Cones

📁 Source: Mathlib/CategoryTheory/Limits/Cones.lean

Statistics

Metric	Count
Definitions cocones, cones, functorialityCompPostcompose, functorialityCompPrecompose, mapCocone, mapCoconeInv, mapCoconeInvMapCocone, mapCoconeMapCocone, mapCoconeMapCoconeInv, mapCoconeMorphism, mapCoconeOp, mapCoconePrecompose, mapCoconePrecomposeEquivalenceFunctor, mapCoconeWhisker, mapCone, mapConeInv, mapConeInvMapCone, mapConeMapCone, mapConeMapConeInv, mapConeMorphism, mapConeOp, mapConePostcompose, mapConePostcomposeEquivalenceFunctor, mapConeWhisker, postcomposeWhiskerLeftMapCone, precomposeWhiskerLeftMapCocone, Cocone, category, equiv, equivalenceOfReindexing, eta, ext, ext_inv, extend, extendComp, extendHom, extendId, extendIso, extensions, forget, functoriality, functorialityCompFunctoriality, functorialityEquivalence, op, precompose, precomposeComp, precomposeEquivalence, precomposeId, pt, unop, whisker, whiskering, whiskeringEquivalence, ι, CoconeMorphism, hom, equivalenceOfReindexing, eta, ext, extend, extendComp, extendId, extendIso, forget, functoriality, functorialityCompFunctoriality, functorialityEquivalence, postcompose, postcomposeComp, postcomposeEquivalence, postcomposeId, whiskering, whiskeringEquivalence, category, equiv, equivalenceOfReindexing, eta, ext, ext_inv, extend, extendComp, extendHom, extendId, extendIso, extensions, forget, functoriality, functorialityCompFunctoriality, functorialityEquivalence, op, postcompose, postcomposeComp, postcomposeEquivalence, postcomposeId, pt, unop, whisker, whiskering, whiskeringEquivalence, π, ConeMorphism, hom, equivalenceOfReindexing, eta, ext, extend, extendComp, extendId, extendIso, forget, functoriality, functorialityCompFunctoriality, functorialityEquivalence, postcompose, postcomposeComp, postcomposeEquivalence, postcomposeId, whiskering, whiskeringEquivalence, coconeEquivalenceOpConeOp, coconeLeftOpOfCone, coconeLeftOpOfConeEquiv, coconeOfConeLeftOp, coconeOfConeRightOp, coconeOfConeUnop, coconeOpEquiv, coconeRightOpOfCone, coconeRightOpOfConeEquiv, coconeUnopOfCone, coconeUnopOfConeEquiv, coneEquivalenceOpCoconeOp, coneLeftOpOfCocone, coneLeftOpOfCoconeEquiv, coneOfCoconeLeftOp, coneOfCoconeRightOp, coneOfCoconeUnop, coneOpEquiv, coneRightOpOfCocone, coneRightOpOfCoconeEquiv, coneUnopOfCocone, coneUnopOfCoconeEquiv, inhabitedCocone, inhabitedCoconeMorphism, inhabitedCone, inhabitedConeMorphism, cocones, cones	147
Theorems cocones_map_app, cocones_obj, cones_map_app, cones_obj, functorialityCompPostcompose_hom_app_hom, functorialityCompPostcompose_inv_app_hom, functorialityCompPrecompose_hom_app_hom, functorialityCompPrecompose_inv_app_hom, mapCoconeMapCocone_hom_hom, mapCoconeMapCocone_inv_hom, mapCoconeOp_hom_hom, mapCoconeOp_inv_hom, mapCoconePrecomposeEquivalenceFunctor_hom_hom, mapCoconePrecomposeEquivalenceFunctor_inv_hom, mapCoconePrecompose_hom_hom, mapCoconePrecompose_inv_hom, mapCoconeWhisker_hom_hom, mapCoconeWhisker_inv_hom, mapCocone_pt, mapCocone_ι_app, mapConeMapCone_hom_hom, mapConeMapCone_inv_hom, mapConeOp_hom_hom, mapConeOp_inv_hom, mapConePostcomposeEquivalenceFunctor_hom_hom, mapConePostcomposeEquivalenceFunctor_inv_hom, mapConePostcompose_hom_hom, mapConePostcompose_inv_hom, mapConeWhisker_hom_hom, mapConeWhisker_inv_hom, mapCone_pt, mapCone_π_app, postcomposeWhiskerLeftMapCone_hom_hom, postcomposeWhiskerLeftMapCone_inv_hom, precomposeWhiskerLeftMapCocone_hom_hom, precomposeWhiskerLeftMapCocone_inv_hom, category_comp_hom, category_id_hom, cocone_iso_of_hom_iso, equivalenceOfReindexing_counitIso, equivalenceOfReindexing_functor, equivalenceOfReindexing_inverse, equivalenceOfReindexing_unitIso, eta_hom_hom, eta_inv_hom, ext_hom_hom, ext_inv_hom, ext_inv_hom_hom, ext_inv_inv_hom, extendComp_hom_hom, extendComp_inv_hom, extendHom_hom, extendId_hom_hom, extendId_inv_hom, extendIso_hom_hom, extendIso_inv_hom, extend_pt, extend_ι, extensions_app, forget_map, forget_obj, functorialityEquivalence_counitIso, functorialityEquivalence_functor, functorialityEquivalence_inverse, functorialityEquivalence_unitIso, functoriality_faithful, functoriality_full, functoriality_map_hom, functoriality_obj_pt, functoriality_obj_ι_app, instIsIsoExtendHom, op_pt, op_π, precomposeComp_hom_app_hom, precomposeComp_inv_app_hom, precomposeEquivalence_counitIso, precomposeEquivalence_functor, precomposeEquivalence_inverse, precomposeEquivalence_unitIso, precomposeId_hom_app_hom, precomposeId_inv_app_hom, precompose_map_hom, precompose_obj_pt, precompose_obj_ι, reflects_cocone_isomorphism, unop_pt, unop_π, w, w_assoc, whisker_pt, whisker_ι, whiskeringEquivalence_counitIso, whiskeringEquivalence_functor, whiskeringEquivalence_inverse, whiskeringEquivalence_unitIso, whiskering_map_hom, whiskering_obj, ext, ext_iff, hom_inv_id, hom_inv_id_assoc, inv_hom_id, inv_hom_id_assoc, map_w, map_w_assoc, w, w_assoc, cone_iso_of_hom_iso, functoriality_faithful, functoriality_full, reflects_cone_isomorphism, category_comp_hom, category_id_hom, cone_iso_of_hom_iso, equiv_hom_fst, equiv_hom_snd, equiv_inv_pt, equiv_inv_π, equivalenceOfReindexing_counitIso, equivalenceOfReindexing_functor, equivalenceOfReindexing_inverse, equivalenceOfReindexing_unitIso, eta_hom_hom, eta_inv_hom, ext_hom_hom, ext_inv_hom, ext_inv_hom_hom, ext_inv_inv_hom, extendComp_hom_hom, extendComp_inv_hom, extendHom_hom, extendId_hom_hom, extendId_inv_hom, extendIso_hom_hom, extendIso_inv_hom, extend_pt, extend_π, extensions_app, forget_map, forget_obj, functorialityEquivalence_counitIso, functorialityEquivalence_functor, functorialityEquivalence_inverse, functorialityEquivalence_unitIso, functoriality_faithful, functoriality_full, functoriality_map_hom, functoriality_obj_pt, functoriality_obj_π_app, instIsIsoExtendHom, op_pt, op_ι, postcomposeComp_hom_app_hom, postcomposeComp_inv_app_hom, postcomposeEquivalence_counitIso, postcomposeEquivalence_functor, postcomposeEquivalence_inverse, postcomposeEquivalence_unitIso, postcomposeId_hom_app_hom, postcomposeId_inv_app_hom, postcompose_map_hom, postcompose_obj_pt, postcompose_obj_π, reflects_cone_isomorphism, unop_pt, unop_ι, w, w_assoc, whisker_pt, whisker_π, whiskeringEquivalence_counitIso, whiskeringEquivalence_functor, whiskeringEquivalence_inverse, whiskeringEquivalence_unitIso, whiskering_map_hom, whiskering_obj, ext, ext_iff, hom_inv_id, hom_inv_id_assoc, inv_hom_id, inv_hom_id_assoc, map_w, map_w_assoc, w, w_assoc, cone_iso_of_hom_iso, functoriality_faithful, functoriality_full, reflects_cone_isomorphism, coconeLeftOpOfConeEquiv_counitIso, coconeLeftOpOfConeEquiv_functor_map_hom, coconeLeftOpOfConeEquiv_functor_obj, coconeLeftOpOfConeEquiv_inverse_map, coconeLeftOpOfConeEquiv_inverse_obj, coconeLeftOpOfConeEquiv_unitIso, coconeLeftOpOfCone_pt, coconeLeftOpOfCone_ι_app, coconeOfConeLeftOp_pt, coconeOfConeLeftOp_ι_app, coconeOfConeRightOp_pt, coconeOfConeRightOp_ι, coconeOfConeUnop_pt, coconeOfConeUnop_ι, coconeOpEquiv_counitIso, coconeOpEquiv_functor_map_hom, coconeOpEquiv_functor_obj, coconeOpEquiv_inverse_map, coconeOpEquiv_inverse_obj, coconeOpEquiv_unitIso, coconeRightOpOfConeEquiv_counitIso, coconeRightOpOfConeEquiv_functor_map_hom, coconeRightOpOfConeEquiv_functor_obj, coconeRightOpOfConeEquiv_inverse_map, coconeRightOpOfConeEquiv_inverse_obj, coconeRightOpOfConeEquiv_unitIso, coconeRightOpOfCone_pt, coconeRightOpOfCone_ι, coconeUnopOfConeEquiv_counitIso, coconeUnopOfConeEquiv_functor_map_hom, coconeUnopOfConeEquiv_functor_obj, coconeUnopOfConeEquiv_inverse_map, coconeUnopOfConeEquiv_inverse_obj, coconeUnopOfConeEquiv_unitIso, coconeUnopOfCone_pt, coconeUnopOfCone_ι, coneLeftOpOfCoconeEquiv_counitIso, coneLeftOpOfCoconeEquiv_functor_map_hom, coneLeftOpOfCoconeEquiv_functor_obj, coneLeftOpOfCoconeEquiv_inverse_map, coneLeftOpOfCoconeEquiv_inverse_obj, coneLeftOpOfCoconeEquiv_unitIso, coneLeftOpOfCocone_pt, coneLeftOpOfCocone_π_app, coneOfCoconeLeftOp_pt, coneOfCoconeLeftOp_π_app, coneOfCoconeRightOp_pt, coneOfCoconeRightOp_π, coneOfCoconeUnop_pt, coneOfCoconeUnop_π, coneOpEquiv_counitIso, coneOpEquiv_functor_map_hom, coneOpEquiv_functor_obj, coneOpEquiv_inverse_map, coneOpEquiv_inverse_obj, coneOpEquiv_unitIso, coneRightOpOfCoconeEquiv_counitIso, coneRightOpOfCoconeEquiv_functor_map_hom, coneRightOpOfCoconeEquiv_functor_obj, coneRightOpOfCoconeEquiv_inverse_map, coneRightOpOfCoconeEquiv_inverse_obj, coneRightOpOfCoconeEquiv_unitIso, coneRightOpOfCocone_pt, coneRightOpOfCocone_π, coneUnopOfCoconeEquiv_counitIso, coneUnopOfCoconeEquiv_functor_map_hom, coneUnopOfCoconeEquiv_functor_obj, coneUnopOfCoconeEquiv_inverse_map, coneUnopOfCoconeEquiv_inverse_obj, coneUnopOfCoconeEquiv_unitIso, coneUnopOfCocone_pt, coneUnopOfCocone_π, instIsIsoHomHomCocone, instIsIsoHomHomCone, instIsIsoHomInvCocone, instIsIsoHomInvCone, cocones_map_app_app, cocones_obj_map_app, cocones_obj_obj, cones_map_app_app, cones_obj_map_app, cones_obj_obj	272
Total	419

