEπ, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.comm_assoc, CochainComplex.homologyMap_comp_eq_zero_of_distTriang_assoc, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, CategoryTheory.Bicategory.Adj.iso₂Mk_inv_τr, CategoryTheory.Abelian.SpectralObject.δ_eq_zero_of_isIso₁, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.Functor.toPreimages_obj, CategoryTheory.ShortComplex.liftCycles_homologyπ_eq_zero_of_boundary, CategoryTheory.Bicategory.rightUnitor_comp_assoc, CategoryTheory.HomOrthogonal.matrixDecomposition_symm_apply, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.NonPreadditiveAbelian.lift_map, CategoryTheory.FreeBicategory.locally_thin, CategoryTheory.Functor.homEquivOfIsRightKanExtension_apply_app, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_obj_str, Mathlib.Tactic.Bicategory.evalComp_nil_cons, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, HomologicalComplex.homologyι_descOpcycles_eq_zero_of_boundary, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τr, CategoryTheory.Pseudofunctor.mapId'_hom_naturality, CategoryTheory.IsDiscrete.subsingleton, CategoryTheory.Pseudofunctor.DescentData.hom_self, imageToKernel_zero_left, CategoryTheory.conjugateIsoEquiv_symm_apply_hom, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_apply, Mathlib.Tactic.Bicategory.evalWhiskerRightAux_of, HomotopicalAlgebra.CofibrantObject.exists_bifibrant, CategoryTheory.Limits.IsZero.iff_isSplitMono_eq_zero, HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff', CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_left_assoc, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_nsmul_f, dNext_comp_right, HomologicalComplex.homotopyCofiber.inlX_desc_f, CategoryTheory.Pseudofunctor.DescentData.comp_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app, AlgebraicTopology.DoldKan.QInfty_comp_PInfty_assoc, CategoryTheory.Limits.Cotrident.ofπ_ι_app, CategoryTheory.Bicategory.LeftExtension.IsKan.fac, TopologicalSpace.Opens.apply_def, HomologicalComplex.fromOpcycles_d, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapId, CategoryTheory.conj_eqToHom_iff_heq, CategoryTheory.Oplax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.Adjunction.homAddEquiv_apply, HomologicalComplex.iCycles_d_assoc, CategoryTheory.Limits.op_zero, CategoryTheory.Functor.linear_iff, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι_app_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomLeft_op, HomotopyCategory.quotient_map_out, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles, CategoryTheory.Pseudofunctor.ObjectProperty.map_obj_obj, CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_inv_right, CategoryTheory.Limits.coconeOfIsSplitEpi_ι_app, SheafOfModules.Presentation.IsFinite.finite_relations, SemimoduleCat.hom_add, LightProfinite.proj_comp_transitionMapLE, CategoryTheory.FreeBicategory.lift_mapComp, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃, CategoryTheory.ShortComplex.Homotopy.add_h₃, HomologicalComplex₂.d₁_eq', CategoryTheory.Bicategory.Comonad.comul_counit, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_add_f, HomotopicalAlgebra.bijective_leftHomotopyClassToHom, CategoryTheory.ObjectProperty.rightOrthogonal_iff, CategoryTheory.Preadditive.one_def, CategoryTheory.Over.lift_left, CategoryTheory.Bicategory.leftZigzagIso_inv, CategoryTheory.Functor.toOplaxFunctor'_mapComp, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_id, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_mono₃, CategoryTheory.Mat_.id_def, AlgebraicTopology.DoldKan.Γ₂_map_f_app, CategoryTheory.Abelian.Preradical.ι_π_app_assoc, CategoryTheory.Bicategory.Adjunction.comp_right_triangle_aux, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, CategoryTheory.ShortComplex.cyclesMap'_neg, CategoryTheory.DifferentialObject.d_squared_apply_assoc, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype_assoc, CategoryTheory.MorphismProperty.map_eq_iff_precomp, SSet.Truncated.HomotopyCategory.BinaryProduct.functor_map, CochainComplex.HomComplex.Cocycle.fromSingleMk_mem_coboundaries_iff, CategoryTheory.Adjunction.homEquiv_naturality_right_square_assoc, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, CochainComplex.HomComplex.Cochain.equivHomotopy_symm_apply_hom, groupHomology.d₁₀_comp_coinvariantsMk_assoc, CategoryTheory.op_neg, CategoryTheory.Limits.CokernelCofork.map_condition_assoc, CategoryTheory.Lax.OplaxTrans.isoMk_hom_as_app, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.π_comp_isoHomology_hom, CategoryTheory.Pseudofunctor.DescentData'.comp_pullHom''_assoc, CategoryTheory.Bicategory.Adj.lIso_hom, CategoryTheory.Lax.OplaxTrans.isoMk_inv_as_app, AlgebraicTopology.DoldKan.decomposition_Q, CategoryTheory.Limits.hasPullback_over_zero, CategoryTheory.Limits.colimitCoconeOfUnique_cocone_ι, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, HomologicalComplex.extendMap_zero, CochainComplex.Lifting.coe_cocycle₁'_v_comp_eq_zero, HomologicalComplex.extendMap_f_eq_zero, CategoryTheory.isCardinalFiltered_iff, CategoryTheory.Bicategory.Prod.sectL_map₂, CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory_leftUnitor_inv_as_app, Prefunctor.symmetrify_map, CategoryTheory.Oplax.StrongTrans.toOplax_naturality, CategoryTheory.Pseudofunctor.mapId'_hom_naturality_assoc, CategoryTheory.ShortComplex.opcyclesMap'_add, CategoryTheory.ShortComplex.Exact.isZero_X₂_iff, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, SheafOfModules.sectionsMap_freeHomEquiv_symm_freeSection, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.PreGaloisCategory.fiberEqualizerEquiv_symm_ι_apply, CategoryTheory.prod_id_snd, HomotopicalAlgebra.CofibrantObject.HoCat.exists_resolution, CategoryTheory.SmallObject.ιFunctorObj_extension, CategoryTheory.instSmallHomFunctorOppositeTypeColimitCompYoneda, AlgebraicTopology.DoldKan.σ_comp_P_eq_zero, CategoryTheory.Bicategory.Adjunction.homEquiv₁_symm_apply, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.Bicategory.toNatTrans_conjugateEquiv, CategoryTheory.Lax.StrongTrans.categoryStruct_comp_naturality, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, CategoryTheory.Over.opEquivOpUnder_functor_map, CategoryTheory.op_sub, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.ShortComplex.rightHomologyMap'_smul, CategoryTheory.NonPreadditiveAbelian.add_neg_cancel, HasFibers.inducedFunctor_map_coe, CategoryTheory.FreeBicategory.lift_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Subobject.factors_zero, CategoryTheory.IsPullback.inr_fst', SSet.Truncated.HomotopyCategory.subsingleton_hom, CategoryTheory.Pseudofunctor.comp_mapComp, CategoryTheory.Sheaf.instIsLocallyInjectiveHomImageι, Prefunctor.star_snd, CategoryTheory.ComposableArrows.isoMk₀_hom_app, CategoryTheory.Bicategory.Prod.swap_mapComp_inv, homOfEq_heq_left_iff, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.IsFilteredOrEmpty.cocone_maps, CategoryTheory.PrelaxFunctor.map₂Iso_eqToIso, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, CategoryTheory.Limits.Cofork.IsColimit.homIso_symm_apply, CategoryTheory.ShortComplex.LeftHomologyData.wi_assoc, CategoryTheory.Pretriangulated.Triangle.isZero₁_iff, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, CategoryTheory.Subgroupoid.id_mem_of_nonempty_isotropy, Bicategory.Opposite.opFunctor_map, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.Pseudofunctor.DescentData'.pullHom'₁₂_eq_pullHom_of_chosenPullback₃_assoc, CategoryTheory.CartesianClosed.curry_injective, HomologicalComplex₂.