Documentation Verification Report

Iso

📁 Source: Mathlib/CategoryTheory/Limits/Shapes/Pullback/Iso.lean

Statistics

MetricCount
DefinitionsIso, pullbackConeOfLeftIso, pullbackConeOfLeftIsoIsLimit, pullbackConeOfRightIso, pullbackConeOfRightIsoIsLimit, pushoutCoconeOfLeftIso, pushoutCoconeOfLeftIsoIsLimit, pushoutCoconeOfRightIso, pushoutCoconeOfRightIsoIsLimit, Iso, Iso
11
TheoremshasPullback_of_left_iso, hasPullback_of_right_iso, hasPushout_of_left_iso, hasPushout_of_right_iso, pullbackConeOfLeftIso_fst, pullbackConeOfLeftIso_snd, pullbackConeOfLeftIso_x, pullbackConeOfLeftIso_π_app_left, pullbackConeOfLeftIso_π_app_none, pullbackConeOfLeftIso_π_app_right, pullbackConeOfRightIso_fst, pullbackConeOfRightIso_snd, pullbackConeOfRightIso_x, pullbackConeOfRightIso_π_app_left, pullbackConeOfRightIso_π_app_none, pullbackConeOfRightIso_π_app_right, pullback_fst_iso_of_right_iso, pullback_inv_fst_snd_of_right_isIso, pullback_inv_fst_snd_of_right_isIso_assoc, pullback_inv_snd_fst_of_left_isIso, pullback_inv_snd_fst_of_left_isIso_assoc, pullback_snd_iso_of_left_iso, pushoutCoconeOfLeftIso_inl, pushoutCoconeOfLeftIso_inr, pushoutCoconeOfLeftIso_x, pushoutCoconeOfLeftIso_ι_app_left, pushoutCoconeOfLeftIso_ι_app_none, pushoutCoconeOfLeftIso_ι_app_right, pushoutCoconeOfRightIso_inl, pushoutCoconeOfRightIso_inr, pushoutCoconeOfRightIso_x, pushoutCoconeOfRightIso_ι_app_left, pushoutCoconeOfRightIso_ι_app_none, pushoutCoconeOfRightIso_ι_app_right, pushout_inl_inv_inr_of_right_isIso, pushout_inl_inv_inr_of_right_isIso_assoc, pushout_inl_iso_of_right_iso, pushout_inr_inv_inl_of_right_isIso, pushout_inr_inv_inl_of_right_isIso_assoc, pushout_inr_iso_of_left_iso
40
Total51