CategoryTheory

Definitions

Name	Category	Theorems
cocones 📖	CompOp	5 math math: cocones_map_app_app, Limits.opHomCompWhiskeringLimYonedaIsoCocones_hom_app_app_app, cocones_obj_map_app, cocones_obj_obj, Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app
cones 📖	CompOp	5 math math: Limits.whiskeringLimYonedaIsoCones_inv_app_app, cones_obj_map_app, Limits.whiskeringLimYonedaIsoCones_hom_app_app_app, cones_map_app_app, cones_obj_obj

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cocones_map_app_app 📖	mathematical	—	NatTrans.app Opposite.unop Functor Opposite.op Functor.obj Functor.category Functor.const types Functor.comp Opposite Category.opposite coyoneda Functor.map cocones CategoryStruct.comp Category.toCategoryStruct Quiver.Hom.unop CategoryStruct.toQuiver	—	—
cocones_obj_map_app 📖	mathematical	—	NatTrans.app Opposite.unop Functor Opposite.op Functor.obj Functor.category Functor.const Functor.map types Opposite Category.opposite cocones CategoryStruct.comp Category.toCategoryStruct	—	—
cocones_obj_obj 📖	mathematical	—	Functor.obj types Opposite Functor Category.opposite Functor.category cocones Quiver.Hom CategoryStruct.toQuiver Category.toCategoryStruct Opposite.unop Functor.const	—	—
cones_map_app_app 📖	mathematical	—	NatTrans.app Opposite.unop Functor Functor.obj Opposite Category.opposite Functor.category Functor.op Functor.const types Functor.comp yoneda Functor.map cones CategoryStruct.comp Category.toCategoryStruct	—	—
cones_obj_map_app 📖	mathematical	—	NatTrans.app Opposite.unop Functor Functor.obj Opposite Category.opposite Functor.category Functor.op Functor.const Functor.map types cones CategoryStruct.comp Category.toCategoryStruct Quiver.Hom.unop CategoryStruct.toQuiver	—	—
cones_obj_obj 📖	mathematical	—	Functor.obj Opposite Category.opposite types Functor Functor.category cones Quiver.Hom CategoryStruct.toQuiver Category.toCategoryStruct Functor.const Opposite.unop	—	—

CategoryTheory.Functor

Definitions

Name	Category	Theorems
cocones 📖	CompOp	6 math math: CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.Limits.yonedaCompLimIsoCocones_hom_app_app, cocones_obj, cocones_map_app, CategoryTheory.Limits.Cocone.extensions_app
cones 📖	CompOp	10 math math: CategoryTheory.Limits.Cone.equiv_inv_pt, cones_map_app, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, cones_obj, CategoryTheory.Limits.Cone.equiv_hom_fst, CategoryTheory.Limits.Cone.equiv_inv_π, CategoryTheory.Limits.Cone.equiv_hom_snd, CategoryTheory.Limits.limit.homIso_hom, CategoryTheory.Limits.Cone.extensions_app, CategoryTheory.Limits.coyonedaCompLimIsoCones_hom_app_app
functorialityCompPostcompose 📖	CompOp	2 math math: functorialityCompPostcompose_hom_app_hom, functorialityCompPostcompose_inv_app_hom
functorialityCompPrecompose 📖	CompOp	2 math math: functorialityCompPrecompose_hom_app_hom, functorialityCompPrecompose_inv_app_hom
mapCocone 📖	CompOp	47 math math: mapCocone_ι_app, mapCoconePrecomposeEquivalenceFunctor_inv_hom, mapCoconePrecompose_inv_hom, mapCoconeWhisker_hom_hom, LeftExtension.coconeAtWhiskerRightIso_inv_hom, mapCoconeOp_inv_hom, CategoryTheory.preservesColimitIso_inv_comp_desc, mapCoconeMapCocone_hom_hom, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, Condensed.isColimitLocallyConstantPresheaf_desc_apply, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, CategoryTheory.Limits.PreservesColimit.preserves, CategoryTheory.IsVanKampenColimit.map_reflective, CategoryTheory.IsUniversalColimit.map_reflective, CategoryTheory.Comma.coconeOfPreserves_ι_app_right, precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.Comma.coconeOfPreserves_pt_hom, precomposeWhiskerLeftMapCocone_inv_hom, mapCoconePrecomposeEquivalenceFunctor_hom_hom, Accessible.Limits.isColimitMapCocone.surjective, CategoryTheory.Limits.Cocone.toCostructuredArrowCocone_ι_app, CategoryTheory.preservesColimitIso_inv_comp_desc_assoc, CategoryTheory.Comma.coconeOfPreserves_ι_app_left, LeftExtension.coconeAtWhiskerRightIso_hom_hom, SheafOfModules.Presentation.map_relations_I, mapCoconeWhisker_inv_hom, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isColimit, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Limits.Cocone.mapCoconeToOver_inv_hom, mapConeOp_inv_hom, CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCoconeIsColimit_desc_f, mapCoconeOp_hom_hom, AddCommGrpCat.Colimits.Quot.desc_quotQuotUliftAddEquiv, LightCondensed.isColimitLocallyConstantPresheaf_desc_apply, CategoryTheory.Limits.colimit.post_desc, mapCoconePrecompose_hom_hom, CategoryTheory.IsVanKampenColimit.mapCocone_iff, mapConeOp_hom_hom, CategoryTheory.Limits.Cocone.toCostructuredArrowCocone_pt, mapCocone_pt, CategoryTheory.Limits.Cocone.mapCoconeToOver_hom_hom, CategoryTheory.preserves_desc_mapCocone, mapCoconeMapCocone_inv_hom, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, AlgebraicGeometry.nonempty_isColimit_Γ_mapCocone, CategoryTheory.Monad.ForgetCreatesColimits.liftedCoconeIsColimit_desc_f
mapCoconeInv 📖	CompOp	—
mapCoconeInvMapCocone 📖	CompOp	—
mapCoconeMapCocone 📖	CompOp	2 math math: mapCoconeMapCocone_hom_hom, mapCoconeMapCocone_inv_hom
mapCoconeMapCoconeInv 📖	CompOp	—
mapCoconeMorphism 📖	CompOp	—
mapCoconeOp 📖	CompOp	2 math math: mapCoconeOp_inv_hom, mapCoconeOp_hom_hom
mapCoconePrecompose 📖	CompOp	2 math math: mapCoconePrecompose_inv_hom, mapCoconePrecompose_hom_hom
mapCoconePrecomposeEquivalenceFunctor 📖	CompOp	2 math math: mapCoconePrecomposeEquivalenceFunctor_inv_hom, mapCoconePrecomposeEquivalenceFunctor_hom_hom
mapCoconeWhisker 📖	CompOp	2 math math: mapCoconeWhisker_hom_hom, mapCoconeWhisker_inv_hom
mapCone 📖	CompOp	59 math math: mapConeMapCone_hom_hom, CategoryTheory.Mon.forgetMapConeLimitConeIso_inv_hom, CategoryTheory.Monad.ForgetCreatesLimits.liftedConeIsLimit_lift_f, CategoryTheory.Limits.PreservesLimit.preserves, CategoryTheory.Mon.forgetMapConeLimitConeIso_hom_hom, CategoryTheory.Presheaf.isSheaf_iff_isLimit_coverage, CategoryTheory.CostructuredArrow.CreatesConnected.mapCone_raiseCone, mapConePostcompose_inv_hom, CategoryTheory.Comma.coneOfPreserves_π_app_right, CategoryTheory.Mon.limitConeIsLimit_lift_hom, CategoryTheory.Limits.limit.lift_post, CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve, mapCoconeOp_inv_hom, CategoryTheory.regularTopology.equalizerConditionMap_iff_nonempty_isLimit, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, CategoryTheory.lift_comp_preservesLimitIso_hom_assoc, CategoryTheory.Limits.Cone.toStructuredArrowCone_π_app, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, RightExtension.coneAtWhiskerRightIso_inv_hom, postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.lift_comp_preservesLimitIso_hom, CategoryTheory.Limits.Cone.mapConeToUnder_inv_hom, CategoryTheory.Comma.limitAuxiliaryCone_π_app, CategoryTheory.Presheaf.isSheaf_iff_isLimit, mapCone_pt, CategoryTheory.Limits.colimitLimitToLimitColimitCone_iso, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, mapConePostcomposeEquivalenceFunctor_inv_hom, mapConePostcomposeEquivalenceFunctor_hom_hom, mapCone_π_app, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isLimit, mapConeWhisker_hom_hom, CategoryTheory.Comma.coneOfPreserves_pt_hom, postcomposeWhiskerLeftMapCone_hom_hom, mapConeOp_inv_hom, TopCat.Presheaf.IsSheaf.isSheafPairwiseIntersections, mapConePostcompose_hom_hom, TopCat.Presheaf.isGluing_iff_pairwise, RightExtension.coneAtWhiskerRightIso_hom_hom, mapCoconeOp_hom_hom, CategoryTheory.Limits.Cone.mapConeToUnder_hom_hom, mapConeOp_hom_hom, mapConeMapCone_inv_hom, CategoryTheory.Presheaf.isLimit_iff_isSheafFor, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, CategoryTheory.preserves_lift_mapCone, mapConeWhisker_inv_hom, TopCat.Presheaf.IsSheaf.isSheafOpensLeCover, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.CategoryOfElements.CreatesLimitsAux.map_lift_mapCone, CategoryTheory.PreservesFiniteLimitsOfFlat.fac, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedConeIsLimit_lift_f, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.Limits.Cone.toStructuredArrowCone_pt, FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone, CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology, CategoryTheory.Comma.coneOfPreserves_π_app_left
mapConeInv 📖	CompOp	—
mapConeInvMapCone 📖	CompOp	—
mapConeMapCone 📖	CompOp	2 math math: mapConeMapCone_hom_hom, mapConeMapCone_inv_hom
mapConeMapConeInv 📖	CompOp	—
mapConeMorphism 📖	CompOp	—
mapConeOp 📖	CompOp	2 math math: mapConeOp_inv_hom, mapConeOp_hom_hom
mapConePostcompose 📖	CompOp	2 math math: mapConePostcompose_inv_hom, mapConePostcompose_hom_hom
mapConePostcomposeEquivalenceFunctor 📖	CompOp	2 math math: mapConePostcomposeEquivalenceFunctor_inv_hom, mapConePostcomposeEquivalenceFunctor_hom_hom
mapConeWhisker 📖	CompOp	2 math math: mapConeWhisker_hom_hom, mapConeWhisker_inv_hom
postcomposeWhiskerLeftMapCone 📖	CompOp	2 math math: postcomposeWhiskerLeftMapCone_inv_hom, postcomposeWhiskerLeftMapCone_hom_hom
precomposeWhiskerLeftMapCocone 📖	CompOp	2 math math: precomposeWhiskerLeftMapCocone_hom_hom, precomposeWhiskerLeftMapCocone_inv_hom