ιTotalOrZero_eq_zero, HomologicalComplex.double_d_eq_zero₁, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapComp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, CategoryTheory.uliftYonedaMap_app_apply, CategoryTheory.AddMon.Hom.hom_nsmul, CategoryTheory.Pseudofunctor.toOplax_mapId', Rep.ofHom_zsmul, CategoryTheory.ShortComplex.Exact.epi_f_iff, CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq, CategoryTheory.Preadditive.zsmul_comp, HomologicalComplex.truncGE'.homologyι_truncGE'XIsoOpcycles_inv_d, CategoryTheory.subterminals_thin, CategoryTheory.Bicategory.LeftLift.whiskering_obj, Mathlib.Tactic.Bicategory.eval_monoidalComp, Hom.unmop_inj, LightCondensed.internallyProjective_iff_tensor_condition', CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, CategoryTheory.opEquiv_symm_apply, CategoryTheory.Limits.CokernelCofork.π_eq_zero, CategoryTheory.Limits.bicone_ι_π_ne, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac_assoc, CategoryTheory.Triangulated.TStructure.eTruncLT_ι_bot, CategoryTheory.congrArg_mpr_hom_right, CategoryTheory.ShrinkHoms.functor_map, CategoryTheory.ShortComplex.neg_τ₃, CategoryTheory.Bicategory.Prod.snd_mapComp_inv, CategoryTheory.Sieve.equalizer_eq_equalizerSieve, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τl, CategoryTheory.NonPreadditiveAbelian.lift_σ, CategoryTheory.StrictPseudofunctor.mk''_obj, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity, AlgebraicGeometry.Scheme.exists_hom_hom_comp_eq_comp_of_locallyOfFiniteType, AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff, CategoryTheory.Bicategory.Pith.comp₂_iso_inv, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app, CategoryTheory.Abelian.Ext.homEquiv₀_symm_apply, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₁, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerLeft_naturality, CategoryTheory.Bicategory.conjugateEquiv_symm_apply', AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_r, CategoryTheory.Limits.hasPushout_over_zero, CategoryTheory.cones_obj_obj, CategoryTheory.NonPreadditiveAbelian.lift_σ_assoc, CategoryTheory.Functor.FullyFaithful.homNatIso_hom_app_down, CategoryTheory.NonPreadditiveAbelian.comp_sub, ModuleCat.homAddEquiv_apply, FreeGroupoid.congr_reverse_comp, CategoryTheory.Functor.PreOneHypercoverDenseData.sieve₁₀_apply, CategoryTheory.IsPushout.isVanKampen_iff', CategoryTheory.ComposableArrows.precomp_surjective, CategoryTheory.shrinkYoneda_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Pseudofunctor.CoGrothendieck.instFaithfulαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, CategoryTheory.Adjunction.homAddEquiv_symm_sub, CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm, CategoryTheory.Limits.kernel.lift_zero, CategoryTheory.ShortComplex.RightHomologyData.ofZeros_g', HomologicalComplex₂.D₁_totalShift₂XIso_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_iso, CategoryTheory.Bicategory.InducedBicategory.isoMk_hom_hom, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.Limits.Cofork.ofπ_ι_app, SkyscraperPresheafFunctor.map'_app, CategoryTheory.Bicategory.whiskerLeft_rightUnitor, Path.isChain_toList_nonempty, CategoryTheory.Limits.WalkingCospan.instSubsingletonHom, CategoryTheory.Limits.FintypeCat.instPreservesFiniteColimitsFintypeCatForgetHomObjFinite, CategoryTheory.Functor.currying_functor_obj_map, CategoryTheory.yonedaGrp_map_app, CategoryTheory.comp_eqToHom_heq, CategoryTheory.Preadditive.comp_sub_assoc, AlgebraicGeometry.tilde.map_neg, CategoryTheory.Equalizer.FirstObj.ext_iff, HomologicalComplex.mapBifunctor₁₂.d₁_eq, AlgebraicTopology.DoldKan.Q_zero, CategoryTheory.WithInitial.pseudofunctor_mapComp, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, CategoryTheory.leftUnitor_def, CategoryTheory.Iso.eHomCongr_inv_comp, CategoryTheory.MonObj.one_eq_one, ChainComplex.mkHom_f_succ_succ, CategoryTheory.ShortComplex.sub_liftCycles, HomologicalComplex.opcyclesMap_zero, CategoryTheory.FintypeCat.instPreservesFiniteLimitsActionFintypeCatForgetHomSubtypeHomObjFiniteV, HomologicalComplex₂.D₂_totalShift₂XIso_hom, CategoryTheory.Limits.IsLimit.existsUnique, CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, Rep.tensorHomEquiv_symm_apply, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp, CategoryTheory.Localization.homEquiv_map, CategoryTheory.FreeBicategory.preinclusion_obj, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, imageToKernel_epi_of_epi_of_zero, CategoryTheory.CatEnriched.hComp_comp, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f_assoc, CategoryTheory.ShortComplex.rightHomologyMap_smul, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_assoc, AlgebraicGeometry.IsImmersion.isImmersion_iff_exists_of_quasiCompact, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_η_unmop_app, CategoryTheory.Pseudofunctor.map₂_right_unitor_app_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, CategoryTheory.Pseudofunctor.map₂_right_unitor_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.FreeBicategory.lift_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, CategoryTheory.LaxFunctor.comp_mapComp, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_mono₁, CategoryTheory.Join.opEquiv_functor_map_op_inclLeft, CategoryTheory.Abelian.Pseudoelement.eq_zero_iff, CategoryTheory.ObjectProperty.ind_iff_exists, CategoryTheory.finallySmall_iff_exists_small_weakly_terminal_set, HomologicalComplex.shortComplexTruncLE_shortExact_δ_eq_zero, CategoryTheory.ShortComplex.RightHomologyData.ofIsLimitKernelFork_H, CategoryTheory.conjugateEquiv_comp, CategoryTheory.map_shrinkYonedaEquiv, CategoryTheory.NatTrans.app_zsmul, CategoryTheory.Mat_.comp_def, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_sigmaDesc_uliftYoneda_map, CategoryTheory.WithInitial.opEquiv_inverse_map, AlgebraicGeometry.Scheme.Cover.intersectionOfLocallyDirected_f, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.hf, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, AddCommGrpCat.hom_add_apply, SingleObj.toPrefunctor_symm_apply, CategoryTheory.PrelaxFunctor.map₂_hom_inv_isIso_assoc, CategoryTheory.Biprod.inl_ofComponents, CategoryTheory.Under.opEquivOpOver_functor_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_ε_unmop_app, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, CategoryTheory.ShortComplex.Exact.lift', CategoryTheory.Limits.biproduct.map_eq, CategoryTheory.Preadditive.comp_sub, CategoryTheory.Limits.WalkingSpan.instSubsingletonHom, CategoryTheory.prod.leftUnitor_map, CategoryTheory.Adjunction.homEquiv_apply_eq, CategoryTheory.yonedaEquiv_symm_map, CategoryTheory.tensorLeftHomEquiv_whiskerRight_comp_evaluation, CategoryTheory.Limits.IsLimit.homIso_hom, CategoryTheory.Cat.Hom.equivFunctor_apply, CategoryTheory.Limits.BinaryBicone.inr_fst, CategoryTheory.Functor.map_nsmul, CategoryTheory.Limits.cokernelZeroIsoTarget_hom, AddCommGrpCat.ofHom_injective, DerivedCategory.HomologySequence.