Documentation Verification Report

Groupoid

📁 Source: Mathlib/CategoryTheory/Groupoid.lean

Statistics

MetricCount
Definitionsinv, invEquiv, invEquivalence, invFunctor, isoEquivHom, ofFullyFaithfulToGroupoid, ofHomUnique, ofIsGroupoid, ofIsIso, toCategory, groupoid, IsGroupoid, LargeGroupoid, SmallGroupoid, groupoidHasInvolutiveReverse, groupoidPi, groupoidProd
17
Theoremscomp_inv, invEquiv_apply, invEquiv_symm_apply, invEquivalence_counitIso, invEquivalence_functor_map, invEquivalence_functor_obj, invEquivalence_inverse_map, invEquivalence_inverse_obj, invEquivalence_unitIso, invFunctor_map, invFunctor_obj, inv_comp, inv_eq_inv, isoEquivHom_apply, isoEquivHom_symm_apply_hom, isoEquivHom_symm_apply_inv, reverse_eq_inv, isGroupoid, all_isIso, of_groupoid, functorMapReverse, instIsGroupoid, isGroupoidPi, isGroupoidProd, isGroupoid_iff_isomorphisms_eq_top, isGroupoid_of_reflects_iso
26
Total43

CategoryTheory

Definitions

NameCategoryTheorems
IsGroupoid 📖CompData
12 mathmath: InducedCategory.isGroupoid, groupoid_of_isCodetecting_empty, groupoid_of_isDetecting_empty, Localization.isGroupoid, instIsGroupoidOfIsDiscrete, instIsGroupoid, isGroupoidProd, ObjectProperty.isGroupoid_of_isDetecting_bot, isGroupoid_of_reflects_iso, ObjectProperty.isGroupoid_of_isCodetecting_bot, isGroupoid_iff_isomorphisms_eq_top, Localization.instIsGroupoidLocalizationTopMorphismProperty
LargeGroupoid 📖CompOp
SmallGroupoid 📖CompOp
groupoidHasInvolutiveReverse 📖CompOp
2 mathmath: Groupoid.reverse_eq_inv, functorMapReverse
groupoidPi 📖CompOp
3 mathmath: FundamentalGroupoidFunctor.piIso_hom, Grpd.piIsoPi_hom_π, FundamentalGroupoidFunctor.piIso_inv
groupoidProd 📖CompOp
2 mathmath: FundamentalGroupoidFunctor.prodIso_hom, FundamentalGroupoidFunctor.prodIso_inv

Theorems

NameKindAssumesProvesValidatesDepends On
functorMapReverse 📖mathematicalPrefunctor.MapReverse
CategoryStruct.toQuiver
Category.toCategoryStruct
Groupoid.toCategory
Quiver.HasInvolutiveReverse.toHasReverse
groupoidHasInvolutiveReverse
Functor.toPrefunctor
Functor.map_isIso
IsIso.of_groupoid
Groupoid.inv_eq_inv
Functor.map_inv
instIsGroupoid 📖mathematicalIsGroupoid
Groupoid.toCategory
IsIso.of_groupoid
isGroupoidPi 📖mathematicalIsGroupoidpiisIso_pi_iff
IsGroupoid.all_isIso
isGroupoidProd 📖mathematicalIsGroupoid
prod'
isIso_prod_iff
IsGroupoid.all_isIso
isGroupoid_iff_isomorphisms_eq_top 📖mathematicalIsGroupoid
MorphismProperty.isomorphisms
Top.top
MorphismProperty
Category.toCategoryStruct
BooleanAlgebra.toTop
CompleteBooleanAlgebra.toBooleanAlgebra
MorphismProperty.instCompleteBooleanAlgebra
eq_top_iff
IsGroupoid.all_isIso
MorphismProperty.of_eq_top
isGroupoid_of_reflects_iso 📖mathematicalIsGroupoidisIso_of_reflects_iso
IsGroupoid.all_isIso