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cocones_map_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite.unop CategoryTheory.Functor Opposite.op obj category const map CategoryTheory.types cocones CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	—	—
cocones_obj 📖	mathematical	—	obj CategoryTheory.types cocones Quiver.Hom CategoryTheory.Functor CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct category const	—	—
cones_map_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite.unop CategoryTheory.Functor obj Opposite CategoryTheory.Category.opposite category op const map CategoryTheory.types cones CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver	—	—
cones_obj 📖	mathematical	—	obj Opposite CategoryTheory.Category.opposite CategoryTheory.types cones Quiver.Hom CategoryTheory.Functor CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct category const Opposite.unop	—	—
functorialityCompPostcompose_hom_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Limits.Cone.functoriality CategoryTheory.Limits.Cone.postcompose whiskerLeft CategoryTheory.Iso.hom CategoryTheory.Functor category CategoryTheory.NatTrans.app functorialityCompPostcompose CategoryTheory.Limits.Cone.pt	—	—
functorialityCompPostcompose_inv_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Limits.Cone.functoriality CategoryTheory.Limits.Cone.postcompose whiskerLeft CategoryTheory.Iso.hom CategoryTheory.Functor category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv functorialityCompPostcompose CategoryTheory.Limits.Cone.pt	—	—
functorialityCompPrecompose_hom_app_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Limits.Cocone.functoriality CategoryTheory.Limits.Cocone.precompose whiskerLeft CategoryTheory.Iso.inv CategoryTheory.Functor category CategoryTheory.NatTrans.app CategoryTheory.Iso.hom functorialityCompPrecompose CategoryTheory.Limits.Cocone.pt	—	—
functorialityCompPrecompose_inv_app_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Limits.Cocone.functoriality CategoryTheory.Limits.Cocone.precompose whiskerLeft CategoryTheory.Iso.inv CategoryTheory.Functor category CategoryTheory.NatTrans.app functorialityCompPrecompose CategoryTheory.Limits.Cocone.pt	—	—
mapCoconeMapCocone_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp mapCocone CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category mapCoconeMapCocone CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct obj CategoryTheory.Limits.Cocone.pt	—	—
mapCoconeMapCocone_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp mapCocone CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category mapCoconeMapCocone CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct obj CategoryTheory.Limits.Cocone.pt	—	—
mapCoconeOp_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom Opposite CategoryTheory.Category.opposite op comp CategoryTheory.Limits.Cocone.op mapCocone mapCone CategoryTheory.Iso.hom CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category mapCoconeOp CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct Opposite.op obj CategoryTheory.Limits.Cocone.pt	—	—
mapCoconeOp_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom Opposite CategoryTheory.Category.opposite op comp mapCone CategoryTheory.Limits.Cocone.op mapCocone CategoryTheory.Iso.inv CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category mapCoconeOp CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct Opposite.op obj CategoryTheory.Limits.Cocone.pt	—	—
mapCoconePrecomposeEquivalenceFunctor_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp mapCocone obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone.precomposeEquivalence isoWhiskerRight CategoryTheory.Iso.hom mapCoconePrecomposeEquivalenceFunctor CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt	—	—
mapCoconePrecomposeEquivalenceFunctor_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone.precomposeEquivalence isoWhiskerRight mapCocone CategoryTheory.Iso.inv mapCoconePrecomposeEquivalenceFunctor CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt	—	—
mapCoconePrecompose_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp mapCocone obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Limits.Cocone.precompose whiskerRight CategoryTheory.Iso.hom mapCoconePrecompose CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt	—	—
mapCoconePrecompose_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Limits.Cocone.precompose whiskerRight mapCocone CategoryTheory.Iso.inv mapCoconePrecompose CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt	—	—
mapCoconeWhisker_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp mapCocone CategoryTheory.Limits.Cocone.whisker CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category mapCoconeWhisker CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct obj CategoryTheory.Limits.Cocone.pt	—	—
mapCoconeWhisker_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp CategoryTheory.Limits.Cocone.whisker mapCocone CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category mapCoconeWhisker CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct obj CategoryTheory.Limits.Cocone.pt	—	—
mapCocone_pt 📖	mathematical	—	CategoryTheory.Limits.Cocone.pt comp mapCocone obj	—	—
mapCocone_ι_app 📖	mathematical	—	CategoryTheory.NatTrans.app comp obj CategoryTheory.Functor category const CategoryTheory.Limits.Cocone.pt CategoryTheory.Limits.Cocone.ι mapCocone map	—	—
mapConeMapCone_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp mapCone CategoryTheory.Iso.hom CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category mapConeMapCone CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct obj CategoryTheory.Limits.Cone.pt	—	—
mapConeMapCone_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp mapCone CategoryTheory.Iso.inv CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category mapConeMapCone CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct obj CategoryTheory.Limits.Cone.pt	—	—
mapConeOp_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom Opposite CategoryTheory.Category.opposite op comp CategoryTheory.Limits.Cone.op mapCone mapCocone CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category mapConeOp CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct Opposite.op obj CategoryTheory.Limits.Cone.pt	—	—
mapConeOp_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom Opposite CategoryTheory.Category.opposite op comp mapCocone CategoryTheory.Limits.Cone.op mapCone CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category mapConeOp CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct Opposite.op obj CategoryTheory.Limits.Cone.pt	—	—
mapConePostcomposeEquivalenceFunctor_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp mapCone obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone.postcomposeEquivalence isoWhiskerRight CategoryTheory.Iso.hom mapConePostcomposeEquivalenceFunctor CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt	—	—
mapConePostcomposeEquivalenceFunctor_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone.postcomposeEquivalence isoWhiskerRight mapCone CategoryTheory.Iso.inv mapConePostcomposeEquivalenceFunctor CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt	—	—
mapConePostcompose_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp mapCone obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Limits.Cone.postcompose whiskerRight CategoryTheory.Iso.hom mapConePostcompose CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt	—	—
mapConePostcompose_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Limits.Cone.postcompose whiskerRight mapCone CategoryTheory.Iso.inv mapConePostcompose CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt	—	—
mapConeWhisker_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp mapCone CategoryTheory.Limits.Cone.whisker CategoryTheory.Iso.hom CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category mapConeWhisker CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct obj CategoryTheory.Limits.Cone.pt	—	—
mapConeWhisker_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp CategoryTheory.Limits.Cone.whisker mapCone CategoryTheory.Iso.inv CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category mapConeWhisker CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct obj CategoryTheory.Limits.Cone.pt	—	—
mapCone_pt 📖	mathematical	—	CategoryTheory.Limits.Cone.pt comp mapCone obj	—	—
mapCone_π_app 📖	mathematical	—	CategoryTheory.NatTrans.app obj CategoryTheory.Functor category const CategoryTheory.Limits.Cone.pt comp CategoryTheory.Limits.Cone.π mapCone map	—	—
postcomposeWhiskerLeftMapCone_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Limits.Cone.functoriality CategoryTheory.Limits.Cone.postcompose whiskerLeft CategoryTheory.Iso.hom CategoryTheory.Functor category mapCone postcomposeWhiskerLeftMapCone CategoryTheory.NatTrans.app CategoryTheory.Limits.Cone.pt	—	—
postcomposeWhiskerLeftMapCone_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom comp obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Limits.Cone.functoriality CategoryTheory.Limits.Cone.postcompose whiskerLeft CategoryTheory.Iso.hom CategoryTheory.Functor category CategoryTheory.Iso.inv mapCone postcomposeWhiskerLeftMapCone CategoryTheory.NatTrans.app CategoryTheory.Limits.Cone.pt	—	—
precomposeWhiskerLeftMapCocone_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Limits.Cocone.functoriality CategoryTheory.Limits.Cocone.precompose whiskerLeft CategoryTheory.Iso.inv CategoryTheory.Functor category CategoryTheory.Iso.hom mapCocone precomposeWhiskerLeftMapCocone CategoryTheory.NatTrans.app CategoryTheory.Limits.Cocone.pt	—	—
precomposeWhiskerLeftMapCocone_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom comp obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Limits.Cocone.functoriality CategoryTheory.Limits.Cocone.precompose whiskerLeft CategoryTheory.Iso.inv CategoryTheory.Functor category mapCocone precomposeWhiskerLeftMapCocone CategoryTheory.NatTrans.app CategoryTheory.Limits.Cocone.pt	—	—