CategoryTheory

Definitions

NameCategoryTheorems
Iso 📖CompData
178 mathmath: Discrete.sumEquiv_counitIso_inv_app, Limits.diagramIsoPair_hom_app, ObjectProperty.prop_isoClosure_iff, Limits.WalkingMultispan.functorExt_hom_app, ObjectProperty.prop_map_iff, Iso.nonempty_iso_refl, Discrete.sumEquiv_unitIso_inv_app, Iso.isoCongr_symm_apply, WithInitial.opEquiv_unitIso_inv_app, Limits.cospanIsoMk_inv_app, FintypeCat.instFiniteIso, WithInitial.liftToInitialUnique_hom_app, FintypeCat.uSwitch_map_uSwitch_map, Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, equivEquivIso_hom, Pretriangulated.Opposite.mem_distinguishedTriangles_iff', Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, Limits.PushoutCocone.unop_π_app, finrank_hom_simple_simple_eq_one_iff, Limits.mapPairIso_inv_app, Sequential.isoEquivHomeo_apply, linearEquivIsoModuleIso_hom, Sequential.isoEquivHomeo_symm_apply, CatCenter.smul_iso_inv_eq', WithTerminal.mapComp_hom_app, Limits.WidePullbackShape.functorExt_hom_app, FintypeCat.equivEquivIso_apply_hom, Functor.FullyFaithful.isoEquiv_apply, WithInitial.opEquiv_counitIso_hom_app, Limits.cospanIsoMk_hom_app, ThinSkeleton.fromThinSkeleton_map, Limits.parallelPairIsoMk_inv_app, equivIsoIso_hom, WithTerminal.opEquiv_counitIso_inv_app, CommBialgCat.isoEquivBialgEquiv_apply, CatCenter.smul_iso_inv_eq'_assoc, Limits.spanOp_hom_app, skeletonEquivalence_unitIso, WithTerminal.opEquiv_unitIso_hom_app, Functor.map_isoCongr, Preadditive.smul_iso_hom, WithTerminal.opEquiv_counitIso_hom_app, CompHausLike.isoEquivHomeo_symm_apply, FintypeCat.equivEquivIso_symm_apply_symm_apply, Preadditive.neg_iso_hom, WithInitial.mapId_inv_app, Limits.PullbackCone.op_ι_app, Limits.MultispanIndex.multispanMapIso_inv_app, Functor.mapIso_injective, toSkeleton_eq_iff, Preadditive.smul_iso_inv, subsingleton_iso, Limits.HasZeroObject.instSubsingletonIsoOfNat, Limits.parallelPairIsoMk_hom_app, Pi.optionEquivalence_unitIso, Limits.idZeroEquivIsoZero_apply_inv, CommAlgCat.isoEquivAlgEquiv_apply, Limits.spanOp_inv_app, PreGaloisCategory.exists_lift_of_continuous, Ind.exists_nonempty_arrow_mk_iso_ind_lim, FintypeCat.equivEquivIso_apply_inv, Limits.opSpan_hom_app, CatCenter.smul_iso_hom_eq'_assoc, Discrete.sumEquiv_unitIso_hom_app, Bicategory.conjugateIsoEquiv_apply_inv, GrothendieckTopology.Cover.multicospanComp_inv_app, Groupoid.isoEquivHom_apply, Groupoid.isoEquivHom_symm_apply_hom, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, WithTerminal.liftToTerminalUnique_inv_app, WithTerminal.mapComp_inv_app, Limits.opCospan_hom_app, finrank_hom_simple_simple_eq_zero_iff, linearEquivIsoModuleIsoₛ_hom, Discrete.sumEquiv_counitIso_hom_app, Iso.trans_def, Functor.RepresentableBy.equivUliftYonedaIso_symm_apply_homEquiv, FintypeCat.equivEquivIso_symm_apply_apply, Limits.WalkingMultispan.functorExt_inv_app, Limits.PushoutCocone.op_π_app, Limits.parallelPair.ext_hom_app, CommBialgCat.isoEquivBialgEquiv_symm_apply, Limits.opCospan_inv_app, Equivalence.ext_iff, Limits.idZeroEquivIsoZero_apply_hom, Limits.PullbackCone.unop_ι_app, Pretriangulated.mem_distTriang_op_iff', Limits.cospanOp_hom_app, AlgebraicGeometry.Scheme.local_affine, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, algEquivIsoAlgebraIso_inv, CatCenter.smul_iso_inv_eq_assoc, CochainComplex