CategoryTheory.Groupoid

Definitions

NameCategoryTheorems
inv 📖CompOp
23 mathmath: reverse_eq_inv, invEquivalence_inverse_map, invFunctor_map, CategoryTheory.coreCategory_inv_iso_inv, vertexGroup_inv, invEquivalence_functor_map, invEquiv_apply, inv_comp, vertexGroupIsomOfMap_apply, CategoryTheory.coreCategory_inv_iso_hom, CategoryTheory.Quotient.inv_mk, vertexGroupIsomOfMap_symm_apply, CategoryTheory.Subgroupoid.IsNormal.conjugation_bij, invEquiv_symm_apply, invEquivalence_counitIso, CategoryTheory.Subgroupoid.IsNormal.conj', CategoryTheory.Subgroupoid.coe_inv_coe, CategoryTheory.Subgroupoid.inv_mem_iff, CategoryTheory.Subgroupoid.inv, invEquivalence_unitIso, inv_eq_inv, comp_inv, CategoryTheory.Subgroupoid.IsNormal.conj
invEquiv 📖CompOp
2 mathmath: invEquiv_apply, invEquiv_symm_apply
invEquivalence 📖CompOp
7 mathmath: invEquivalence_inverse_map, invEquivalence_inverse_obj, invEquivalence_functor_map, CategoryTheory.Functor.closedIhom_map_app, invEquivalence_functor_obj, invEquivalence_counitIso, invEquivalence_unitIso
invFunctor 📖CompOp
2 mathmath: invFunctor_map, invFunctor_obj
isoEquivHom 📖CompOp
3 mathmath: isoEquivHom_apply, isoEquivHom_symm_apply_hom, isoEquivHom_symm_apply_inv
ofFullyFaithfulToGroupoid 📖CompOp
ofHomUnique 📖CompOp
ofIsGroupoid 📖CompOp
ofIsIso 📖CompOp
toCategory 📖CompOp
232 mathmath: reverse_eq_inv, CategoryTheory.Functor.coreComp_hom_app_iso_inv, FundamentalGroupoid.eqToHom_eq, FundamentalGroupoid.map_comp, CategoryTheory.Core.forgetFunctorToCore_map_app, invEquivalence_inverse_map, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_hom_iso, CategoryTheory.Iso.core_inv_app_iso_hom, FundamentalGroupoid.conj_eqToHom_assoc, ContinuousMap.Homotopy.apply_zero_path, CategoryTheory.Core.isoMk_hom_iso, CategoryTheory.Equivalence.core_inverse_map_iso_hom, CategoryTheory.Grpd.piIsoPi_hom_π, CategoryTheory.FreeGroupoid.map_comp_lift, CategoryTheory.Subgroupoid.full_arrow_eq_iff, CategoryTheory.Functor.closedIhom_obj_map, CategoryTheory.FreeGroupoid.lift_comp, ContinuousMap.Homotopy.evalAt_eq, CategoryTheory.Subgroupoid.inclusion_inj_on_objects, FundamentalGroupoid.map_map, CategoryTheory.FreeGroupoid.functorEquiv_apply, CategoryTheory.Functor.coreId_hom_app_iso_hom, CategoryTheory.Subgroupoid.le_iff, CategoryTheory.Grpd.id_to_functor, CategoryTheory.Bicategory.Pith.leftUnitor_inv_iso_hom, CategoryTheory.nonempty_hom_of_preconnected_groupoid, CategoryTheory.FreeGroupoid.mapComp_hom_app, CategoryTheory.Subgroupoid.inclusion_refl, vertexGroup.inv_eq_inv, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_inv, CategoryTheory.Bicategory.Pith.comp₂_iso_hom_assoc, ContinuousMap.Homotopy.heq_path_of_eq_image, invFunctor_map, CategoryTheory.coreCategory_id_iso_inv, CategoryTheory.FreeGroupoid.mapId_hom_app, isThin_iff, ContinuousMap.Homotopy.eq_path_of_eq_image, CategoryTheory.Functor.coreComp_hom_app_iso_hom, CategoryTheory.Subgroupoid.IsWide.eqToHom_mem, IsFreeGroupoid.SpanningTree.endIsFree, CategoryTheory.Functor.core_obj_of, IsFreeGroupoid.SpanningTree.functorOfMonoidHom_map, CategoryTheory.FreeGroupoid.lift_map_homMk, CategoryTheory.Core.forgetFunctorToCore_obj_obj, CategoryTheory.Functor.coreId_inv_app_iso_inv, CategoryTheory.FreeGroupoid.liftNatIso_hom_app, FundamentalGroupoidFunctor.prodToProdTop_obj, CategoryTheory.FreeGroupoid.mapCompLift_inv_app, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_inv, CategoryTheory.coreFunctor_obj_map_iso_inv, CategoryTheory.Bicategory.Pith.id₂_iso_inv, CategoryTheory.FreeGroupoid.lift_obj_mk, CategoryTheory.Core.functorToCore_comp_right, vertexGroup_inv, FundamentalGroupoid.instSubsingletonHomPUnit, CategoryTheory.Subgroupoid.coe_comp_coe, FundamentalGroupoidFunctor.piToPiTop_map, CategoryTheory.Functor.ihom_ev_app, CategoryTheory.Subgroupoid.mem_discrete_iff, CategoryTheory.Functor.coreId_inv_app_iso_hom, CategoryTheory.FreeGroupoid.map_id, ContinuousMap.Homotopy.apply_one_path, CategoryTheory.Iso.coreId, CategoryTheory.Iso.coreLeftUnitor, CategoryTheory.coreCategory_comp_iso_inv, simply_connected_def, CategoryTheory.coreFunctor_obj_obj_of, invEquivalence_inverse_obj, FundamentalGroupoidFunctor.projLeft_map, Quiver.FreeGroupoid.lift_spec, CategoryTheory.Bicategory.Pith.rightUnitor_hom_iso, CategoryTheory.Functor.ihom_map, CategoryTheory.FreeGroupoid.map_map_homMk, CategoryTheory.Subgroupoid.IsWide.wide, CategoryTheory.Subgroupoid.isThin_iff, FundamentalGroupoid.comp_eq, IsFreeGroupoid.SpanningTree.loopOfHom_eq_id, CategoryTheory.Subgroupoid.IsNormal.generatedNormal_le, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply, vertexGroup_one, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_inv, CategoryTheory.Iso.coreAssociator, isoEquivHom_apply, invEquivalence_functor_map, isoEquivHom_symm_apply_hom, IsFreeGroupoid.ext_functor_iff, invEquiv_apply, CategoryTheory.Subgroupoid.hom.faithful, CategoryTheory.Subgroupoid.mem_ker_iff, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_inv, CategoryTheory.Functor.coreCompInclusionIso_hom_app, CategoryTheory.Bicategory.Pith.associator_hom_iso, FundamentalGroupoidFunctor.instIsIsoFunctorFundamentalGroupoidHomotopicMapsNatIso, inv_comp, SimplyConnectedSpace.equiv_unit, CategoryTheory.Subgroupoid.IsWide.id_mem, CategoryTheory.Functor.mapVertexGroup_apply, vertexGroupIsomOfMap_apply, IsFreeGroupoid.SpanningTree.functorOfMonoidHom_obj, CategoryTheory.coreCategory_comp_iso, CategoryTheory.Bicategory.Pith.id₂_iso_hom, CategoryTheory.Grpd.freeForgetAdjunction_counit_app, CategoryTheory.FreeGroupoid.mapComp_inv_app, CategoryTheory.Functor.core_comp_inclusion, CategoryTheory.Core.functorToCore_map_iso_hom, CategoryTheory.Functor.closedUnit_app_app, CategoryTheory.coreCategory_id_iso_hom, CategoryTheory.FreeGroupoid.mapId_inv_app, CategoryTheory.Functor.coreCompInclusionIso_inv_app, CategoryTheory.FreeGroupoid.liftNatIso_inv_app, CategoryTheory.Subgroupoid.mem_sInf, CategoryTheory.Functor.ihom_coev_app, CategoryTheory.Equivalence.core_functor_obj_of, FundamentalGroupoid.punitEquivDiscretePUnit_unitIso, CategoryTheory.FreeGroupoid.lift_id_comp_of, FundamentalGroupoid.map_eq, CategoryTheory.Equivalence.core_functor_map_iso_inv, CategoryTheory.Grpd.id_eq_id, CategoryTheory.Iso.core_hom_app_iso_inv, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_hom, CategoryTheory.Equivalence.core_inverse_map_iso_inv, CategoryTheory.Quotient.inv_mk, vertexGroupIsomOfMap_symm_apply, CategoryTheory.Functor.coreId_hom_app_iso_inv, CategoryTheory.coreFunctor_map_app_iso_inv, CategoryTheory.Functor.closedIhom_obj_obj, IsCoveringMap.monodromyFunctor_obj, isIsomorphic_iff_nonempty_hom, CategoryTheory.Functor.closedIhom_map_app, CategoryTheory.Equivalence.core_inverse_obj_of, CategoryTheory.Subgroupoid.IsNormal.conjugation_bij, CategoryTheory.Subgroupoid.comap_comp, FundamentalGroupoid.map_id, simplyConnectedSpace_iff, CategoryTheory.functorMapReverse, CategoryTheory.Bicategory.Pith.associator_inv_iso_inv, CategoryTheory.Subgroupoid.coe_inv_coe', CategoryTheory.Iso.coreRightUnitor, CategoryTheory.instIsGroupoid, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_apply, CategoryTheory.Subgroupoid.IsNormal.vertexSubgroup, invEquiv_symm_apply, CategoryTheory.Core.isoMk_inv_iso, invEquivalence_functor_obj, FundamentalGroupoidFunctor.piToPiTop_obj_as, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_inv, invEquivalence_counitIso, CategoryTheory.FreeGroupoid.of_obj_bijective, CategoryTheory.coreFunctor_map_app_iso_hom, CategoryTheory.Bicategory.Pith.comp₂_iso_hom, FundamentalGroupoidFunctor.piIso_inv, CategoryTheory.Subgroupoid.coe_inv_coe, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_hom, CategoryTheory.FreeGroupoid.map_obj_mk, CategoryTheory.FreeGroupoid.functorEquiv_symm_apply, FundamentalGroupoidFunctor.prodIso_inv, CategoryTheory.Subgroupoid.inv_mem_iff, FundamentalGroupoid.map_obj_as, IsFreeGroupoid.unique_lift, IsFreeGroupoid.endIsFreeOfConnectedFree, CategoryTheory.Iso.core_inv_app_iso_inv, CategoryTheory.Subgroupoid.mem_full_iff, FundamentalGroupoidFunctor.projRight_map, CategoryTheory.Core.inclusion_obj, CategoryTheory.Grpd.comp_eq_comp, CategoryTheory.Subgroupoid.mem_iff, IsCoveringMap.monodromyFunctor_map, FundamentalGroupoid.conj_eqToHom, CategoryTheory.Bicategory.Pith.associator_inv_iso_hom, CategoryTheory.FreeGroupoid.instIsLocalizationOfTopMorphismProperty, isoEquivHom_symm_apply_inv, CategoryTheory.FreeGroupoid.of_comp_map, CategoryTheory.Subgroupoid.subset_generated, CategoryTheory.coreCategory_comp_iso_hom, CategoryTheory.Functor.core_map_iso_hom, CategoryTheory.Functor.core_map_iso_inv, CategoryTheory.Core.inclusion_comp_functorToCore, CategoryTheory.Functor.closedCounit_app_app, CategoryTheory.FreeGroupoid.lift_spec, CategoryTheory.Bicategory.Pith.leftUnitor_hom_iso, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_hom, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_hom, CategoryTheory.Bicategory.Pith.comp₂_iso_inv_assoc, CategoryTheory.Iso.coreComp, CategoryTheory.Core.forgetFunctorToCore_obj_map, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_hom, CategoryTheory.Subgroupoid.mem_top, CategoryTheory.Subgroupoid.inclusion_trans, CategoryTheory.Functor.monoidalClosed_closed_adj, CategoryTheory.Equivalence.core_functor_map_iso_hom, IsFreeGroupoid.SpanningTree.treeHom_root, CategoryTheory.Subgroupoid.hom.inj_on_objects, FundamentalGroupoid.punitEquivDiscretePUnit_counitIso, CategoryTheory.Iso.core_hom_app_iso_hom, CategoryTheory.IsIso.of_groupoid, CategoryTheory.Core.instFaithfulInclusion, invEquivalence_unitIso, CategoryTheory.Subgroupoid.id_mem_of_nonempty_isotropy, CategoryTheory.Core.functorToCore_inclusion, FundamentalGroupoid.id_eq_path_refl, CategoryTheory.Iso.coreWhiskerRight, CategoryTheory.Bicategory.Pith.comp₂_iso_inv, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_hom, FundamentalGroupoid.punitEquivDiscretePUnit_inverse, CategoryTheory.Subgroupoid.ker_comp, CategoryTheory.Grpd.hom_to_functor, CategoryTheory.Subgroupoid.inclusion_faithful, CategoryTheory.Subgroupoid.mem_sInf_arrows, CategoryTheory.FreeGroupoid.mapCompLift_hom_app, FundamentalGroupoidFunctor.prodToProdTop_map, CategoryTheory.Core.inclusion_map, inv_eq_inv, CategoryTheory.Subgroupoid.inclusion_comp_embedding, FundamentalGroupoidFunctor.proj_map, CategoryTheory.Functor.coreComp_inv_app_iso_hom, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_inv, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_hom, CategoryTheory.coreFunctor_obj_map_iso_hom, CategoryTheory.Functor.coreComp_inv_app_iso_inv, vertexGroup_mul, CategoryTheory.Core.functorToCore_comp_left, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_inv, CategoryTheory.Core.functorToCore_obj_of, comp_inv, CategoryTheory.Iso.coreWhiskerLeft, CategoryTheory.Core.functorToCore_map_iso_inv, ContinuousMap.Homotopy.hcast_def, invFunctor_obj, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_hom_iso, CategoryTheory.FreeGroupoid.map_comp, ContinuousMap.Homotopy.eq_diag_path, FundamentalGroupoid.punitEquivDiscretePUnit_functor