CategoryTheory.Limits

Definitions

Name	Category	Theorems
Cocone 📖	CompData	205 math math: CategoryTheory.Functor.LeftExtension.coconeAtFunctor_map_hom, Cocone.category_id_hom, IsColimit.uniqueUpToIso_hom, coneOpEquiv_unitIso, coconeLeftOpOfConeEquiv_functor_map_hom, coneRightOpOfCoconeEquiv_functor_obj, Cocone.whiskeringEquivalence_counitIso, coneRightOpOfCoconeEquiv_functor_map_hom, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, coneUnopOfCoconeEquiv_counitIso, CategoryTheory.WithInitial.coconeEquiv_functor_obj_pt, Cocone.equivalenceOfReindexing_inverse, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, PushoutCocone.unop_π_app, Types.isColimit_iff_coconeTypesIsColimit, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_right, Cocone.extendComp_inv_hom, CategoryTheory.Functor.Final.colimitCoconeOfComp_isColimit, CategoryTheory.Functor.Final.coconesEquiv_unitIso, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, coconeUnopOfConeEquiv_unitIso, Cocone.extendIso_inv_hom, instIsIsoHomHomCocone, PushoutCocone.isoMk_inv_hom, Cocone.equivalenceOfReindexing_functor, colimit.map_desc, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, CategoryTheory.Functor.Final.extendCocone_obj_ι_app, CategoryTheory.Functor.Final.coconesEquiv_functor, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, CoconeMorphism.hom_inv_id_assoc, coconeLeftOpOfConeEquiv_inverse_obj, Cocone.functorialityEquivalence_counitIso, coconeRightOpOfConeEquiv_functor_map_hom, coneRightOpOfCoconeEquiv_inverse_obj, CategoryTheory.Functor.coconeTypesEquiv_apply_pt, Cocone.extendIso_hom_hom, Cocone.functorialityEquivalence_unitIso, Cocone.category_comp_hom, CategoryTheory.IsUniversalColimit.precompose_isIso, HasColimit.isoOfNatIso_inv_desc_assoc, IsColimit.ofCoconeEquiv_symm_apply_desc, HasColimit.isoOfNatIso_hom_desc, Cocone.equivalenceOfReindexing_counitIso, IsInitial.to_eq_descCoconeMorphism, Cocone.functoriality_obj_ι_app, coneOpEquiv_inverse_obj, DiagramOfCocones.coconePoints_map, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, coconeUnopOfConeEquiv_counitIso, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_pt, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, coconeUnopOfConeEquiv_functor_obj, CategoryTheory.Adjunction.functorialityUnit_app_hom, Cocone.cocone_iso_of_hom_iso, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.Functor.mapCoconeMapCocone_hom_hom, Cocone.precomposeComp_hom_app_hom, Cocone.functoriality_map_hom, coconeUnopOfConeEquiv_functor_map_hom, Cocone.extendId_inv_hom, CategoryTheory.IsFiltered.cocone_nonempty, coconeOpEquiv_inverse_map, Cocone.reflects_cocone_isomorphism, Cocone.whiskering_map_hom, coconeOpEquiv_functor_obj, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, Cocone.toStructuredArrow_obj, CategoryTheory.IsCardinalFiltered.nonempty_cocone, coconeUnopOfConeEquiv_inverse_map, CategoryTheory.IsVanKampenColimit.precompose_isIso, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, IsColimit.coconePointsIsoOfEquivalence_hom, Cocone.precomposeId_hom_app_hom, DiagramOfCocones.comp, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_left_as, Cofork.π_precompose, Cocone.precomposeEquivalence_counitIso, Cocone.equivStructuredArrow_unitIso, coneLeftOpOfCoconeEquiv_inverse_obj, Cocone.precompose_map_hom, Cocones.cone_iso_of_hom_iso, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.IsFiltered.iff_cocone_nonempty, Cocone.fromStructuredArrow_obj_pt, coconeRightOpOfConeEquiv_inverse_obj, Cocone.forget_map, DiagramOfCocones.mkOfHasColimits_map_hom, coneOpEquiv_functor_obj, coconeRightOpOfConeEquiv_unitIso, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, coneOpEquiv_counitIso, coneUnopOfCoconeEquiv_functor_map_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, Cocone.functorialityEquivalence_inverse, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_hom_hom, CategoryTheory.Adjunction.functorialityCounit_app_hom, IsColimit.coconePointsIsoOfEquivalence_inv, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_of, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_ι, reflexiveCoforkEquivCofork_functor_obj_pt, IsColimit.descCoconeMorphism_eq_isInitial_to, CategoryTheory.Functor.Final.extendCocone_obj_ι_app', Cocone.precomposeId_inv_app_hom, coconeRightOpOfConeEquiv_inverse_map, CategoryTheory.IsVanKampenColimit.precompose_isIso_iff, CategoryTheory.Functor.LeftExtension.coconeAtFunctor_obj, coneRightOpOfCoconeEquiv_inverse_map, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, Cocone.precompose_obj_ι, SheafOfModules.Presentation.map_relations_I, coneUnopOfCoconeEquiv_functor_obj, reflexiveCoforkEquivCofork_inverse_obj_pt, coneUnopOfCoconeEquiv_inverse_obj, Cocone.eta_inv_hom, Cocones.reflects_cone_isomorphism, IsColimit.ofCoconeEquiv_apply_desc, coconeLeftOpOfConeEquiv_unitIso, CategoryTheory.Functor.coconeTypesEquiv_apply_ι_app, Cocones.functoriality_faithful, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, coconeOpEquiv_inverse_obj, Cocone.fromStructuredArrow_map_hom, Cocone.ext_hom_hom, CoconeMorphism.hom_inv_id, HasColimit.isoOfNatIso_hom_desc_assoc, coneOpEquiv_functor_map_hom, Cocones.functoriality_full, Cocone.ext_inv_hom_hom, Cocone.functoriality_obj_pt, Cocone.forget_obj, coconeOpEquiv_unitIso, Cocone.whiskeringEquivalence_inverse, Cocone.precomposeEquivalence_functor, pointwiseBinaryBicone.isBilimit_isColimit, coneLeftOpOfCoconeEquiv_functor_map_hom, Cocone.functorialityEquivalence_functor, coneLeftOpOfCoconeEquiv_functor_obj, Cocone.equivStructuredArrow_inverse, coneLeftOpOfCoconeEquiv_unitIso, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, coneLeftOpOfCoconeEquiv_inverse_map, coconeRightOpOfConeEquiv_counitIso, Cocone.mapCoconeToOver_inv_hom, coconeRightOpOfConeEquiv_functor_obj, IsColimit.equivIsoColimit_symm_apply, colimit.map_desc_assoc, Cocone.precomposeEquivalence_unitIso, CategoryTheory.Functor.mapConeOp_inv_hom, CategoryTheory.Functor.Final.coconesEquiv_counitIso, IsColimit.hom_isIso, IsColimit.uniqueUpToIso_inv, coneOpEquiv_inverse_map, coconeUnopOfConeEquiv_inverse_obj, CoconeMorphism.inv_hom_id, Cocone.ext_inv_hom, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, DiagramOfCocones.id, IsColimit.ofIsoColimit_desc, Cocone.functoriality_faithful, Cocone.whiskeringEquivalence_unitIso, coneLeftOpOfCoconeEquiv_counitIso, PushoutCocone.isoMk_hom_hom, Cocone.whiskering_obj, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, hasColimit_iff_hasInitial_cocone, Cocone.equivalenceOfReindexing_unitIso, Cocone.functoriality_full, Cocone.extendComp_hom_hom, CategoryTheory.Functor.mapConeOp_hom_hom, coneUnopOfCoconeEquiv_inverse_map, Cocone.toStructuredArrow_map, coconeOpEquiv_counitIso, CategoryTheory.Functor.Final.extendCocone_obj_pt, Cocone.ext_inv_inv_hom, coconeLeftOpOfConeEquiv_counitIso, Cocone.precomposeEquivalence_inverse, instIsIsoHomInvCocone, CategoryTheory.Functor.Final.extendCocone_map_hom, Cocone.mapCoconeToOver_hom_hom, coneRightOpOfCoconeEquiv_unitIso, CoconeMorphism.inv_hom_id_assoc, Cocone.eta_hom_hom, CategoryTheory.Functor.CoconeTypes.isColimit_iff, Cocone.precomposeComp_inv_app_hom, Cocone.equivStructuredArrow_functor, Cocone.fromStructuredArrow_obj_ι, Cocone.equivStructuredArrow_counitIso, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, Cocone.extendId_hom_hom, coconeLeftOpOfConeEquiv_inverse_map, HasColimit.isoOfNatIso_inv_desc, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, coconeOpEquiv_functor_map_hom, Cocone.instIsIsoExtendHom, CategoryTheory.Functor.Final.coconesEquiv_inverse, Cocone.whiskeringEquivalence_functor, coneUnopOfCoconeEquiv_unitIso, coconeLeftOpOfConeEquiv_functor_obj, Cocone.precompose_obj_pt, coneRightOpOfCoconeEquiv_counitIso, CategoryTheory.Functor.Final.colimitCoconeOfComp_cocone
CoconeMorphism 📖	CompData	—
ConeMorphism 📖	CompData	—
coconeEquivalenceOpConeOp 📖	CompOp	—
coconeLeftOpOfCone 📖	CompOp	8 math math: coconeLeftOpOfConeEquiv_functor_map_hom, isColimitCoconeLeftOpOfCone_desc, isLimitOfCoconeLeftOpOfCone_lift, isLimitConeOfCoconeLeftOp_lift, coconeLeftOpOfCone_ι_app, coconeLeftOpOfConeEquiv_counitIso, coconeLeftOpOfConeEquiv_functor_obj, coconeLeftOpOfCone_pt
coconeLeftOpOfConeEquiv 📖	CompOp	6 math math: coconeLeftOpOfConeEquiv_functor_map_hom, coconeLeftOpOfConeEquiv_inverse_obj, coconeLeftOpOfConeEquiv_unitIso, coconeLeftOpOfConeEquiv_counitIso, coconeLeftOpOfConeEquiv_inverse_map, coconeLeftOpOfConeEquiv_functor_obj
coconeOfConeLeftOp 📖	CompOp	8 math math: coconeOfConeLeftOp_pt, isLimitOfCoconeOfConeLeftOp_lift, coneLeftOpOfCoconeEquiv_inverse_obj, isLimitConeLeftOpOfCocone_lift, coneLeftOpOfCoconeEquiv_inverse_map, coconeOfConeLeftOp_ι_app, coneLeftOpOfCoconeEquiv_counitIso, isColimitCoconeOfConeLeftOp_desc
coconeOfConeRightOp 📖	CompOp	8 math math: isLimitConeRightOpOfCocone_lift, isLimitOfCoconeOfConeRightOp_lift, coneRightOpOfCoconeEquiv_inverse_obj, coconeOfConeRightOp_ι, coconeOfConeRightOp_pt, coneRightOpOfCoconeEquiv_inverse_map, isColimitCoconeOfConeRightOp_desc, coneRightOpOfCoconeEquiv_counitIso
coconeOfConeUnop 📖	CompOp	8 math math: coneUnopOfCoconeEquiv_counitIso, coconeOfConeUnop_pt, isLimitConeUnopOfCocone_lift, coneUnopOfCoconeEquiv_inverse_obj, isLimitOfCoconeOfConeUnop_lift, coconeOfConeUnop_ι, coneUnopOfCoconeEquiv_inverse_map, isColimitCoconeOfConeUnop_desc
coconeOpEquiv 📖	CompOp	6 math math: coconeOpEquiv_inverse_map, coconeOpEquiv_functor_obj, coconeOpEquiv_inverse_obj, coconeOpEquiv_unitIso, coconeOpEquiv_counitIso, coconeOpEquiv_functor_map_hom
coconeRightOpOfCone 📖	CompOp	9 math math: coconeRightOpOfConeEquiv_functor_map_hom, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, isLimitOfCoconeRightOpOfCone_lift, isLimitConeOfCoconeRightOp_lift, isColimitCoconeRightOpOfCone_desc, coconeRightOpOfCone_ι, coconeRightOpOfConeEquiv_counitIso, coconeRightOpOfConeEquiv_functor_obj, coconeRightOpOfCone_pt
coconeRightOpOfConeEquiv 📖	CompOp	6 math math: coconeRightOpOfConeEquiv_functor_map_hom, coconeRightOpOfConeEquiv_inverse_obj, coconeRightOpOfConeEquiv_unitIso, coconeRightOpOfConeEquiv_inverse_map, coconeRightOpOfConeEquiv_counitIso, coconeRightOpOfConeEquiv_functor_obj
coconeUnopOfCone 📖	CompOp	8 math math: coconeUnopOfConeEquiv_counitIso, coconeUnopOfConeEquiv_functor_obj, isLimitConeOfCoconeUnop_lift, coconeUnopOfConeEquiv_functor_map_hom, isColimitCoconeUnopOfCone_desc, coconeUnopOfCone_pt, isLimitOfCoconeUnopOfCone_lift, coconeUnopOfCone_ι
coconeUnopOfConeEquiv 📖	CompOp	6 math math: coconeUnopOfConeEquiv_unitIso, coconeUnopOfConeEquiv_counitIso, coconeUnopOfConeEquiv_functor_obj, coconeUnopOfConeEquiv_functor_map_hom, coconeUnopOfConeEquiv_inverse_map, coconeUnopOfConeEquiv_inverse_obj
coneEquivalenceOpCoconeOp 📖	CompOp	—
coneLeftOpOfCocone 📖	CompOp	8 math math: coneLeftOpOfCocone_π_app, isColimitOfConeLeftOpOfCocone_desc, coneLeftOpOfCocone_pt, isLimitConeLeftOpOfCocone_lift, coneLeftOpOfCoconeEquiv_functor_map_hom, coneLeftOpOfCoconeEquiv_functor_obj, coneLeftOpOfCoconeEquiv_counitIso, isColimitCoconeOfConeLeftOp_desc
coneLeftOpOfCoconeEquiv 📖	CompOp	6 math math: coneLeftOpOfCoconeEquiv_inverse_obj, coneLeftOpOfCoconeEquiv_functor_map_hom, coneLeftOpOfCoconeEquiv_functor_obj, coneLeftOpOfCoconeEquiv_unitIso, coneLeftOpOfCoconeEquiv_inverse_map, coneLeftOpOfCoconeEquiv_counitIso
coneOfCoconeLeftOp 📖	CompOp	8 math math: isColimitCoconeLeftOpOfCone_desc, coconeLeftOpOfConeEquiv_inverse_obj, coneOfCoconeLeftOp_π_app, isColimitOfConeOfCoconeLeftOp_desc, coneOfCoconeLeftOp_pt, isLimitConeOfCoconeLeftOp_lift, coconeLeftOpOfConeEquiv_counitIso, coconeLeftOpOfConeEquiv_inverse_map