.exists_iso_single, WithInitial.opEquiv_counitIso_inv_app, finrank_hom_simple_simple, DerivedCategory.exists_iso_singleFunctor_obj_of_isGE_of_isLE, equivIsoIso_inv, Functor.CorepresentableBy.equivUliftCoyonedaIso_symm_apply_homEquiv, GrothendieckTopology.Cover.multicospanComp_hom_app, Bicategory.conjugateIsoEquiv_apply_hom, Bicategory.conjugateIsoEquiv_symm_apply_hom, WithInitial.equivComma_unitIso_inv_app_app, DerivedCategory.exists_iso_Q_obj_of_isGE_of_isLE, CatCenter.smul_iso_hom_eq_assoc, IsPreconnected.iso_constant, Iso.nonempty_iso_symm, Iso.isoCongr_apply, ContinuousMap.piComparison_fac, Limits.Types.isConnected_iff_colimit_constPUnitFunctor_iso_pUnit, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, isoOpEquiv_symm_apply, Limits.MultispanIndex.multispanMapIso_hom_app, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, DerivedCategory.exists_iso_Q_obj_of_isGE, WithInitial.equivComma_unitIso_hom_app_app, Functor.CorepresentableBy.equivUliftCoyonedaIso_apply, CatCenter.smul_iso_inv_eq, CommAlgCat.isoEquivAlgEquiv_symm_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, CompactlyGenerated.isoEquivHomeo_symm_apply, PreGaloisCategory.has_decomp_quotients, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, WithTerminal.mapId_hom_app, Limits.WalkingMulticospan.functorExt_hom_app, HomotopyCategory.distinguished_iff_iso_trianglehOfDegreewiseSplit, CompactlyGenerated.isoEquivHomeo_apply, Limits.WidePullbackShape.functorExt_inv_app, CatCenter.smul_iso_hom_eq', Limits.spanIsoMk_hom_app, Limits.WalkingMulticospan.functorExt_inv_app, Functor.FullyFaithful.isoEquiv_symm_apply, conjugateIsoEquiv_apply_hom, conjugateIsoEquiv_apply_inv, Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq, linearEquivIsoModuleIso_inv, FDRep.char_orthonormal, conjugateIsoEquiv_symm_apply_inv, algEquivIsoAlgebraIso_hom, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, Groupoid.isoEquivHom_symm_apply_inv, Limits.cospanOp_inv_app, Functor.RepresentableBy.equivUliftYonedaIso_apply, isoOpEquiv_apply, ShortComplex.exact_iff_homology_iso_zero, DerivedCategory.exists_iso_Q_obj_of_isLE, WithTerminal.mapId_inv_app, AlgebraicGeometry.Scheme.affineBasisCover_map_range, Limits.parallelPair.eqOfHomEq_hom_app, conjugateIsoEquiv_symm_apply_hom, CompHausLike.isoEquivHomeo_apply, PreGaloisCategory.exists_lift_of_quotient_openSubgroup, AlgebraicGeometry.Scheme.affineOpenCover_X, Limits.diagramIsoPair_inv_app, DerivedCategory.mem_distTriang_iff, CatCenter.smul_iso_hom_eq, toSkeleton_eq_toSkeleton_iff, Limits.parallelPair.eqOfHomEq_inv_app, WithInitial.liftToInitialUnique_inv_app, WithInitial.mapComp_inv_app, Iso.symm_bijective, Limits.opSpan_inv_app, Limits.mapPairIso_hom_app, equivEquivIso_inv, WithInitial.opEquiv_unitIso_hom_app, WithTerminal.equivComma_unitIso_hom_app_app, WithTerminal.opEquiv_unitIso_inv_app, Functor.mem_mapTriangle_essImage_of_distinguished, Limits.spanIsoMk_inv_app, Bicategory.conjugateIsoEquiv_symm_apply_inv, linearEquivIsoModuleIsoₛ_inv, WithTerminal.liftToTerminalUnique_hom_app, WithTerminal.equivComma_unitIso_inv_app_app, Preadditive.neg_iso_inv, WithInitial.mapId_hom_app, WithInitial.mapComp_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, Limits.parallelPair.ext_inv_app, FDRep.finrank_hom_simple_simple