Theorems

NameKindAssumesProvesValidatesDepends On
comp_inv 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
toCategory
inv
CategoryTheory.CategoryStruct.id
invEquiv_apply 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
toCategory
EquivLike.toFunLike
Equiv.instEquivLike
invEquiv
inv
invEquiv_symm_apply 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
toCategory
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
invEquiv
inv
invEquivalence_counitIso 📖mathematicalCategoryTheory.Equivalence.counitIso
Opposite
toCategory
CategoryTheory.Category.opposite
invEquivalence
CategoryTheory.NatIso.ofComponents
CategoryTheory.Functor.comp
Opposite.unop
inv
Quiver.Hom.unop
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
Opposite.op
Quiver.Hom.op
CategoryTheory.Functor.id
CategoryTheory.Iso.refl
CategoryTheory.Functor.obj
invEquivalence_functor_map 📖mathematicalCategoryTheory.Functor.map
toCategory
Opposite
CategoryTheory.Category.opposite
CategoryTheory.Equivalence.functor
invEquivalence
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
inv
invEquivalence_functor_obj 📖mathematicalCategoryTheory.Functor.obj
toCategory
Opposite
CategoryTheory.Category.opposite
CategoryTheory.Equivalence.functor
invEquivalence
Opposite.op
invEquivalence_inverse_map 📖mathematicalCategoryTheory.Functor.map
Opposite
CategoryTheory.Category.opposite
toCategory
CategoryTheory.Equivalence.inverse
invEquivalence
inv
Opposite.unop
Quiver.Hom.unop
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
invEquivalence_inverse_obj 📖mathematicalCategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
toCategory
CategoryTheory.Equivalence.inverse
invEquivalence
Opposite.unop
invEquivalence_unitIso 📖mathematicalCategoryTheory.Equivalence.unitIso
Opposite
toCategory
CategoryTheory.Category.opposite
invEquivalence
CategoryTheory.NatIso.ofComponents
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
Opposite.op
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
inv
Opposite.unop
Quiver.Hom.unop
CategoryTheory.Iso.refl
CategoryTheory.Functor.obj
invFunctor_map 📖mathematicalCategoryTheory.Functor.map
toCategory
Opposite
CategoryTheory.Category.opposite
invFunctor
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
inv
invFunctor_obj 📖mathematicalCategoryTheory.Functor.obj
toCategory
Opposite
CategoryTheory.Category.opposite
invFunctor
Opposite.op
inv_comp 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
toCategory
inv
CategoryTheory.CategoryStruct.id
inv_eq_inv 📖mathematicalinv
CategoryTheory.inv
toCategory
CategoryTheory.IsIso.of_groupoid
CategoryTheory.IsIso.eq_inv_of_hom_inv_id
CategoryTheory.IsIso.of_groupoid
comp_inv
isoEquivHom_apply 📖mathematicalDFunLike.coe
Equiv
CategoryTheory.Iso
toCategory
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
EquivLike.toFunLike
Equiv.instEquivLike
isoEquivHom
CategoryTheory.Iso.hom
isoEquivHom_symm_apply_hom 📖mathematicalCategoryTheory.Iso.hom
toCategory
DFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Iso
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
isoEquivHom
isoEquivHom_symm_apply_inv 📖mathematicalCategoryTheory.Iso.inv
toCategory
DFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Iso
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
isoEquivHom
CategoryTheory.inv
CategoryTheory.IsIso.of_groupoid
inv_eq_inv
reverse_eq_inv 📖mathematicalQuiver.reverse
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
toCategory
Quiver.HasInvolutiveReverse.toHasReverse
CategoryTheory.groupoidHasInvolutiveReverse
inv

CategoryTheory.InducedCategory

Definitions

NameCategoryTheorems
groupoid 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
isGroupoid 📖mathematicalCategoryTheory.IsGroupoid
CategoryTheory.InducedCategory
instCategory
CategoryTheory.isGroupoid_of_reflects_iso
CategoryTheory.reflectsIsomorphisms_of_full_and_faithful
full
faithful

CategoryTheory.IsGroupoid

Theorems

NameKindAssumesProvesValidatesDepends On
all_isIso 📖mathematicalCategoryTheory.IsIso

CategoryTheory.IsIso

Theorems

NameKindAssumesProvesValidatesDepends On
of_groupoid 📖mathematicalCategoryTheory.IsIso
CategoryTheory.Groupoid.toCategory
CategoryTheory.Groupoid.comp_inv
CategoryTheory.Groupoid.inv_comp

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