δ_comp_assoc, ContinuousCohomology.MultiInd.d_succ, CategoryTheory.Subgroupoid.inclusion_faithful, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_apply, ModuleCat.semilinearMapAddEquiv_symm_apply_apply, CategoryTheory.MorphismProperty.Comma.mapLeftEq_hom_app_right, CategoryTheory.Limits.CokernelCofork.IsColimit.isZero_of_epi, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Cat.Hom.toNatIso_inv, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_cocone, AlgebraicGeometry.Proj.res_apply, CategoryTheory.IsIso.out, CategoryTheory.Bicategory.postcomposing₂_obj_app_toFunctor_obj, Rep.coinvariantsAdjunction_homEquiv_apply_hom, CategoryTheory.CostructuredArrow.projectQuotient_factors, CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT_app, CategoryTheory.Sieve.toFunctor_app_coe, HomologicalComplex.mapBifunctor₁₂.d₃_eq, CochainComplex.Lifting.comp_coe_cocyle₁'_v_eq_zero_assoc, DerivedCategory.HomologySequence.δ_comp, CategoryTheory.Join.mapIsoWhiskerLeft_hom_app, HomologicalComplex.biprod_inr_fst_f_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, CategoryTheory.Subgroupoid.mem_sInf_arrows, CategoryTheory.Bicategory.conjugateEquiv_iso, CategoryTheory.Limits.kernelSubobject_arrow_comp, CategoryTheory.Bicategory.conjugateEquiv_comm, CategoryTheory.effectiveEpi_iff_effectiveEpiFamily, CategoryTheory.Cat.HasLimits.homDiagram_obj, CategoryTheory.Sheaf.isLocallySurjective_iff_isIso, CategoryTheory.uliftCoyonedaEquiv_symm_map, CategoryTheory.Bicategory.Prod.sectR_mapId_hom, CategoryTheory.AddMonObj.comp_add_assoc, CategoryTheory.TwoSquare.lanBaseChange_app, MonObj.mopMonObj_mul_unmop, CategoryTheory.Functor.hcongr_hom, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, CategoryTheory.NonPreadditiveAbelian.neg_def, CategoryTheory.Linear.toCatCenter_apply_app, CategoryTheory.OplaxFunctor.mapComp_naturality_right, CategoryTheory.Bicategory.Strict.leftUnitor_eqToIso, AlgebraicGeometry.spread_out_of_isGermInjective, DerivedCategory.mem_distTriang_iff, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux_assoc, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_apply_coe, CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsLimitKernelFork_φK, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_map_base, CategoryTheory.yonedaEquiv_symm_naturality_left, CategoryTheory.InjectiveResolution.comp_descHomotopyZeroSucc, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_add_f, CategoryTheory.Bicategory.Prod.swap_mapId_hom, CategoryTheory.PreGaloisCategory.exists_galois_representative, CategoryTheory.CatCenter.app_neg, CategoryTheory.Limits.HasLimitOfHasProductsOfHasEqualizers.buildLimit_π_app, CategoryTheory.Over.isMonHom_pullbackFst_id_right, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand', FundamentalGroupoidFunctor.prodToProdTop_map, TopModuleCat.kerι_comp, HomologicalComplex.homotopyCofiber.d_sndX_assoc, AlgebraicGeometry.Scheme.JointlySurjective.exists_eq, CategoryTheory.Adjunction.homEquiv_ofNatIsoLeft_symm_apply, CategoryTheory.MorphismProperty.ind_iff_exists, ModuleCat.hom_neg, CategoryTheory.Pseudofunctor.DescentData'.pullHom'₂₃_eq_pullHom_of_chosenPullback₃_assoc, CategoryTheory.Pretriangulated.Opposite.complete_distinguished_triangle_morphism, FDRep.scalar_product_char_eq_finrank_equivariant, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_i, CategoryTheory.Bicategory.conjugateEquiv_whiskerLeft, Hom.toLoc_as, CategoryTheory.GrothendieckTopology.diagramNatTrans_zero, CondensedSet.epi_iff_locallySurjective_on_compHaus, CategoryTheory.LocalizerMorphism.RightResolution.mk_surjective, CategoryTheory.Hom.mulEquivCongrRight_apply, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_δ, CategoryTheory.StrictlyUnitaryLaxFunctor.id_mapId, dNext_nat, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_cofanIsColimitDesc_uliftYoneda_map, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁, CategoryTheory.LaxFunctor.map₂_associator_app, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_sub_f, CategoryTheory.FreeBicategory.mk_right_unitor_hom, CategoryTheory.Bicategory.LeftExtension.whiskering_obj, CategoryTheory.Presheaf.instIsLocallyInjectiveHomιOpposite, CategoryTheory.Functor.map_dite, CategoryTheory.Pseudofunctor.toLax_mapComp', CategoryTheory.yonedaEquiv_symm_naturality_right, CategoryTheory.OplaxFunctor.mapComp'_comp_mapComp'_whiskerRight_assoc, SheafOfModules.pushforwardSections_unitHomEquiv, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂_assoc, HomologicalComplex.extend.mapX_none, CategoryTheory.Prod.fst_map, CategoryTheory.AddMonObj.ofRepresentableBy_zero, CategoryTheory.Equalizer.Sieve.SecondObj.ext_iff, HomologicalComplex.neg_f_apply, CategoryTheory.Over.mapCongr_rfl, CategoryTheory.MonoidalCategory.prodMonoidal_tensorHom, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero_assoc, Mathlib.Tactic.Bicategory.structuralIsoOfExpr_whiskerRight, CategoryTheory.AddMonObj.zero_comp_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_map_coe, CategoryTheory.Pseudofunctor.DescentData'.pullHom_pullHom'_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_apply, LightCondensed.instSmallHom, CategoryTheory.GrothendieckTopology.uliftYoneda_map_hom_app_down, CategoryTheory.Limits.biproduct.ι_π_ne_assoc, CategoryTheory.StrictPseudofunctor.comp_obj, CategoryTheory.ShortComplex.leftHomologyMap_zero, Bicategory.Opposite.homCategory_id_unop2, CategoryTheory.Sieve.shrinkFunctorIsoFunctor_inv_app_coe, CategoryTheory.Limits.cokernelZeroIsoTarget_inv, CategoryTheory.Grp.Hom.hom_one, AlgebraicTopology.DoldKan.PInfty_comp_QInfty_assoc, CategoryTheory.StrictPseudofunctor.id_mapComp_inv, CategoryTheory.Bicategory.yoneda₀_mapComp_hom_toNatTrans_app, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm, CategoryTheory.ProjectiveResolution.neg_extMk, CategoryTheory.Triangulated.TStructure.isLE_iff_orthogonal, CategoryTheory.Bicategory.InducedBicategory.mkHom_eqToHom, CategoryTheory.Bicategory.comp_whiskerLeft_symm_assoc, HomologicalComplex.shape, CategoryTheory.AsSmall.down_map, SSet.stdSimplex.objEquiv_symm_apply, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, Homotopy.refl_hom, CategoryTheory.Localization.HasSmallLocalizedHom.small, CategoryTheory.Localization.Preadditive.map_add, CochainComplex.mappingCocone.inl_v_snd_v_assoc, CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk, CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork_g', CategoryTheory.Abelian.SpectralObject.iCycles_δ_assoc, CategoryTheory.Oplax.LaxTrans.leftUnitor_inv_as_app, CommRingCat.moduleCatRestrictScalarsPseudofunctor_obj, CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_val, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_nsmul_f, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, SemimoduleCat.homLinearEquiv_symm_apply, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_map_f, CategoryTheory.Abelian.SpectralObject.zero₁_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, CochainComplex.HomComplex.Cochain.ofHoms_zero, SSet.KanComplex.hornFilling, CategoryTheory.uliftYonedaEquiv_symm_map_assoc, CategoryTheory.comp_dite, HomologicalComplex.mapBifunctor₁₂.d₂_eq, CochainComplex.Lifting.coe_cocycle₁'_v_comp_eq_zero_assoc, HasFibers.fiber_factorization, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, TopCat.Presheaf.coveringOfPresieve_apply, CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomLeft, Bicategory.Opposite.op2_id_unbop, CategoryTheory.isIso_prod_iff, CategoryTheory.PreGaloisCategory.instFaithfulContActionFintypeCatHomObjFiniteAutFunctorFunctorToContAction, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit_f_aux, CategoryTheory.ShortComplex.liftCycles_leftHomologyπ_eq_zero_of_boundary, CategoryTheory.Sieve.generate_apply, CategoryTheory.Limits.colimitCoconeOfUnique_isColimit_desc, CategoryTheory.Pretriangulated.contractible_distinguished₁, CategoryTheory.Bicategory.leftUnitor_comp, CategoryTheory.Presheaf.isLocallyInjective_toPlus, SimplexCategory.eq_comp_δ_of_not_surjective, HomologicalComplex.mapBifunctor₂₃.d₁_eq_zero, CategoryTheory.BicategoricalCoherence.assoc'_iso, CategoryTheory.Bicategory.LeftExtension.w, CategoryTheory.Lax.OplaxTrans.vComp_naturality_id, CategoryTheory.Comonad.adj_unit, CategoryTheory.NonPreadditiveAbelian.neg_neg, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, SheafOfModules.generatorsOfIsCokernelFree_s, CategoryTheory.Bicategory.yoneda_mapComp_inv_as_app_toNatTrans_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.Sum.functorEquiv_unitIso, DerivedCategory.HomologySequence.epi_homologyMap_mor₂_iff, TopModuleCat.hom_neg, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_app_π, CategoryTheory.Limits.coprod.inl_snd_assoc, CategoryTheory.toQuotientPaths_map, CategoryTheory.Cat.associator_hom_toNatTrans, CategoryTheory.Presheaf.isLocallyInjective_forget, Mathlib.Tactic.Bicategory.evalComp_nil_nil, HomologicalComplex.alternatingConst_iCycles_even_comp_assoc, CategoryTheory.Cat.Hom.instIsIsoFunctorαCategoryToNatTransHomHom, CategoryTheory.unop_sub, CategoryTheory.Localization.Preadditive.zero_add', dNext_eq_zero, CategoryTheory.ActionCategory.hom_as_subtype, SimplicialObject.Split.cofan_inj_naturality_symm, CategoryTheory.MonoidalOpposite.tensorLeftIso_inv_app_unmop, CategoryTheory.Pretriangulated.productTriangle.zero₃₁, CategoryTheory.Pseudofunctor.isoMapOfCommSq_eq, CategoryTheory.Oplax.LaxTrans.whiskerLeft_as_app, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, CategoryTheory.cocones_obj_obj, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimitRightOp_π_apply, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, CategoryTheory.Localization.Preadditive.neg'_add'_self, CategoryTheory.LaxFunctor.mapComp_naturality_left, CategoryTheory.LaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_inv_right, CategoryTheory.GrothendieckTopology.plusMap_zero, CategoryTheory.Functor.RepresentableBy.ofIsoObj_homEquiv, CochainComplex.mappingCone.lift_f, CategoryTheory.ComposableArrows.IsComplex.zero, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_inv, CategoryTheory.Functor.CorepresentableBy.coyoneda_homEquiv, ModuleCat.monoidalClosed_pre_app, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.π_comp_isoHomology_hom_assoc, AlgebraicGeometry.pointsPi_surjective, CategoryTheory.Bicategory.associatorNatIsoMiddle_inv_app, SemimoduleCat.hom_smul, HomologicalComplex.liftCycles_comp_homologyπ_eq_zero_iff_up_to_refinements, CategoryTheory.Limits.pullback_fst_map_snd_isPullback, HomologicalComplex₂.totalAux.d₁_eq', CategoryTheory.ShortComplex.add_τ₁, CategoryTheory.Bicategory.postcomp₂_naturality_inv_toNatTrans_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_obj_map, SSet.stdSimplex.nonDegenerateEquiv_symm_apply_coe, CategoryTheory.Adjunction.rightAdjointOfEquiv_map, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff', CategoryTheory.InducedCategory.homLinearEquiv_symm_apply_hom, CategoryTheory.Pseudofunctor.map₂_whisker_right_assoc, CategoryTheory.Arrow.equivSigma_apply_snd_fst, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork_φH, CategoryTheory.WithInitial.ofCommaMorphism_app, SimplicialObject.Splitting.cofan_inj_comp_app_assoc, HomologicalComplex.ι_mapBifunctorFlipIso_hom_assoc, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.Comonad.beckCoalgebraFork_π_app, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_φ, TopologicalSpace.OpenNhds.apply_mk, CategoryTheory.MorphismProperty.Comma.mapLeftEq_hom_app_left, CategoryTheory.MonoidalOpposite.tensorIso_inv_app_unmop, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, CommGrpCat.ofHom_injective, CochainComplex.HomComplex.CohomologyClass.toHom_mk, CategoryTheory.ShortComplex.leftHomologyMap'_zero, CategoryTheory.Limits.prod.inr_fst, CategoryTheory.Adjunction.homEquiv_naturality_right, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_hom, CategoryTheory.GrpObj.zpow_comp_assoc, CategoryTheory.IsPreFibered.exists_isCartesian, CategoryTheory.Functor.IsRepresentedBy.iff_exists_representableBy, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_assoc, CategoryTheory.Abelian.AbelianStruct.ι_imageπ, CochainComplex.HomComplex.Cochain.add_v, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_hom, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_hom_comp_ι, CategoryTheory.CosimplicialObject.cechConerveEquiv_apply, CategoryTheory.Bicategory.prod_rightUnitor_hom_snd, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, CategoryTheory.Bicategory.precomp_map, CategoryTheory.Discrete.productEquiv_functor_map, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Bicategory.conjugateEquiv_symm_apply, CategoryTheory.Limits.preservesCokernel_zero', CategoryTheory.Pseudofunctor.DescentData'.descentDataEquivalence_counitIso, CategoryTheory.Bicategory.prod_associator_hom_snd, CategoryTheory.Bicategory.Adjunction.right_triangle, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app, CategoryTheory.injective_iff_rlp_monomorphisms_zero, CategoryTheory.ShortComplex.rightHomologyMap'_zero, HomologicalComplex.biprod_inl_snd_f, CochainComplex.toSingle₀Equiv_symm_apply_f_zero, DerivedCategory.left_fac_of_isStrictlyGE, CategoryTheory.ComposableArrows.homMk₀_app, CategoryTheory.Limits.preservesCokernel_zero, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_mapId_inv_toNatTrans_app, CategoryTheory.Oplax.LaxTrans.comp_naturality, ModuleCat.semilinearMapAddEquiv_apply, Path.isChain_cons_toList_nonempty, Homotopy.mkInductiveAux₂_zero, CategoryTheory.Preadditive.comp_add_assoc, CategoryTheory.curryingIso_hom_toFunctor_map_app, CategoryTheory.quotientPathsTo_map, CategoryTheory.Oplax.OplaxTrans.Modification.naturality, CategoryTheory.Quotient.comp_mk, CategoryTheory.ShortComplex.HomologyMapData.smul_left, CategoryTheory.Functor.mapZeroObject_hom, CategoryTheory.SimplicialObject.Homotopy.ToChainHomotopy.hom_eq, CategoryTheory.AddMonObj.nsmul_comp, ChainComplex.alternatingConst_map_f, CategoryTheory.BicategoricalCoherence.right_iso, CategoryTheory.Bicategory.Equivalence.right_triangle_hom, CategoryTheory.Triangulated.TStructure.truncLTι_comp_truncGEπ_app, ModuleCat.freeHomEquiv_symm_apply, CategoryTheory.Bicategory.Prod.fst_obj, CategoryTheory.MonObj.comp_pow_assoc, CategoryTheory.Functor.homologySequenceδ_comp, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, CategoryTheory.Pseudofunctor.DescentData'.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpPullHom'Hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_inv, ChainComplex.of_d_ne, ChainComplex.fromSingle₀Equiv_symm_apply_f_succ, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_functor_obj_A, CategoryTheory.LaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.Pseudofunctor.DescentData'.comp_pullHom'_assoc, CategoryTheory.shrinkYonedaGrpObjObjEquiv_symm_comp, SemimoduleCat.hom_sum, CategoryTheory.instEffectiveEpiFamily, CategoryTheory.Bicategory.associatorNatIsoRight_inv_app, CategoryTheory.Comma.ext_iff, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right, CategoryTheory.ExponentiableMorphism.homEquiv_apply_eq, CategoryTheory.Groupoid.vertexGroup_mul, CategoryTheory.ShortComplex.Homotopy.symm_h₁, CategoryTheory.PreZeroHypercover.shrink_I₀, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, CategoryTheory.Localization.homEquiv_isoOfHom_inv, CategoryTheory.Bicategory.leftUnitor_comp_inv_assoc, CategoryTheory.Localization.homEquiv_id, CategoryTheory.NatTrans.app_sub, CategoryTheory.Bicategory.leftUnitor_whiskerRight_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two_assoc, AlgebraicTopology.DoldKan.P_add_Q_f, CategoryTheory.Abelian.comp_coimage_π_eq_zero, ModuleCat.homEquiv_extendScalarsId, CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory_rightUnitor_inv_as_app, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_inverse_map, CategoryTheory.NatTrans.app_neg, CategoryTheory.Limits.kernelForkBiproductToSubtype_isLimit, CategoryTheory.ShortComplex.SnakeInput.w₁₃, CategoryTheory.Injective.factors, groupHomology.d₂₁_comp_d₁₀_assoc, AlgebraicGeometry.Scheme.exists_hom_isAffine_of_isZariskiLocalAtSource, AddCommGrpCat.hom_neg, CategoryTheory.Limits.hasImage_zero, AlgebraicTopology.DoldKan.hσ'_eq', CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, CategoryTheory.Abelian.epiWithInjectiveKernel_iff, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, CategoryTheory.Bicategory.leftUnitor_inv_congr, Hom.cast_heq, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_inv, CategoryTheory.Limits.kernelBiproductToSubtypeIso_inv, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range, CategoryTheory.Bicategory.Adj.forget₁_mapComp, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom, CategoryTheory.Limits.Trident.IsLimit.homIso_natural, HomologicalComplex.dFrom_comp_xNextIsoSelf_assoc, CategoryTheory.Bicategory.rightUnitor_hom_congr, SemiNormedGrp.hom_zsum, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_inv, CategoryTheory.Preadditive.sum_comp', CategoryTheory.CatEnrichedOrdinary.homEquiv_id, AlgebraicTopology.DoldKan.HigherFacesVanish.induction, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, CategoryTheory.ObjectProperty.SerreClassLocalization.preservesCokernel, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc, CategoryTheory.Pseudofunctor.comp_mapId, HomologicalComplex₂.D₁_D₂, CategoryTheory.Limits.HasColimitOfHasCoproductsOfHasCoequalizers.buildColimit_ι_app, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_μ_unmop_unmop, CategoryTheory.Subobject.factorThru_zero, CategoryTheory.Bicategory.Prod.swap_mapId_inv, CategoryTheory.Mon.uniqueHomToTrivial_default_hom, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app, CochainComplex.HomComplex.Cochain.toSingleMk_sub, CategoryTheory.Limits.HasZeroMorphisms.comp_zero, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.unop_sum, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_η_unmop_unmop, CategoryTheory.Discrete.productEquiv_inverse_map, CategoryTheory.Bicategory.Prod.sectR_map, CategoryTheory.Sieve.toUliftFunctor_app_down_coe, CategoryTheory.ShortComplex.leftHomologyMap'_add, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst, CategoryTheory.Pseudofunctor.mkOfLax'_mapComp_inv, CategoryTheory.StrictPseudofunctor.mk''_map₂, CategoryTheory.Bicategory.associatorNatIsoMiddleCat_inv_toNatTrans_app, CategoryTheory.Linear.rightComp_apply, CategoryTheory.ShiftedHom.mk₀_smul, CategoryTheory.OplaxFunctor.mapComp'_comp_whiskerLeft_mapComp'_assoc, CategoryTheory.Oplax.LaxTrans.OplaxFunctor.bicategory_whiskerLeft_as_app, CategoryTheory.MonoidalCategory.tensor_dite, CategoryTheory.NonPreadditiveAbelian.sub_self, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_inv, HomotopicalAlgebra.PathObject.RightHomotopy.homotopy_extension, CategoryTheory.ShortComplex.Homotopy.h₀_f, Bicategory.Opposite.op2_associator_hom, CategoryTheory.ShortComplex.opcyclesMap'_neg, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued, SimplicialObject.Splitting.cofan_inj_eq_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom, FintypeCat.homMk_apply, imageToKernel_comp_mono, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_apply_hom, CategoryTheory.PreZeroHypercover.sum_f, CategoryTheory.Abelian.Ext.mk₀_homEquiv₀_apply, CochainComplex.HomComplex.Cocycle.equivHomShift_apply, ComplexShape.Embedding.AreComplementary.hom_ext', CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, CategoryTheory.Adjunction.homEquiv_id, CommRingCat.coproductCocone_ι, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τr, CategoryTheory.CatEnriched.hComp_id, CategoryTheory.instReflectsIsomorphismsForgetTypeHom, CategoryTheory.LaxFunctor.mapComp_assoc_left_app_assoc, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom, CategoryTheory.Adjunction.homEquiv_naturality_left, HomologicalComplex.mapBifunctor.d₁_eq, CategoryTheory.Lax.OplaxTrans.id_app, CategoryTheory.Oplax.StrongTrans.homCategory_comp_as_app, CategoryTheory.Bicategory.rightZigzagIso_hom, CategoryTheory.LaxFunctor.id_mapComp, CategoryTheory.Functor.FullyFaithful.hasZeroMorphisms_def, CategoryTheory.Functor.IsRepresentedBy.representableBy_homEquiv_apply, CategoryTheory.Preadditive.sub_comp, CategoryTheory.Functor.map_one, ChainComplex.alternatingConst_obj, CategoryTheory.Pseudofunctor.DescentData'.pullHom'_hom_comp_assoc, CategoryTheory.Cat.leftUnitor_inv_app, CategoryTheory.GradedObject.ιMapObjOrZero_eq_zero, CategoryTheory.Bicategory.associator_inv_naturality_middle_assoc, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, CategoryTheory.Preadditive.mono_iff_cancel_zero, CategoryTheory.BicategoricalCoherence.refl_iso, CategoryTheory.Bicategory.rightUnitor_comp_inv_assoc, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, CategoryTheory.Limits.inl_pushoutZeroZeroIso_hom, Rep.ofHom_zero, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂_assoc, CategoryTheory.WithTerminal.opEquiv_functor_map, CategoryTheory.PreGaloisCategory.evaluation_aut_injective_of_isConnected, PresheafOfModules.zero_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, CategoryTheory.Lax.OplaxTrans.naturality_naturality_assoc, CategoryTheory.Limits.Cotrident.IsColimit.homIso_apply_coe, CategoryTheory.CatEnrichedOrdinary.Hom.base_eqToHom, AddCommGrpCat.homAddEquiv_apply, CategoryTheory.Over.coreHomEquivToOverSections_homEquiv, CategoryTheory.Functor.PreservesHomology.preservesKernel, CategoryTheory.MorphismProperty.isColocal_iff, Homotopy.nullHomotopy'_hom, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_hom_hom, AlgebraicGeometry.spread_out_of_isGermInjective', CategoryTheory.Limits.IsInitial.subsingleton_to, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_fiber, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage_ι_assoc, CategoryTheory.Preadditive.neg_comp_assoc, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_map₂, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'_assoc, CategoryTheory.Abelian.Pseudoelement.zero_apply, CategoryTheory.Limits.biprod.lift_desc, Hom.unop_mk, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, CategoryTheory.Preadditive.instEpiNegHom, CategoryTheory.eqToHom_heq_id_dom, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.epi_f, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₂_iff, Bicategory.Opposite.bicategory_rightUnitor_hom_unop2, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_map_f, CategoryTheory.Functor.FullyFaithful.homAddEquiv_apply, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_hom, CategoryTheory.Functor.prod_δ_fst, CategoryTheory.Preadditive.neg_iso_inv, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv, SemiNormedGrp.hom_nsum, CategoryTheory.Limits.ChosenPullback₃.exists_lift, CategoryTheory.CostructuredArrow.homMk_surjective, CategoryTheory.cokernel_zero_of_nonzero_to_simple, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three, CategoryTheory.ShortComplex.zero_τ₂, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomLeft_unop, CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map, CategoryTheory.Pseudofunctor.DescentData'.id_hom, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_hom_app, CategoryTheory.Pseudofunctor.DescentData.hom_comp, CategoryTheory.Functor.IsStronglyCocartesian.map_self, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_hom_app, CochainComplex.cm5b, CategoryTheory.ComposableArrows.homMk₁_app, CategoryTheory.Bicategory.Strict.associator_eqToIso, CategoryTheory.Linear.smul_comp, CategoryTheory.Pretriangulated.Triangle.smul_hom₁, CategoryTheory.ShortComplex.RightHomologyMapData.add_φQ, CategoryTheory.Functor.PreservesZeroMorphisms.map_zero, CategoryTheory.Pseudofunctor.IsPrestackFor.nonempty_fullyFaithful, Rep.FiniteCyclicGroup.resolution.π_f, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, CategoryTheory.ShortComplex.leftHomologyMap_smul, CategoryTheory.Cat.Hom.equivFunctor_symm_apply, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByRight_homEquiv, CategoryTheory.Functor.comp_homologySequenceδ_assoc, HomologicalComplex.homotopyCofiber.d_fstX_assoc, CategoryTheory.Pseudofunctor.mapComp'_hom_comp_mapComp'_hom_whiskerRight, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, CategoryTheory.OplaxFunctor.mapComp'_eq_mapComp, CategoryTheory.ShortComplex.opcyclesMap'_smul, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, CategoryTheory.Bicategory.RightLift.w, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_symm_apply, CategoryTheory.ShortComplex.LeftHomologyData.liftK_π_eq_zero_of_boundary_assoc, CategoryTheory.Pseudofunctor.ObjectProperty.map₂_app_hom, SSet.stdSimplex.face_singleton_compl, CategoryTheory.Functor.partialRightAdjointHomEquiv_map_comp, CategoryTheory.Pretriangulated.Triangle.coyoneda_exact₁, CategoryTheory.Bicategory.triangle_assoc, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inr, CategoryTheory.Bicategory.leftUnitorNatIso_inv_app, TopologicalSpace.Opens.val_apply, HomologicalComplex.Hom.fAddMonoidHom_apply, CategoryTheory.down_comp, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.ext_iff, Hom.eq_cast_iff_heq, CategoryTheory.equiv_punit_iff_unique, CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_map, CategoryTheory.Bicategory.rightUnitorNatIsoCat_inv_toNatTrans_app, AlgebraicGeometry.IsOpenImmersion.lift_app, CategoryTheory.Functor.CoconeTypes.descColimitType_injective_iff_of_isFiltered, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, CochainComplex.shiftFunctor_obj_d, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zero_f, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, CategoryTheory.PreZeroHypercover.shrink_f, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_π_app, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight, Mathlib.Tactic.Bicategory.structuralIsoOfExpr_comp, CategoryTheory.shrinkYonedaEquiv_symm_map, CategoryTheory.ComposableArrows.IsComplex.zero', CategoryTheory.Oplax.StrongTrans.vcomp_naturality_inv, CategoryTheory.ShortComplex.leftHomologyMap'_smul, CategoryTheory.Functor.isMittagLeffler_iff_eventualRange, CategoryTheory.Functor.currying_functor_map_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv, CategoryTheory.map_coyonedaEquiv, CategoryTheory.Adjunction.homEquiv_symm_apply, CategoryTheory.Functor.toPseudofunctor_mapComp, CategoryTheory.ShortComplex.cyclesMap_add, CochainComplex.mappingCone.d_fst_v, CategoryTheory.DifferentialObject.zero_f, CategoryTheory.Oplax.OplaxTrans.whiskerRight_as_app, CategoryTheory.Limits.isCokernelEpiComp_desc, CategoryTheory.MonObj.mul_eq_mul, AlgebraicGeometry.Scheme.stalkMap_congr, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_naturality_hom_toNatTrans_app, CategoryTheory.Bicategory.associator_naturality_middle_assoc, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, AlgebraicGeometry.Spec.homEquiv_symm_apply, ModuleCat.ihom_ev_app, Bicategory.Opposite.bicategory_rightUnitor_inv_unop2, CategoryTheory.ShortComplex.hasHomology_of_hasKernel, CategoryTheory.Lax.LaxTrans.vComp_naturality, HomologicalComplex.mapBifunctor₂₃.d₂_eq_zero, SimplicialObject.Splitting.IndexSet.eqId_iff_len_le, CategoryTheory.ObjectProperty.smul_mem_trW_iff, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, Rep.ofHom_smul, CategoryTheory.Pseudofunctor.whiskerRightIso_mapId, CategoryTheory.Pseudofunctor.Grothendieck.map_map_base, CategoryTheory.Limits.ImageMap.mk.injEq', CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_left, CategoryTheory.Subgroupoid.IsNormal.conj, CategoryTheory.map_yonedaEquiv', Rep.ofHom_neg, CategoryTheory.Functor.toPseudofunctor_map, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_inv_as_app, CategoryTheory.Pseudofunctor.toOplax_mapComp', CategoryTheory.Oplax.OplaxTrans.leftUnitor_inv_as_app, CategoryTheory.ObjectProperty.leftOrthogonal_iff, CategoryTheory.Limits.initial.subsingleton_to, CategoryTheory.Functor.map_sum, CategoryTheory.FreeBicategory.lift_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.Abelian.Preradical.toColon_hom_left_app_colonπ_app, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, CategoryTheory.kernelCokernelCompSequence.