CategoryTheory.Limits

Definitions

NameCategoryTheorems
pullbackConeOfLeftIso 📖CompOp
6 mathmath: pullbackConeOfLeftIso_π_app_left, pullbackConeOfLeftIso_π_app_right, pullbackConeOfLeftIso_snd, pullbackConeOfLeftIso_fst, pullbackConeOfLeftIso_π_app_none, pullbackConeOfLeftIso_x
pullbackConeOfLeftIsoIsLimit 📖CompOp
pullbackConeOfRightIso 📖CompOp
6 mathmath: pullbackConeOfRightIso_π_app_right, pullbackConeOfRightIso_fst, pullbackConeOfRightIso_x, pullbackConeOfRightIso_snd, pullbackConeOfRightIso_π_app_left, pullbackConeOfRightIso_π_app_none
pullbackConeOfRightIsoIsLimit 📖CompOp
pushoutCoconeOfLeftIso 📖CompOp
6 mathmath: pushoutCoconeOfLeftIso_ι_app_right, pushoutCoconeOfLeftIso_inl, pushoutCoconeOfLeftIso_ι_app_left, pushoutCoconeOfLeftIso_ι_app_none, pushoutCoconeOfLeftIso_x, pushoutCoconeOfLeftIso_inr
pushoutCoconeOfLeftIsoIsLimit 📖CompOp
pushoutCoconeOfRightIso 📖CompOp
6 mathmath: pushoutCoconeOfRightIso_x, pushoutCoconeOfRightIso_ι_app_left, pushoutCoconeOfRightIso_ι_app_none, pushoutCoconeOfRightIso_inr, pushoutCoconeOfRightIso_ι_app_right, pushoutCoconeOfRightIso_inl
pushoutCoconeOfRightIsoIsLimit 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
hasPullback_of_left_iso 📖mathematicalHasPullback
hasPullback_of_right_iso 📖mathematicalHasPullback
hasPushout_of_left_iso 📖mathematicalHasPushout
hasPushout_of_right_iso 📖mathematicalHasPushout
pullbackConeOfLeftIso_fst 📖mathematicalPullbackCone.fst
pullbackConeOfLeftIso
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.inv
pullbackConeOfLeftIso_snd 📖mathematicalPullbackCone.snd
pullbackConeOfLeftIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
Cone.pt
WalkingCospan
WidePullbackShape.category
WalkingPair
cospan
pullbackConeOfLeftIso_x 📖mathematicalCone.pt
WalkingCospan
WidePullbackShape.category
WalkingPair
cospan
pullbackConeOfLeftIso
pullbackConeOfLeftIso_π_app_left 📖mathematicalCategoryTheory.NatTrans.app
WalkingCospan
WidePullbackShape.category
WalkingPair
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cone.pt
cospan
pullbackConeOfLeftIso
Cone.π
WalkingCospan.left
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.inv
pullbackConeOfLeftIso_π_app_none 📖mathematicalCategoryTheory.NatTrans.app
WalkingCospan
WidePullbackShape.category
WalkingPair
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cone.pt
cospan
pullbackConeOfLeftIso
Cone.π
PullbackCone.condition_one
CategoryTheory.Category.assoc
CategoryTheory.IsIso.inv_hom_id
CategoryTheory.Category.comp_id
pullbackConeOfLeftIso_π_app_right 📖mathematicalCategoryTheory.NatTrans.app
WalkingCospan
WidePullbackShape.category
WalkingPair
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cone.pt
cospan
pullbackConeOfLeftIso
Cone.π
WalkingCospan.right
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
pullbackConeOfRightIso_fst 📖mathematicalPullbackCone.fst
pullbackConeOfRightIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
Cone.pt
WalkingCospan
WidePullbackShape.category
WalkingPair
cospan
pullbackConeOfRightIso_snd 📖mathematicalPullbackCone.snd
pullbackConeOfRightIso
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.inv
pullbackConeOfRightIso_x 📖mathematicalCone.pt
WalkingCospan
WidePullbackShape.category
WalkingPair
cospan
pullbackConeOfRightIso
pullbackConeOfRightIso_π_app_left 📖mathematicalCategoryTheory.NatTrans.app
WalkingCospan
WidePullbackShape.category
WalkingPair
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cone.pt
cospan
pullbackConeOfRightIso
Cone.π
WalkingCospan.left
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
pullbackConeOfRightIso_π_app_none 📖mathematicalCategoryTheory.NatTrans.app
WalkingCospan
WidePullbackShape.category
WalkingPair
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cone.pt
cospan
pullbackConeOfRightIso
Cone.π
PullbackCone.condition_one
CategoryTheory.Category.id_comp
pullbackConeOfRightIso_π_app_right 📖mathematicalCategoryTheory.NatTrans.app
WalkingCospan
WidePullbackShape.category
WalkingPair
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cone.pt
cospan
pullbackConeOfRightIso
Cone.π
WalkingCospan.right
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.inv
pullback_fst_iso_of_right_iso 📖mathematicalCategoryTheory.IsIso
pullback
hasPullback_of_right_iso
pullback.fst
hasPullback_of_right_iso
CategoryTheory.Category.id_comp
CategoryTheory.Category.assoc
CategoryTheory.IsIso.inv_hom_id
CategoryTheory.Category.comp_id
pullback.hom_ext
limit.lift_π
pullback.condition_assoc
CategoryTheory.IsIso.hom_inv_id
pullback_inv_fst_snd_of_right_isIso 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
pullback
hasPullback_of_right_iso
CategoryTheory.inv
pullback.fst
pullback_fst_iso_of_right_iso
pullback.snd
hasPullback_of_right_iso
pullback_fst_iso_of_right_iso
CategoryTheory.IsIso.inv_comp_eq
pullback.condition_assoc
CategoryTheory.IsIso.hom_inv_id
CategoryTheory.Category.comp_id
pullback_inv_fst_snd_of_right_isIso_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
pullback
hasPullback_of_right_iso
CategoryTheory.inv
pullback.fst
pullback_fst_iso_of_right_iso
pullback.snd
hasPullback_of_right_iso
pullback_fst_iso_of_right_iso
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
pullback_inv_fst_snd_of_right_isIso
pullback_inv_snd_fst_of_left_isIso 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
pullback
hasPullback_of_left_iso
CategoryTheory.inv
pullback.snd
pullback_snd_iso_of_left_iso
pullback.fst
hasPullback_of_left_iso
pullback_snd_iso_of_left_iso