coneOfCoconeRightOp 📖	CompOp	8 math math: coneOfCoconeRightOp_π, coconeRightOpOfConeEquiv_inverse_obj, coconeRightOpOfConeEquiv_inverse_map, isLimitConeOfCoconeRightOp_lift, coneOfCoconeRightOp_pt, isColimitCoconeRightOpOfCone_desc, coconeRightOpOfConeEquiv_counitIso, isColimitOfConeOfCoconeRightOp_desc
coneOfCoconeUnop 📖	CompOp	8 math math: coconeUnopOfConeEquiv_counitIso, coneOfCoconeUnop_π, isLimitConeOfCoconeUnop_lift, isColimitCoconeUnopOfCone_desc, coconeUnopOfConeEquiv_inverse_map, coconeUnopOfConeEquiv_inverse_obj, isColimitOfConeOfCoconeUnop_desc, coneOfCoconeUnop_pt
coneOpEquiv 📖	CompOp	6 math math: coneOpEquiv_unitIso, coneOpEquiv_inverse_obj, coneOpEquiv_functor_obj, coneOpEquiv_counitIso, coneOpEquiv_functor_map_hom, coneOpEquiv_inverse_map
coneRightOpOfCocone 📖	CompOp	8 math math: isLimitConeRightOpOfCocone_lift, coneRightOpOfCoconeEquiv_functor_obj, coneRightOpOfCoconeEquiv_functor_map_hom, isColimitOfConeRightOpOfCocone_desc, coneRightOpOfCocone_π, coneRightOpOfCocone_pt, isColimitCoconeOfConeRightOp_desc, coneRightOpOfCoconeEquiv_counitIso
coneRightOpOfCoconeEquiv 📖	CompOp	6 math math: coneRightOpOfCoconeEquiv_functor_obj, coneRightOpOfCoconeEquiv_functor_map_hom, coneRightOpOfCoconeEquiv_inverse_obj, coneRightOpOfCoconeEquiv_inverse_map, coneRightOpOfCoconeEquiv_unitIso, coneRightOpOfCoconeEquiv_counitIso
coneUnopOfCocone 📖	CompOp	8 math math: coneUnopOfCoconeEquiv_counitIso, coneUnopOfCocone_pt, isColimitOfConeUnopOfCocone_desc, isLimitConeUnopOfCocone_lift, coneUnopOfCoconeEquiv_functor_map_hom, coneUnopOfCoconeEquiv_functor_obj, coneUnopOfCocone_π, isColimitCoconeOfConeUnop_desc
coneUnopOfCoconeEquiv 📖	CompOp	6 math math: coneUnopOfCoconeEquiv_counitIso, coneUnopOfCoconeEquiv_functor_map_hom, coneUnopOfCoconeEquiv_functor_obj, coneUnopOfCoconeEquiv_inverse_obj, coneUnopOfCoconeEquiv_inverse_map, coneUnopOfCoconeEquiv_unitIso
inhabitedCocone 📖	CompOp	—
inhabitedCoconeMorphism 📖	CompOp	—
inhabitedCone 📖	CompOp	—
inhabitedConeMorphism 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coconeLeftOpOfConeEquiv_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso Opposite Cone CategoryTheory.Category.opposite Cocone CategoryTheory.Functor.leftOp Cone.category Cocone.category coconeLeftOpOfConeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp Opposite.op coneOfCoconeLeftOp Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Quiver.Hom.op Cocone.pt CoconeMorphism.hom coconeLeftOpOfCone Quiver.Hom.unop Cone.pt ConeMorphism.hom	—	—
coconeLeftOpOfConeEquiv_functor_map_hom 📖	mathematical	—	CoconeMorphism.hom Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp coconeLeftOpOfCone Opposite.unop Cone CategoryTheory.Functor.map Cone.category Cocone Cocone.category CategoryTheory.Equivalence.functor coconeLeftOpOfConeEquiv Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cone.pt ConeMorphism.hom	—	—
coconeLeftOpOfConeEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj Opposite Cone CategoryTheory.Category.opposite Cone.category Cocone CategoryTheory.Functor.leftOp Cocone.category CategoryTheory.Equivalence.functor coconeLeftOpOfConeEquiv coconeLeftOpOfCone Opposite.unop	—	—
coconeLeftOpOfConeEquiv_inverse_map 📖	mathematical	—	CategoryTheory.Functor.map Cocone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp Cocone.category Cone Cone.category CategoryTheory.Equivalence.inverse coconeLeftOpOfConeEquiv Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop coneOfCoconeLeftOp Quiver.Hom.op Cocone.pt CoconeMorphism.hom	—	—
coconeLeftOpOfConeEquiv_inverse_obj 📖	mathematical	—	CategoryTheory.Functor.obj Cocone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp Cocone.category Cone Cone.category CategoryTheory.Equivalence.inverse coconeLeftOpOfConeEquiv Opposite.op coneOfCoconeLeftOp	—	—
coconeLeftOpOfConeEquiv_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso Opposite Cone CategoryTheory.Category.opposite Cocone CategoryTheory.Functor.leftOp Cone.category Cocone.category coconeLeftOpOfConeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id	—	—
coconeLeftOpOfCone_pt 📖	mathematical	—	Cocone.pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp coconeLeftOpOfCone Opposite.unop Cone.pt	—	—
coconeLeftOpOfCone_ι_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Cone.pt Cocone.ι coconeLeftOpOfCone Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Cone.π	—	—
coconeOfConeLeftOp_pt 📖	mathematical	—	Cocone.pt Opposite CategoryTheory.Category.opposite coconeOfConeLeftOp Opposite.op Cone.pt CategoryTheory.Functor.leftOp	—	—
coconeOfConeLeftOp_ι_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Opposite.op Cone.pt CategoryTheory.Functor.leftOp Cocone.ι coconeOfConeLeftOp Quiver.Hom.op CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Cone.π	—	—
coconeOfConeRightOp_pt 📖	mathematical	—	Cocone.pt Opposite CategoryTheory.Category.opposite coconeOfConeRightOp Opposite.unop Cone.pt CategoryTheory.Functor.rightOp	—	—
coconeOfConeRightOp_ι 📖	mathematical	—	Cocone.ι Opposite CategoryTheory.Category.opposite coconeOfConeRightOp CategoryTheory.NatTrans.removeRightOp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Opposite.unop Cone.pt CategoryTheory.Functor.rightOp Cone.π	—	—
coconeOfConeUnop_pt 📖	mathematical	—	Cocone.pt Opposite CategoryTheory.Category.opposite coconeOfConeUnop Opposite.op Cone.pt CategoryTheory.Functor.unop	—	—
coconeOfConeUnop_ι 📖	mathematical	—	Cocone.ι Opposite CategoryTheory.Category.opposite coconeOfConeUnop CategoryTheory.NatTrans.removeUnop CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Opposite.op Cone.pt CategoryTheory.Functor.unop Cone.π	—	—
coconeOpEquiv_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso Opposite Cocone Cone CategoryTheory.Category.opposite CategoryTheory.Functor.op Cocone.category Cone.category coconeOpEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp Opposite.op Cone.unop Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Quiver.Hom.unop Cone.pt ConeMorphism.hom Cocone.op Quiver.Hom.op Cocone.pt CoconeMorphism.hom	—	—
coconeOpEquiv_functor_map_hom 📖	mathematical	—	ConeMorphism.hom Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op Cocone.op Opposite.unop Cocone CategoryTheory.Functor.map Cocone.category Cone Cone.category CategoryTheory.Equivalence.functor coconeOpEquiv Quiver.Hom.op CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cocone.pt CoconeMorphism.hom Quiver.Hom.unop	—	—
coconeOpEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj Opposite Cocone CategoryTheory.Category.opposite Cocone.category Cone CategoryTheory.Functor.op Cone.category CategoryTheory.Equivalence.functor coconeOpEquiv Cocone.op Opposite.unop	—	—
coconeOpEquiv_inverse_map 📖	mathematical	—	CategoryTheory.Functor.map Cone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op Cone.category Cocone Cocone.category CategoryTheory.Equivalence.inverse coconeOpEquiv Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Cone.unop Quiver.Hom.unop Cone.pt ConeMorphism.hom	—	—
coconeOpEquiv_inverse_obj 📖	mathematical	—	CategoryTheory.Functor.obj Cone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op Cone.category Cocone Cocone.category CategoryTheory.Equivalence.inverse coconeOpEquiv Opposite.op Cone.unop	—	—
coconeOpEquiv_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso Opposite Cocone Cone CategoryTheory.Category.opposite CategoryTheory.Functor.op Cocone.category Cone.category coconeOpEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id	—	—
coconeRightOpOfConeEquiv_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso Opposite Cone CategoryTheory.Category.opposite Cocone CategoryTheory.Functor.rightOp Cone.category Cocone.category coconeRightOpOfConeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp Opposite.op coneOfCoconeRightOp Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Quiver.Hom.unop Cocone.pt CoconeMorphism.hom coconeRightOpOfCone Quiver.Hom.op Cone.pt ConeMorphism.hom	—	—
coconeRightOpOfConeEquiv_functor_map_hom 📖	mathematical	—	CoconeMorphism.hom Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp coconeRightOpOfCone Opposite.unop Cone CategoryTheory.Functor.map Cone.category Cocone Cocone.category CategoryTheory.Equivalence.functor coconeRightOpOfConeEquiv Quiver.Hom.op CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cone.pt ConeMorphism.hom Quiver.Hom.unop	—	—
coconeRightOpOfConeEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj Opposite Cone CategoryTheory.Category.opposite Cone.category Cocone CategoryTheory.Functor.rightOp Cocone.category CategoryTheory.Equivalence.functor coconeRightOpOfConeEquiv coconeRightOpOfCone Opposite.unop	—	—
coconeRightOpOfConeEquiv_inverse_map 📖	mathematical	—	CategoryTheory.Functor.map Cocone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp Cocone.category Cone Cone.category CategoryTheory.Equivalence.inverse coconeRightOpOfConeEquiv Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop coneOfCoconeRightOp Quiver.Hom.unop Cocone.pt CoconeMorphism.hom	—	—
coconeRightOpOfConeEquiv_inverse_obj 📖	mathematical	—	CategoryTheory.Functor.obj Cocone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp Cocone.category Cone Cone.category CategoryTheory.Equivalence.inverse coconeRightOpOfConeEquiv Opposite.op coneOfCoconeRightOp	—	—
coconeRightOpOfConeEquiv_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso Opposite Cone CategoryTheory.Category.opposite Cocone CategoryTheory.Functor.rightOp Cone.category Cocone.category coconeRightOpOfConeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id	—	—
coconeRightOpOfCone_pt 📖	mathematical	—	Cocone.pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp coconeRightOpOfCone Opposite.op Cone.pt	—	—
coconeRightOpOfCone_ι 📖	mathematical	—	Cocone.ι Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp coconeRightOpOfCone CategoryTheory.NatTrans.rightOp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Cone.pt Cone.π	—	—
coconeUnopOfConeEquiv_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso Opposite Cone CategoryTheory.Category.opposite Cocone CategoryTheory.Functor.unop Cone.category Cocone.category coconeUnopOfConeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp Opposite.op coneOfCoconeUnop Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Quiver.Hom.op Cocone.pt CoconeMorphism.hom coconeUnopOfCone Quiver.Hom.unop Cone.pt ConeMorphism.hom	—	—
coconeUnopOfConeEquiv_functor_map_hom 📖	mathematical	—	CoconeMorphism.hom CategoryTheory.Functor.unop coconeUnopOfCone Opposite.unop Cone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.map Cone.category Cocone Cocone.category CategoryTheory.Equivalence.functor coconeUnopOfConeEquiv Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cone.pt ConeMorphism.hom	—	—
coconeUnopOfConeEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj Opposite Cone CategoryTheory.Category.opposite Cone.category Cocone CategoryTheory.Functor.unop Cocone.category CategoryTheory.Equivalence.functor coconeUnopOfConeEquiv coconeUnopOfCone Opposite.unop	—	—
coconeUnopOfConeEquiv_inverse_map 📖	mathematical	—	CategoryTheory.Functor.map Cocone CategoryTheory.Functor.unop Cocone.category Opposite Cone CategoryTheory.Category.opposite Cone.category CategoryTheory.Equivalence.inverse coconeUnopOfConeEquiv Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop coneOfCoconeUnop Quiver.Hom.op Cocone.pt CoconeMorphism.hom	—	—
coconeUnopOfConeEquiv_inverse_obj 📖	mathematical	—	CategoryTheory.Functor.obj Cocone CategoryTheory.Functor.unop Cocone.category Opposite Cone CategoryTheory.Category.opposite Cone.category CategoryTheory.Equivalence.inverse coconeUnopOfConeEquiv Opposite.op coneOfCoconeUnop	—	—
coconeUnopOfConeEquiv_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso Opposite Cone CategoryTheory.Category.opposite Cocone CategoryTheory.Functor.unop Cone.category Cocone.category coconeUnopOfConeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id	—	—