ι_φ_assoc, CategoryTheory.CategoryOfElements.toCostructuredArrow_map, CategoryTheory.Functor.toOplaxFunctor'_mapId, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom, CategoryTheory.shrinkYonedaGrp_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.evaluationLeftAdjoint_obj_map, CategoryTheory.Bicategory.RightExtension.w, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.counit_assoc, CategoryTheory.Bicategory.postcomposing₂_obj_naturality_inv_toNatTrans_app, CategoryTheory.Bicategory.Prod.fst_mapId_inv, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τl, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_apply_app, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIso_inv, CategoryTheory.Oplax.OplaxTrans.Modification.id_app, DerivedCategory.left_fac, CategoryTheory.Bicategory.associatorNatIsoRightCat_hom_toNatTrans_app, CategoryTheory.MorphismProperty.Comma.mapRightEq_inv_app_left, CategoryTheory.Sum.functorEquiv_counitIso, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, Hom.cast_eq_iff_heq, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_obj, CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone.injective, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_hom_iso, Profinite.exists_hom, CategoryTheory.Bicategory.mateEquiv_apply', CategoryTheory.Limits.coneRightOpOfCoconeEquiv_counitIso, CategoryTheory.nerve.edgeMk_surjective, CategoryTheory.Subgroupoid.id_mem_of_src, CategoryTheory.Bicategory.Equivalence.left_triangle_hom, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, CategoryTheory.Preadditive.coforkOfCokernelCofork_pt, CategoryTheory.Abelian.SpectralObject.opcyclesMap_threeδ₂Toδ₁_opcyclesToE, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, CategoryTheory.Pretriangulated.Triangle.zero_hom₂, CategoryTheory.Triangulated.TStructure.isIso_truncGE_map_iff, CategoryTheory.Bicategory.conjugateEquiv_comp, CategoryTheory.OplaxFunctor.mapComp_id_left, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.epi_iff_forall_injective, CategoryTheory.ComposableArrows.mk₄_surjective, CategoryTheory.Cat.eqToHom_app, skyscraperPresheaf_map, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_fst, HomologicalComplex.ι_mapBifunctorFlipIso_inv, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three_assoc, StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf_app, CategoryTheory.Functor.IsStronglyCocartesian.universal_property, CategoryTheory.Limits.preservesKernel_zero', CategoryTheory.IsReflexivePair.common_section', CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, CategoryTheory.Bicategory.postcomp_map, CategoryTheory.IsCardinalFiltered.multicoequalizer, CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply, CategoryTheory.LaxFunctor.map₂_rightUnitor, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_hom_right, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, CategoryTheory.ObjectProperty.trW_iff, CategoryTheory.Bicategory.triangle_assoc_comp_right_assoc, CategoryTheory.LaxFunctor.mapId'_eq_mapId, CategoryTheory.ShortComplex.f_pOpcycles, CategoryTheory.Functor.mapLinearMap_apply, CategoryTheory.shrinkYonedaEquiv_shrinkYoneda_map, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc_comp_assoc, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₂_iff, CategoryTheory.Functor.CorepresentableBy.id_homEquiv_apply, HomologicalComplex.cylinder.πCompι₀Homotopy.inlX_nullHomotopy_f, CategoryTheory.WithTerminal.opEquiv_inverse_map, CategoryTheory.StructuredArrow.homMk_surjective, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.isoMk_hom_hom, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_hom_app, CategoryTheory.Equivalence.symmEquivInverse_map_app, CategoryTheory.prod.associator_map, CategoryTheory.ShiftedHom.opEquiv'_add_symm, CategoryTheory.Functor.functorHomEquiv_symm_apply_app_app, CategoryTheory.Pretriangulated.Triangle.yoneda_exact₃, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_map₂, CategoryTheory.Mon.Hom.hom_one, CategoryTheory.Bicategory.rightUnitorNatIso_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, CategoryTheory.MorphismProperty.Comma.mapRightEq_hom_app_right, CategoryTheory.Bicategory.yoneda_mapComp_hom_as_app_toNatTrans_app, AddCommGrpCat.hom_zsmul, HomologicalComplex.mono_homologyMap_iff_up_to_refinements, CategoryTheory.IsIdempotentComplete.idempotents_split, CategoryTheory.colimitYonedaHomEquiv_π_apply, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv_assoc, CategoryTheory.heq_eqToHom_comp_iff, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_sigmaDesc_shrinkYoneda_map, CategoryTheory.Functor.ιColimitType_eq_iff_of_isFiltered', heq_of_homOfEq_ext, CategoryTheory.ShortComplex.Splitting.s_r_assoc, Rep.neg_hom, CategoryTheory.mono_iff_forall_injective, CategoryTheory.ShortComplex.opcyclesMap'_zero, CategoryTheory.ShortComplex.leftHomologyMap_neg, CategoryTheory.kernelCokernelCompSequence.φ_π_assoc, CategoryTheory.uliftCoyonedaEquiv_comp, CategoryTheory.Lax.LaxTrans.Modification.naturality, Action.FintypeCat.ofMulAction_apply, HomologicalComplex.liftCycles_homologyπ_eq_zero_of_boundary_assoc, CategoryTheory.LaxFunctor.PseudoCore.mapIdIso_inv, CategoryTheory.CatEnrichedOrdinary.Hom.base_id, CategoryTheory.yonedaEquiv_symm_app_apply, CategoryTheory.Adjunction.adjunctionOfEquivLeft_unit_app, CategoryTheory.Bicategory.leftUnitor_comp_assoc, SemimoduleCat.homAddEquiv_symm_apply_hom, CategoryTheory.Arrow.equivSigma_symm_apply_right, FDRep.finrank_hom_simple_simple, CategoryTheory.evaluationAdjunctionLeft_counit_app, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.Bicategory.LeftLift.w, CategoryTheory.Join.mapIsoWhiskerRight_inv_app, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst, CategoryTheory.Pseudofunctor.mapId'_inv_naturality, CategoryTheory.LaxFunctor.mapComp_naturality_left_assoc, CategoryTheory.tensorLeftHomEquiv_symm_naturality, CategoryTheory.Functor.map_surjective, AlgebraicGeometry.exists_lift_of_germInjective, CategoryTheory.nerve.homEquiv_symm_apply, CategoryTheory.mono_to_simple_zero_of_not_iso, CategoryTheory.yonedaAddMon_map_app, SheafOfModules.unitHomEquiv_apply_coe, AlgebraicTopology.DoldKan.PInfty_add_QInfty, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.comp_hom, CategoryTheory.preadditiveYonedaObj_map, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_counitIso_inv_app_f, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app, CategoryTheory.ShortComplex.f_pOpcycles_assoc, CategoryTheory.ShortComplex.ShortExact.comp_δ_assoc, AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAt, CategoryTheory.prod.inverseAssociator_map, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, SimplexCategory.toMk₁_injective, CategoryTheory.TransportEnrichment.forgetEnrichmentEquivFunctor_map, CategoryTheory.Limits.IsLimit.homEquiv_apply, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, CategoryTheory.PreGaloisCategory.has_non_trivial_subobject_of_not_isConnected_of_not_initial, CochainComplex.HomComplex.Cochain.single_v_eq_zero, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app, CategoryTheory.Adjunction.homEquiv_naturality_left_square_assoc, CategoryTheory.IsFiltered.wideSpan, CategoryTheory.Limits.cokernel.condition_apply, CategoryTheory.Pseudofunctor.DescentData.Hom.comm, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Limits.KernelFork.map_condition_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_comp, groupCohomology.d₀₁_eq_zero, CategoryTheory.yonedaEquiv_comp, CategoryTheory.prod_comp_snd, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv, CategoryTheory.unitCompPartialBijective_symm_apply, CategoryTheory.PreGaloisCategory.functorToAction_comp_forget₂_eq, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_map, CategoryTheory.Localization.structuredArrowEquiv_apply, CategoryTheory.ComposableArrows.mk₂_surjective, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality_assoc, Homotopy.mkInductiveAux₂_add_one, Rep.coindFunctorIso_hom_app_hom_toFun_hom_toFun, CategoryTheory.Limits.kernelSubobject_zero, CategoryTheory.Limits.Bicone.ι_of_isLimit