CategoryTheory.IsIso.inv_comp_eq
pullback.condition_assoc
CategoryTheory.IsIso.hom_inv_id
CategoryTheory.Category.comp_id
pullback_inv_snd_fst_of_left_isIso_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
pullback
hasPullback_of_left_iso
CategoryTheory.inv
pullback.snd
pullback_snd_iso_of_left_iso
pullback.fst
hasPullback_of_left_iso
pullback_snd_iso_of_left_iso
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
pullback_inv_snd_fst_of_left_isIso
pullback_snd_iso_of_left_iso 📖mathematicalCategoryTheory.IsIso
pullback
hasPullback_of_left_iso
pullback.snd
hasPullback_of_left_iso
CategoryTheory.Category.assoc
CategoryTheory.IsIso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Category.id_comp
pullback.hom_ext
limit.lift_π
CategoryTheory.IsIso.hom_inv_id
pushoutCoconeOfLeftIso_inl 📖mathematicalPushoutCocone.inl
pushoutCoconeOfLeftIso
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.inv
pushoutCoconeOfLeftIso_inr 📖mathematicalPushoutCocone.inr
pushoutCoconeOfLeftIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
pushoutCoconeOfLeftIso_x 📖mathematicalCocone.pt
WalkingSpan
WidePushoutShape.category
WalkingPair
span
pushoutCoconeOfLeftIso
pushoutCoconeOfLeftIso_ι_app_left 📖mathematicalCategoryTheory.NatTrans.app
WalkingSpan
WidePushoutShape.category
WalkingPair
span
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cocone.pt
pushoutCoconeOfLeftIso
Cocone.ι
WalkingSpan.left
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.inv
pushoutCoconeOfLeftIso_ι_app_none 📖mathematicalCategoryTheory.NatTrans.app
WalkingSpan
WidePushoutShape.category
WalkingPair
span
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cocone.pt
pushoutCoconeOfLeftIso
Cocone.ι
PushoutCocone.condition_zero
CategoryTheory.IsIso.hom_inv_id_assoc
pushoutCoconeOfLeftIso_ι_app_right 📖mathematicalCategoryTheory.NatTrans.app
WalkingSpan
WidePushoutShape.category
WalkingPair
span
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cocone.pt
pushoutCoconeOfLeftIso
Cocone.ι
WalkingSpan.right
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
pushoutCoconeOfRightIso_inl 📖mathematicalPushoutCocone.inl
pushoutCoconeOfRightIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
pushoutCoconeOfRightIso_inr 📖mathematicalPushoutCocone.inr
pushoutCoconeOfRightIso
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.inv
pushoutCoconeOfRightIso_x 📖mathematicalCocone.pt
WalkingSpan
WidePushoutShape.category
WalkingPair
span
pushoutCoconeOfRightIso
pushoutCoconeOfRightIso_ι_app_left 📖mathematicalCategoryTheory.NatTrans.app
WalkingSpan
WidePushoutShape.category
WalkingPair
span
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cocone.pt
pushoutCoconeOfRightIso
Cocone.ι
WalkingSpan.left
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
pushoutCoconeOfRightIso_ι_app_none 📖mathematicalCategoryTheory.NatTrans.app
WalkingSpan
WidePushoutShape.category
WalkingPair
span
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cocone.pt
pushoutCoconeOfRightIso
Cocone.ι
PushoutCocone.condition_zero
CategoryTheory.Category.comp_id
pushoutCoconeOfRightIso_ι_app_right 📖mathematicalCategoryTheory.NatTrans.app
WalkingSpan
WidePushoutShape.category
WalkingPair
span
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
Cocone.pt
pushoutCoconeOfRightIso
Cocone.ι
WalkingSpan.right
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.inv
pushout_inl_inv_inr_of_right_isIso 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
pushout
hasPushout_of_left_iso
pushout.inl
CategoryTheory.inv
pushout.inr
pushout_inr_iso_of_left_iso
hasPushout_of_left_iso
pushout_inr_iso_of_left_iso
CategoryTheory.IsIso.eq_inv_comp
pushout.condition_assoc
CategoryTheory.IsIso.hom_inv_id
CategoryTheory.Category.comp_id
pushout_inl_inv_inr_of_right_isIso_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
pushout
hasPushout_of_left_iso
pushout.inl
CategoryTheory.inv
pushout.inr
pushout_inr_iso_of_left_iso
hasPushout_of_left_iso
pushout_inr_iso_of_left_iso
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
pushout_inl_inv_inr_of_right_isIso
pushout_inl_iso_of_right_iso 📖mathematicalCategoryTheory.IsIso
pushout
hasPushout_of_right_iso
pushout.inl
hasPushout_of_right_iso
CategoryTheory.Category.comp_id
CategoryTheory.IsIso.hom_inv_id_assoc
colimit.ι_desc
pushout.hom_ext
colimit.ι_desc_assoc
CategoryTheory.Category.id_comp
CategoryTheory.Category.assoc
pushout.condition
CategoryTheory.IsIso.inv_hom_id_assoc
pushout_inr_inv_inl_of_right_isIso 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
pushout
hasPushout_of_right_iso
pushout.inr
CategoryTheory.inv
pushout.inl
pushout_inl_iso_of_right_iso
hasPushout_of_right_iso
pushout_inl_iso_of_right_iso
CategoryTheory.IsIso.eq_inv_comp
pushout.condition_assoc
CategoryTheory.IsIso.hom_inv_id
CategoryTheory.Category.comp_id
pushout_inr_inv_inl_of_right_isIso_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
pushout
hasPushout_of_right_iso
pushout.inr
CategoryTheory.inv
pushout.inl
pushout_inl_iso_of_right_iso
hasPushout_of_right_iso
pushout_inl_iso_of_right_iso
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
pushout_inr_inv_inl_of_right_isIso
pushout_inr_iso_of_left_iso 📖mathematicalCategoryTheory.IsIso
pushout
hasPushout_of_left_iso
pushout.inr
hasPushout_of_left_iso
CategoryTheory.IsIso.hom_inv_id_assoc
CategoryTheory.Category.comp_id
colimit.ι_desc
pushout.hom_ext
colimit.ι_desc_assoc
CategoryTheory.Category.assoc
CategoryTheory.IsIso.inv_hom_id_assoc
CategoryTheory.Category.id_comp