coconeUnopOfCone_pt 📖	mathematical	—	Cocone.pt CategoryTheory.Functor.unop coconeUnopOfCone Opposite.unop Cone.pt Opposite CategoryTheory.Category.opposite	—	—
coconeUnopOfCone_ι 📖	mathematical	—	Cocone.ι CategoryTheory.Functor.unop coconeUnopOfCone CategoryTheory.NatTrans.unop CategoryTheory.Functor.obj Opposite CategoryTheory.Category.opposite CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Cone.pt Cone.π	—	—
coneLeftOpOfCoconeEquiv_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso Opposite Cocone CategoryTheory.Category.opposite Cone CategoryTheory.Functor.leftOp Cocone.category Cone.category coneLeftOpOfCoconeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp Opposite.op coconeOfConeLeftOp Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Quiver.Hom.op Cone.pt ConeMorphism.hom coneLeftOpOfCocone Quiver.Hom.unop Cocone.pt CoconeMorphism.hom	—	—
coneLeftOpOfCoconeEquiv_functor_map_hom 📖	mathematical	—	ConeMorphism.hom Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp coneLeftOpOfCocone Opposite.unop Cocone CategoryTheory.Functor.map Cocone.category Cone Cone.category CategoryTheory.Equivalence.functor coneLeftOpOfCoconeEquiv Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cocone.pt CoconeMorphism.hom	—	—
coneLeftOpOfCoconeEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj Opposite Cocone CategoryTheory.Category.opposite Cocone.category Cone CategoryTheory.Functor.leftOp Cone.category CategoryTheory.Equivalence.functor coneLeftOpOfCoconeEquiv coneLeftOpOfCocone Opposite.unop	—	—
coneLeftOpOfCoconeEquiv_inverse_map 📖	mathematical	—	CategoryTheory.Functor.map Cone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp Cone.category Cocone Cocone.category CategoryTheory.Equivalence.inverse coneLeftOpOfCoconeEquiv Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop coconeOfConeLeftOp Quiver.Hom.op Cone.pt ConeMorphism.hom	—	—
coneLeftOpOfCoconeEquiv_inverse_obj 📖	mathematical	—	CategoryTheory.Functor.obj Cone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp Cone.category Cocone Cocone.category CategoryTheory.Equivalence.inverse coneLeftOpOfCoconeEquiv Opposite.op coconeOfConeLeftOp	—	—
coneLeftOpOfCoconeEquiv_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso Opposite Cocone CategoryTheory.Category.opposite Cone CategoryTheory.Functor.leftOp Cocone.category Cone.category coneLeftOpOfCoconeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id	—	—
coneLeftOpOfCocone_pt 📖	mathematical	—	Cone.pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp coneLeftOpOfCocone Opposite.unop Cocone.pt	—	—
coneLeftOpOfCocone_π_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.leftOp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Cocone.pt Cone.π coneLeftOpOfCocone Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Cocone.ι	—	—
coneOfCoconeLeftOp_pt 📖	mathematical	—	Cone.pt Opposite CategoryTheory.Category.opposite coneOfCoconeLeftOp Opposite.op Cocone.pt CategoryTheory.Functor.leftOp	—	—
coneOfCoconeLeftOp_π_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Opposite.op Cocone.pt CategoryTheory.Functor.leftOp Cone.π coneOfCoconeLeftOp Quiver.Hom.op CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Cocone.ι	—	—
coneOfCoconeRightOp_pt 📖	mathematical	—	Cone.pt Opposite CategoryTheory.Category.opposite coneOfCoconeRightOp Opposite.unop Cocone.pt CategoryTheory.Functor.rightOp	—	—
coneOfCoconeRightOp_π 📖	mathematical	—	Cone.π Opposite CategoryTheory.Category.opposite coneOfCoconeRightOp CategoryTheory.NatTrans.removeRightOp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Opposite.unop Cocone.pt CategoryTheory.Functor.rightOp Cocone.ι	—	—
coneOfCoconeUnop_pt 📖	mathematical	—	Cone.pt Opposite CategoryTheory.Category.opposite coneOfCoconeUnop Opposite.op Cocone.pt CategoryTheory.Functor.unop	—	—
coneOfCoconeUnop_π 📖	mathematical	—	Cone.π Opposite CategoryTheory.Category.opposite coneOfCoconeUnop CategoryTheory.NatTrans.removeUnop CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Opposite.op Cocone.pt CategoryTheory.Functor.unop Cocone.ι	—	—
coneOpEquiv_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso Opposite Cone Cocone CategoryTheory.Category.opposite CategoryTheory.Functor.op Cone.category Cocone.category coneOpEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp Opposite.op Cocone.unop Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Quiver.Hom.unop Cocone.pt CoconeMorphism.hom Cone.op Quiver.Hom.op Cone.pt ConeMorphism.hom	—	—
coneOpEquiv_functor_map_hom 📖	mathematical	—	CoconeMorphism.hom Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op Cone.op Opposite.unop Cone CategoryTheory.Functor.map Cone.category Cocone Cocone.category CategoryTheory.Equivalence.functor coneOpEquiv Quiver.Hom.op CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cone.pt ConeMorphism.hom Quiver.Hom.unop	—	—
coneOpEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj Opposite Cone CategoryTheory.Category.opposite Cone.category Cocone CategoryTheory.Functor.op Cocone.category CategoryTheory.Equivalence.functor coneOpEquiv Cone.op Opposite.unop	—	—
coneOpEquiv_inverse_map 📖	mathematical	—	CategoryTheory.Functor.map Cocone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op Cocone.category Cone Cone.category CategoryTheory.Equivalence.inverse coneOpEquiv Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Cocone.unop Quiver.Hom.unop Cocone.pt CoconeMorphism.hom	—	—
coneOpEquiv_inverse_obj 📖	mathematical	—	CategoryTheory.Functor.obj Cocone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op Cocone.category Cone Cone.category CategoryTheory.Equivalence.inverse coneOpEquiv Opposite.op Cocone.unop	—	—
coneOpEquiv_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso Opposite Cone Cocone CategoryTheory.Category.opposite CategoryTheory.Functor.op Cone.category Cocone.category coneOpEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id	—	—
coneRightOpOfCoconeEquiv_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso Opposite Cocone CategoryTheory.Category.opposite Cone CategoryTheory.Functor.rightOp Cocone.category Cone.category coneRightOpOfCoconeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp Opposite.op coconeOfConeRightOp Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Quiver.Hom.unop Cone.pt ConeMorphism.hom coneRightOpOfCocone Quiver.Hom.op Cocone.pt CoconeMorphism.hom	—	—
coneRightOpOfCoconeEquiv_functor_map_hom 📖	mathematical	—	ConeMorphism.hom Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp coneRightOpOfCocone Opposite.unop Cocone CategoryTheory.Functor.map Cocone.category Cone Cone.category CategoryTheory.Equivalence.functor coneRightOpOfCoconeEquiv Quiver.Hom.op CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cocone.pt CoconeMorphism.hom Quiver.Hom.unop	—	—
coneRightOpOfCoconeEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj Opposite Cocone CategoryTheory.Category.opposite Cocone.category Cone CategoryTheory.Functor.rightOp Cone.category CategoryTheory.Equivalence.functor coneRightOpOfCoconeEquiv coneRightOpOfCocone Opposite.unop	—	—
coneRightOpOfCoconeEquiv_inverse_map 📖	mathematical	—	CategoryTheory.Functor.map Cone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp Cone.category Cocone Cocone.category CategoryTheory.Equivalence.inverse coneRightOpOfCoconeEquiv Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop coconeOfConeRightOp Quiver.Hom.unop Cone.pt ConeMorphism.hom	—	—
coneRightOpOfCoconeEquiv_inverse_obj 📖	mathematical	—	CategoryTheory.Functor.obj Cone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp Cone.category Cocone Cocone.category CategoryTheory.Equivalence.inverse coneRightOpOfCoconeEquiv Opposite.op coconeOfConeRightOp	—	—
coneRightOpOfCoconeEquiv_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso Opposite Cocone CategoryTheory.Category.opposite Cone CategoryTheory.Functor.rightOp Cocone.category Cone.category coneRightOpOfCoconeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id	—	—
coneRightOpOfCocone_pt 📖	mathematical	—	Cone.pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp coneRightOpOfCocone Opposite.op Cocone.pt	—	—
coneRightOpOfCocone_π 📖	mathematical	—	Cone.π Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.rightOp coneRightOpOfCocone CategoryTheory.NatTrans.rightOp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Cocone.pt Cocone.ι	—	—
coneUnopOfCoconeEquiv_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso Opposite Cocone CategoryTheory.Category.opposite Cone CategoryTheory.Functor.unop Cocone.category Cone.category coneUnopOfCoconeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp Opposite.op coconeOfConeUnop Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop Quiver.Hom.op Cone.pt ConeMorphism.hom coneUnopOfCocone Quiver.Hom.unop Cocone.pt CoconeMorphism.hom	—	—
coneUnopOfCoconeEquiv_functor_map_hom 📖	mathematical	—	ConeMorphism.hom CategoryTheory.Functor.unop coneUnopOfCocone Opposite.unop Cocone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.map Cocone.category Cone Cone.category CategoryTheory.Equivalence.functor coneUnopOfCoconeEquiv Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cocone.pt CoconeMorphism.hom	—	—
coneUnopOfCoconeEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj Opposite Cocone CategoryTheory.Category.opposite Cocone.category Cone CategoryTheory.Functor.unop Cone.category CategoryTheory.Equivalence.functor coneUnopOfCoconeEquiv coneUnopOfCocone Opposite.unop	—	—
coneUnopOfCoconeEquiv_inverse_map 📖	mathematical	—	CategoryTheory.Functor.map Cone CategoryTheory.Functor.unop Cone.category Opposite Cocone CategoryTheory.Category.opposite Cocone.category CategoryTheory.Equivalence.inverse coneUnopOfCoconeEquiv Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop coconeOfConeUnop Quiver.Hom.op Cone.pt ConeMorphism.hom	—	—
coneUnopOfCoconeEquiv_inverse_obj 📖	mathematical	—	CategoryTheory.Functor.obj Cone CategoryTheory.Functor.unop Cone.category Opposite Cocone CategoryTheory.Category.opposite Cocone.category CategoryTheory.Equivalence.inverse coneUnopOfCoconeEquiv Opposite.op coconeOfConeUnop	—	—
coneUnopOfCoconeEquiv_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso Opposite Cocone CategoryTheory.Category.opposite Cone CategoryTheory.Functor.unop Cocone.category Cone.category coneUnopOfCoconeEquiv CategoryTheory.Iso.refl CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id	—	—
coneUnopOfCocone_pt 📖	mathematical	—	Cone.pt CategoryTheory.Functor.unop coneUnopOfCocone Opposite.unop Cocone.pt Opposite CategoryTheory.Category.opposite	—	—
coneUnopOfCocone_π 📖	mathematical	—	Cone.π CategoryTheory.Functor.unop coneUnopOfCocone CategoryTheory.NatTrans.unop CategoryTheory.Functor.obj Opposite CategoryTheory.Category.opposite CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Cocone.pt Cocone.ι	—	—
instIsIsoHomHomCocone 📖	mathematical	—	CategoryTheory.IsIso Cocone.pt CoconeMorphism.hom CategoryTheory.Iso.inv Cocone Cocone.category	—	CategoryTheory.IsIso.mk' CoconeMorphism.hom_inv_id CoconeMorphism.inv_hom_id
instIsIsoHomHomCone 📖	mathematical	—	CategoryTheory.IsIso Cone.pt ConeMorphism.hom CategoryTheory.Iso.hom Cone Cone.category	—	ConeMorphism.hom_inv_id ConeMorphism.inv_hom_id
instIsIsoHomInvCocone 📖	mathematical	—	CategoryTheory.IsIso Cocone.pt CoconeMorphism.hom CategoryTheory.Iso.hom Cocone Cocone.category	—	CategoryTheory.IsIso.mk' CoconeMorphism.inv_hom_id CoconeMorphism.hom_inv_id
instIsIsoHomInvCone 📖	mathematical	—	CategoryTheory.IsIso Cone.pt ConeMorphism.hom CategoryTheory.Iso.inv Cone Cone.category	—	ConeMorphism.inv_hom_id ConeMorphism.hom_inv_id