Rep

Definitions

Name	Category	Theorems
Hom 📖	CompData	3 math math: hom_surjective, hom_bijective, hom_injective

RingCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	3 math math: PresheafOfModules.map_comp, PresheafOfModules.map_id, PresheafOfModules.map_comp_assoc

RootPairing

Definitions

Name	Category	Theorems
Hom 📖	CompData	7 math math: Equiv.toHom_one, Hom.coweightMap_mul, Hom.coweightMap_one, Hom.indexEquiv_one, Hom.indexEquiv_mul, Hom.weightMap_one, Hom.weightMap_mul

SFinKer

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

SSet.OneTruncation₂

Definitions

Name	Category	Theorems
Hom 📖	CompOp	—

SSet.Truncated.HomotopyCategory₂

Definitions

Name	Category	Theorems
Hom 📖	CompOp	—

SemiNormedGrp

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

SemiNormedGrp₁

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

SemiRingCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

Semigrp

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

SemimoduleCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	3 math math: hom_injective, hom_bijective, hom_surjective

SetRel

Definitions

Name	Category	Theorems
Hom 📖	CompOp	3 math math: RelSeries.last_map, RelSeries.head_map, RelSeries.map_apply

SheafOfModules

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

SimpleGraph

Definitions

Name	Category	Theorems
Hom 📖	CompOp	69 math math: coe_induceHom, map_singletonSubgraph, Copy.coe_mk, Hom.instIsEmptyOfForall, Walk.map_copy, Walk.map_injective_of_injective, homOfConnectedComponents_apply, Subgraph.spanningHom_injective, Walk.IsCycle.map, Subgraph.comap_verts, Copy.toHom_apply, Hom.coe_id, Walk.map_isCycle_iff_of_injective, Copy.injective, Walk.darts_map, Walk.map_nil, Hom.map_adj, Walk.map_map, Walk.IsHamiltonian.map, Hom.mapEdgeSet_coe, Hom.map_mem_edgeSet, Walk.map_isPath_iff_of_injective, Hom.mapDart_apply, Walk.IsSubwalk.map, Subgraph.edgeSet_map, induceHom_injective, Subgraph.map_verts, ConnectedComponent.toSimpleGraph_hom_apply, Copy.injective', Hom.coe_comp, Subgraph.map_adj, Walk.reverse_map, Walk.length_map, Subgraph.hom_injective, Reachable.map, Hom.mapNeighborSet_coe, induceHom_comp, Walk.IsPath.injOn_support_of_isPath_map, Hom.instSubsingletonOfForall, ConnectedComponent.map_mk, Walk.map_isTrail_iff_of_injective, Walk.map_isTrail_of_injective, Walk.map_cons, Walk.map_isPath_of_injective, Walk.edgeSet_map, Path.map_coe, Walk.IsHamiltonian.injective_of_isPath_map, Walk.map_append, Walk.map_eq_of_eq, Embedding.coe_toHom, Walk.support_map, Walk.IsHamiltonianCycle.map, Walk.edges_map, Reachable.coe_subgraphMap, Hom.injective_of_top_hom, Path.map_injective, nonempty_hom_of_forall_finite_subgraph_hom, map_subgraphOfAdj, Hom.coe_ofLE, Walk.map_eq_nil_iff, Subgraph.inclusion.injective, Walk.getVert_map, Hom.instFinite, Walk.toSubgraph_map, Subgraph.coe_hom, Subgraph.comap_adj, Hom.apply_mem_neighborSet, Copy.coe_toHom, Hom.ofLE_apply

SimplexCategory

Definitions

Name	Category	Theorems
Hom 📖	CompOp	—

SimplicialObject.Split

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

TopCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

TopModuleCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

UniformSpaceCat

Definitions

Name	Category	Theorems
Hom 📖	CompData	—

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuousAt_hom_bundle 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	ContinuousAt Bundle.TotalSpace ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule AddCommGroup.toAddCommMonoid Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace Bundle.TotalSpace.proj ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.inCoordinates Bundle.TotalSpace.snd	—	FiberBundle.continuousAt_totalSpace SeminormedAddCommGroup.toIsTopologicalAddGroup
continuousWithinAt_hom_bundle 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	ContinuousWithinAt Bundle.TotalSpace ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule AddCommGroup.toAddCommMonoid Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace Bundle.TotalSpace.proj ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.inCoordinates Bundle.TotalSpace.snd	—	FiberBundle.continuousWithinAt_totalSpace SeminormedAddCommGroup.toIsTopologicalAddGroup
hom_trivializationAt 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	FiberBundle.trivializationAt ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup AddCommGroup.toAddCommMonoid Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace Bundle.ContinuousLinearMap.fiberBundle Bundle.Trivialization.continuousLinearMap instMemTrivializationAtlasTrivializationAt	—	SeminormedAddCommGroup.toIsTopologicalAddGroup
hom_trivializationAt_apply 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	Bundle.Trivialization.toFun' ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.TotalSpace AddCommGroup.toAddCommMonoid ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup Bundle.TotalSpace.proj Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace FiberBundle.trivializationAt Bundle.ContinuousLinearMap.fiberBundle ContinuousLinearMap.inCoordinates Bundle.TotalSpace.snd	—	SeminormedAddCommGroup.toIsTopologicalAddGroup
hom_trivializationAt_baseSet 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	Bundle.Trivialization.baseSet ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Bundle.TotalSpace AddCommGroup.toAddCommMonoid ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace Bundle.TotalSpace.proj FiberBundle.trivializationAt Bundle.ContinuousLinearMap.fiberBundle Set Set.instInter	—	SeminormedAddCommGroup.toIsTopologicalAddGroup
hom_trivializationAt_source 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	PartialEquiv.source Bundle.TotalSpace ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule AddCommGroup.toAddCommMonoid OpenPartialHomeomorph.toPartialEquiv Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace instTopologicalSpaceProd ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup Bundle.Trivialization.toOpenPartialHomeomorph Bundle.TotalSpace.proj FiberBundle.trivializationAt Bundle.ContinuousLinearMap.fiberBundle Set.preimage Set Set.instInter Bundle.Trivialization.baseSet	—	SeminormedAddCommGroup.toIsTopologicalAddGroup
hom_trivializationAt_target 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	PartialEquiv.target Bundle.TotalSpace ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule AddCommGroup.toAddCommMonoid OpenPartialHomeomorph.toPartialEquiv Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace instTopologicalSpaceProd ContinuousLinearMap.topologicalSpace NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup Bundle.Trivialization.toOpenPartialHomeomorph Bundle.TotalSpace.proj FiberBundle.trivializationAt Bundle.ContinuousLinearMap.fiberBundle SProd.sprod Set Set.instSProd Set.instInter Bundle.Trivialization.baseSet Set.univ	—	SeminormedAddCommGroup.toIsTopologicalAddGroup
inCoordinates_apply_eq₂ 📖	mathematical	IsTopologicalAddGroup AddCommGroup.toAddGroup ContinuousSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing Set Set.instMembership Bundle.Trivialization.baseSet Bundle.TotalSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup Bundle.TotalSpace.proj FiberBundle.trivializationAt	DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap.funLike ContinuousLinearMap.toNormedAddCommGroup RingHomIsometric.ids SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing ContinuousLinearMap.toNormedSpace smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing ContinuousLinearMap.inCoordinates AddCommGroup.toAddCommMonoid ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup ContinuousLinearMap.module MonoidWithZero.toMonoid Semiring.toMonoidWithZero SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid ContinuousSMul.continuousConstSMul SeminormedRing.toPseudoMetricSpace SMulZeroClass.toSMul NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid DistribSMul.toSMulZeroClass AddMonoid.toAddZeroClass DistribMulAction.toDistribSMul Bundle.ContinuousLinearMap.topologicalSpaceTotalSpace ContinuousLinearMap.topologicalSpace Bundle.ContinuousLinearMap.fiberBundle Bundle.ContinuousLinearMap.vectorBundle LinearMap LinearMap.instFunLike Bundle.Trivialization.linearMapAt FiberBundle.trivializationAt trivialization_linear instMemTrivializationAtlasTrivializationAt AddZero.toZero AddZeroClass.toAddZero Bundle.Trivialization.symm	—	IsTopologicalAddGroup.toContinuousAdd smulCommClass_self ContinuousSMul.continuousConstSMul RingHomIsometric.ids Bundle.ContinuousLinearMap.vectorBundle trivialization_linear instMemTrivializationAtlasTrivializationAt RingHomCompTriple.right_ids RingHomInvPair.ids RingHomCompTriple.ids ContinuousLinearMap.inCoordinates_eq

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