JordanHolderLattice

Definitions

NameCategoryTheorems
Iso 📖MathDef
3 mathmath: second_iso, second_iso_of_eq, IsMaximal.iso_refl

SimpleGraph

Definitions

NameCategoryTheorems
Iso 📖CompOp
28 mathmath: Iso.map_adj_iff, isVertexCover_preimage_iso, Iso.reachable_iff, isContained_iff_exists_iso_subgraph, Iso.symm_apply_reachable, hasseDualIso_apply, Iso.map_symm_apply, Copy.range_toSubgraph, IsTuranMaximal.nonempty_iso_turanGraph, IsContained.exists_iso_subgraph, Iso.map_mem_edgeSet_iff, Iso.apply_mem_neighborSet_iff, ConnectedComponent.iso_inv_image_comp_eq_iff_eq_map, isVertexCover_image_iso, ConnectedComponent.iso_image_comp_eq_map_iff_eq_comp, Iso.mapNeighborSet_apply_coe, Iso.comap_apply, Iso.degree_eq, isTuranMaximal_iff_nonempty_iso_turanGraph, Copy.toSubgraph_surjOn, Iso.mapNeighborSet_symm_apply_coe, hasseDualIso_symm_apply, killCopies_def, Iso.coe_comp, isCompleteMultipartite_iff, card_edgeFinset_eq_extremalNumber_top_iff_nonempty_iso_turanGraph, Iso.map_apply, Iso.comap_symm_apply

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