CategoryTheory.Limits.Cocone

Definitions

Name	Category	Theorems
category 📖	CompOp	236 math math: CategoryTheory.Functor.LeftExtension.coconeAtFunctor_map_hom, category_id_hom, CategoryTheory.Limits.IsColimit.uniqueUpToIso_hom, CategoryTheory.Limits.coneOpEquiv_unitIso, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_functor_map_hom, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_functor_obj, whiskeringEquivalence_counitIso, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_functor_map_hom, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, CategoryTheory.Limits.coneUnopOfCoconeEquiv_counitIso, CategoryTheory.WithInitial.coconeEquiv_functor_obj_pt, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, equivalenceOfReindexing_inverse, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_obj, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, extendComp_inv_hom, CategoryTheory.Functor.Final.colimitCoconeOfComp_isColimit, CategoryTheory.Functor.Final.coconesEquiv_unitIso, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, CategoryTheory.Limits.coconeUnopOfConeEquiv_unitIso, extendIso_inv_hom, CategoryTheory.Limits.instIsIsoHomHomCocone, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, equivalenceOfReindexing_functor, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.colimit.map_desc, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, CategoryTheory.Functor.Final.extendCocone_obj_ι_app, CategoryTheory.Functor.Final.coconesEquiv_functor, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, CategoryTheory.Limits.CoconeMorphism.hom_inv_id_assoc, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_inverse_obj, functorialityEquivalence_counitIso, CategoryTheory.Limits.coconeRightOpOfConeEquiv_functor_map_hom, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_inverse_obj, extendIso_hom_hom, functorialityEquivalence_unitIso, category_comp_hom, CategoryTheory.IsUniversalColimit.precompose_isIso, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc_assoc, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, CategoryTheory.Limits.Cofan.ext_inv_hom, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc, equivalenceOfReindexing_counitIso, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.IsInitial.to_eq_descCoconeMorphism, functoriality_obj_ι_app, CategoryTheory.Limits.coneOpEquiv_inverse_obj, CategoryTheory.Limits.DiagramOfCocones.coconePoints_map, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.Limits.coconeUnopOfConeEquiv_counitIso, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, CategoryTheory.Limits.coconeUnopOfConeEquiv_functor_obj, CategoryTheory.Adjunction.functorialityUnit_app_hom, cocone_iso_of_hom_iso, CategoryTheory.Limits.Multicofork.ext_hom_hom, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.Functor.mapCoconeMapCocone_hom_hom, CategoryTheory.Limits.PushoutCocone.eta_inv_hom, precomposeComp_hom_app_hom, functoriality_map_hom, CategoryTheory.Limits.coconeUnopOfConeEquiv_functor_map_hom, extendId_inv_hom, CategoryTheory.Limits.coconeOpEquiv_inverse_map, reflects_cocone_isomorphism, CategoryTheory.Limits.BinaryCofan.ext_hom_hom, whiskering_map_hom, CategoryTheory.Limits.coconeOpEquiv_functor_obj, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, toStructuredArrow_obj, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_obj, CategoryTheory.Limits.coconeUnopOfConeEquiv_inverse_map, CategoryTheory.IsVanKampenColimit.precompose_isIso, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_hom, precomposeId_hom_app_hom, CategoryTheory.Limits.DiagramOfCocones.comp, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_left_as, CategoryTheory.Limits.Cofork.π_precompose, precomposeEquivalence_counitIso, equivStructuredArrow_unitIso, CategoryTheory.Limits.Cofan.ext_hom_hom, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_inverse_obj, CategoryTheory.Limits.Cowedge.ext_hom_hom, precompose_map_hom, CategoryTheory.Limits.Cocones.cone_iso_of_hom_iso, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, fromStructuredArrow_obj_pt, CategoryTheory.Limits.coconeRightOpOfConeEquiv_inverse_obj, forget_map, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_map_hom, CategoryTheory.Limits.coneOpEquiv_functor_obj, CategoryTheory.Limits.coconeRightOpOfConeEquiv_unitIso, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, CategoryTheory.Limits.coneOpEquiv_counitIso, CategoryTheory.Limits.coneUnopOfCoconeEquiv_functor_map_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, functorialityEquivalence_inverse, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_hom_hom, CategoryTheory.Adjunction.functorialityCounit_app_hom, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_inv, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_of, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_pt, CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_pt, CategoryTheory.Limits.IsColimit.descCoconeMorphism_eq_isInitial_to, CategoryTheory.Functor.Final.extendCocone_obj_ι_app', precomposeId_inv_app_hom, CategoryTheory.Limits.coconeRightOpOfConeEquiv_inverse_map, CategoryTheory.IsVanKampenColimit.precompose_isIso_iff, CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_π, CategoryTheory.Functor.LeftExtension.coconeAtFunctor_obj, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_inverse_map, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, precompose_obj_ι, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, SheafOfModules.Presentation.map_relations_I, CategoryTheory.Limits.coneUnopOfCoconeEquiv_functor_obj, CategoryTheory.Limits.reflexiveCoforkEquivCofork_inverse_obj_pt, CategoryTheory.Limits.coneUnopOfCoconeEquiv_inverse_obj, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt, eta_inv_hom, CategoryTheory.Limits.Cofork.ext_inv, CategoryTheory.Limits.Cocones.reflects_cone_isomorphism, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_unitIso, CategoryTheory.Limits.Cocones.functoriality_faithful, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, CategoryTheory.Limits.coconeOpEquiv_inverse_obj, fromStructuredArrow_map_hom, ext_hom_hom, CategoryTheory.Limits.CoconeMorphism.hom_inv_id, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.coneOpEquiv_functor_map_hom, CategoryTheory.Limits.Cocones.functoriality_full, ext_inv_hom_hom, functoriality_obj_pt, CategoryTheory.Limits.Multicofork.ext_inv_hom, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_obj, forget_obj, CategoryTheory.Limits.coconeOpEquiv_unitIso, whiskeringEquivalence_inverse, precomposeEquivalence_functor, CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, CategoryTheory.Limits.Cowedge.ext_inv_hom, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isColimit, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_functor_map_hom, functorialityEquivalence_functor, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_functor_obj, CategoryTheory.Limits.Cofork.ext_hom, equivStructuredArrow_inverse, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_unitIso, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_inverse_map, CategoryTheory.Limits.coconeRightOpOfConeEquiv_counitIso, mapCoconeToOver_inv_hom, CategoryTheory.Limits.coconeRightOpOfConeEquiv_functor_obj, CategoryTheory.Limits.IsColimit.equivIsoColimit_symm_apply, CategoryTheory.Limits.colimit.map_desc_assoc, precomposeEquivalence_unitIso, CategoryTheory.Functor.mapConeOp_inv_hom, CategoryTheory.Limits.reflexiveCoforkEquivCofork_inverse_obj_π, CategoryTheory.Functor.Final.coconesEquiv_counitIso, CategoryTheory.Limits.IsColimit.hom_isIso, CategoryTheory.Limits.IsColimit.uniqueUpToIso_inv, CategoryTheory.Limits.coneOpEquiv_inverse_map, CategoryTheory.Limits.coconeUnopOfConeEquiv_inverse_obj, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_inverse, CategoryTheory.Limits.CoconeMorphism.inv_hom_id, ext_inv_hom, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, CategoryTheory.Limits.DiagramOfCocones.id, CategoryTheory.Limits.IsColimit.ofIsoColimit_desc, functoriality_faithful, whiskeringEquivalence_unitIso, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_counitIso, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom, whiskering_obj, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, CategoryTheory.Limits.hasColimit_iff_hasInitial_cocone, equivalenceOfReindexing_unitIso, functoriality_full, extendComp_hom_hom, CategoryTheory.Functor.mapConeOp_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.coneUnopOfCoconeEquiv_inverse_map, toStructuredArrow_map, CategoryTheory.Limits.coconeOpEquiv_counitIso, CategoryTheory.Functor.Final.extendCocone_obj_pt, CategoryTheory.Limits.PushoutCocone.eta_hom_hom, ext_inv_inv_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_counitIso, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, precomposeEquivalence_inverse, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.Limits.instIsIsoHomInvCocone, CategoryTheory.Functor.Final.extendCocone_map_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, mapCoconeToOver_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_unitIso, CategoryTheory.Limits.CoconeMorphism.inv_hom_id_assoc, eta_hom_hom, precomposeComp_inv_app_hom, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom, equivStructuredArrow_functor, fromStructuredArrow_obj_ι, equivStructuredArrow_counitIso, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, extendId_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_inverse_map, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.Limits.coconeOpEquiv_functor_map_hom, instIsIsoExtendHom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_functor, CategoryTheory.Functor.Final.coconesEquiv_inverse, whiskeringEquivalence_functor, CategoryTheory.Limits.coneUnopOfCoconeEquiv_unitIso, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_functor_obj, precompose_obj_pt, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_counitIso, CategoryTheory.Functor.Final.colimitCoconeOfComp_cocone
equiv 📖	CompOp	—
equivalenceOfReindexing 📖	CompOp	6 math math: equivalenceOfReindexing_inverse, equivalenceOfReindexing_functor, equivalenceOfReindexing_counitIso, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_hom, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_inv, equivalenceOfReindexing_unitIso
eta 📖	CompOp	3 math math: equivStructuredArrow_unitIso, eta_inv_hom, eta_hom_hom
ext 📖	CompOp	9 math math: CategoryTheory.Functor.Final.coconesEquiv_unitIso, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, SheafOfModules.Presentation.map_relations_I, ext_hom_hom, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isColimit, CategoryTheory.Functor.Final.coconesEquiv_counitIso, ext_inv_hom, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso
ext_inv 📖	CompOp	10 math math: whiskeringEquivalence_counitIso, functorialityEquivalence_counitIso, functorialityEquivalence_unitIso, equivalenceOfReindexing_counitIso, precomposeEquivalence_counitIso, ext_inv_hom_hom, precomposeEquivalence_unitIso, whiskeringEquivalence_unitIso, equivalenceOfReindexing_unitIso, ext_inv_inv_hom
extend 📖	CompOp	17 math math: CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app, extendComp_inv_hom, CategoryTheory.Limits.colimit.desc_extend, CategoryTheory.Limits.IsColimit.homIso_hom, extendIso_inv_hom, extendIso_hom_hom, CategoryTheory.Limits.IsColimit.homEquiv_apply, extendId_inv_hom, CategoryTheory.Limits.IsColimit.OfNatIso.cocone_fac, extendHom_hom, CategoryTheory.Limits.IndObjectPresentation.extend_isColimit_desc_app, extendComp_hom_hom, extend_ι, CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac, extend_pt, extendId_hom_hom, instIsIsoExtendHom
extendComp 📖	CompOp	2 math math: extendComp_inv_hom, extendComp_hom_hom
extendHom 📖	CompOp	2 math math: extendHom_hom, instIsIsoExtendHom
extendId 📖	CompOp	2 math math: extendId_inv_hom, extendId_hom_hom
extendIso 📖	CompOp	2 math math: extendIso_inv_hom, extendIso_hom_hom
extensions 📖	CompOp	1 math math: extensions_app
forget 📖	CompOp	2 math math: forget_map, forget_obj
functoriality 📖	CompOp	19 math math: functorialityEquivalence_counitIso, functorialityEquivalence_unitIso, functoriality_obj_ι_app, CategoryTheory.Adjunction.functorialityUnit_app_hom, functoriality_map_hom, reflects_cocone_isomorphism, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, functorialityEquivalence_inverse, CategoryTheory.Adjunction.functorialityCounit_app_hom, CategoryTheory.Limits.Cocones.reflects_cone_isomorphism, CategoryTheory.Limits.Cocones.functoriality_faithful, CategoryTheory.Limits.Cocones.functoriality_full, functoriality_obj_pt, functorialityEquivalence_functor, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, functoriality_faithful, functoriality_full
functorialityCompFunctoriality 📖	CompOp	—
functorialityEquivalence 📖	CompOp	4 math math: functorialityEquivalence_counitIso, functorialityEquivalence_unitIso, functorialityEquivalence_inverse, functorialityEquivalence_functor
op 📖	CompOp	21 math math: CategoryTheory.Presheaf.isSheaf_iff_isLimit_coverage, CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve, CategoryTheory.Functor.mapCoconeOp_inv_hom, op_pt, CategoryTheory.regularTopology.equalizerConditionMap_iff_nonempty_isLimit, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, CategoryTheory.Limits.coconeOpEquiv_functor_obj, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Presheaf.isSheaf_iff_isLimit, CategoryTheory.Limits.PushoutCocone.op_π_app, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, TopCat.Presheaf.IsSheaf.isSheafPairwiseIntersections, TopCat.Presheaf.isGluing_iff_pairwise, CategoryTheory.Functor.mapCoconeOp_hom_hom, op_π, CategoryTheory.Limits.coconeOpEquiv_counitIso, CategoryTheory.Presheaf.isLimit_iff_isSheafFor, TopCat.Presheaf.IsSheaf.isSheafOpensLeCover, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.Limits.coconeOpEquiv_functor_map_hom, CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology
precompose 📖	CompOp	43 math math: whiskeringEquivalence_counitIso, equivalenceOfReindexing_inverse, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, equivalenceOfReindexing_functor, CategoryTheory.Limits.colimit.map_desc, CategoryTheory.IsUniversalColimit.precompose_isIso, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc, equivalenceOfReindexing_counitIso, CategoryTheory.Limits.DiagramOfCocones.coconePoints_map, precomposeComp_hom_app_hom, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, CategoryTheory.IsVanKampenColimit.precompose_isIso, precomposeId_hom_app_hom, CategoryTheory.Limits.DiagramOfCocones.comp, CategoryTheory.Limits.Cofork.π_precompose, precomposeEquivalence_counitIso, precompose_map_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, precomposeId_inv_app_hom, CategoryTheory.IsVanKampenColimit.precompose_isIso_iff, precompose_obj_ι, SheafOfModules.Presentation.map_relations_I, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, whiskeringEquivalence_inverse, precomposeEquivalence_functor, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isColimit, CategoryTheory.Limits.colimit.map_desc_assoc, precomposeEquivalence_unitIso, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, CategoryTheory.Limits.DiagramOfCocones.id, whiskeringEquivalence_unitIso, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, equivalenceOfReindexing_unitIso, precomposeEquivalence_inverse, precomposeComp_inv_app_hom, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, precompose_obj_pt
precomposeComp 📖	CompOp	2 math math: precomposeComp_hom_app_hom, precomposeComp_inv_app_hom
precomposeEquivalence 📖	CompOp	9 math math: CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, functorialityEquivalence_counitIso, functorialityEquivalence_unitIso, precomposeEquivalence_counitIso, functorialityEquivalence_inverse, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_hom_hom, precomposeEquivalence_functor, precomposeEquivalence_unitIso, precomposeEquivalence_inverse
precomposeId 📖	CompOp	2 math math: precomposeId_hom_app_hom, precomposeId_inv_app_hom
pt 📖	CompOp	928 math math: ModuleCat.HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.IsGrothendieckAbelian.subobjectMk_of_isColimit_eq_iSup, TopCat.binaryCofan_isColimit_iff, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id_assoc, category_id_hom, CategoryTheory.MorphismProperty.exists_isPushout_of_isFiltered, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj_assoc, CategoryTheory.Limits.IsColimit.isZero_pt, CategoryTheory.Monad.ForgetCreatesColimits.commuting, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_right, CategoryTheory.Limits.FormalCoproduct.isColimitCofan_desc_φ, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, CategoryTheory.Limits.Bicone.toCocone_ι_app_mk, CategoryTheory.Limits.isLimitConeRightOpOfCocone_lift, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv_assoc, CategoryTheory.Limits.Types.binaryCofan_isColimit_iff, CategoryTheory.Limits.PushoutCocone.flip_pt, CategoryTheory.Limits.Cotrident.ofCocone_ι, whisker_pt, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv, CategoryTheory.Monad.ForgetCreatesColimits.liftedCocone_pt, CategoryTheory.Limits.IsColimit.fac, CategoryTheory.Over.forgetCocone_pt, Profinite.Extend.cocone_pt, CategoryTheory.Limits.ReflexiveCofork.app_one_eq_π, CommRingCat.pushoutCocone_pt, CategoryTheory.Limits.isIso_app_coconePt_of_preservesColimit, CategoryTheory.Limits.HasColimitOfHasCoproductsOfHasCoequalizers.buildColimit_pt, PartOrdEmb.Limits.cocone_pt_coe, toOver_ι_app, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit, CategoryTheory.Functor.mapCocone_ι_app, whiskeringEquivalence_counitIso, CategoryTheory.PreOneHypercover.forkOfIsColimit_pt, CategoryTheory.Limits.colimit.cocone_ι, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.hf, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_functor_map_hom, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, CategoryTheory.Limits.coneUnopOfCoconeEquiv_counitIso, CategoryTheory.Limits.Fork.π_comp_hom, CategoryTheory.Limits.CoconeMorphism.w, CategoryTheory.WithInitial.coconeEquiv_functor_obj_pt, CategoryTheory.MorphismProperty.exists_hom_of_isFinitelyPresentable, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, CategoryTheory.Functor.Elements.shrinkYoneda_map_app_coconeπOpCompShrinkYonedaObj_ι_app_assoc, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inl, CategoryTheory.Limits.PushoutCocone.mk_ι_app_zero, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_inv_f, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc, CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCocone_pt, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.PreOneHypercover.p₁_sigmaOfIsColimit_assoc, CategoryTheory.Functor.isColimitCoconeOfIsLeftKanExtension_desc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Presheaf.coconeOfRepresentable_pt, whisker_ι, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id_assoc, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.rightHomologyData_Q, CategoryTheory.PreZeroHypercover.sigmaOfIsColimit_X, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_f, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit', CategoryTheory.Functor.mapCoconePrecompose_inv_hom, CategoryTheory.Limits.PushoutCocone.unop_π_app, RingHom.EssFiniteType.exists_eq_comp_ι_app_of_isColimit, CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app, CategoryTheory.Limits.Fork.unop_ι_app_zero, ofCotrident_ι, ModuleCat.directLimitCocone_pt_carrier, unop_π, CategoryTheory.Limits.Multicofork.π_comp_hom_assoc, SimplicialObject.Splitting.cofan_inj_epi_naturality_assoc, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CategoryTheory.Limits.CoproductDisjoint.isPullback_of_isInitial, CategoryTheory.Limits.asEmptyCocone_pt, CategoryTheory.Limits.BinaryCofan.mk_pt, CategoryTheory.Limits.MonoCoprod.mono_of_injective_aux, CategoryTheory.Limits.Cofork.ofCocone_ι, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd_assoc, CategoryTheory.Functor.IsEventuallyConstantFrom.cocone_pt, CategoryTheory.Limits.MonoCoprod.binaryCofan_inl, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_obj, CategoryTheory.Limits.IsColimit.existsUnique, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isPullback, CategoryTheory.ObjectProperty.prop_of_isColimit_cokernelCofork, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_right, CategoryTheory.Monad.beckCoequalizer_desc, toCostructuredArrow_comp_proj, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt_assoc, extendComp_inv_hom, CategoryTheory.Mono.of_coproductDisjoint, CategoryTheory.Functor.Elements.coconeπOpCompShrinkYonedaObj_pt, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLift, CategoryTheory.Limits.coconeOfCoconeCurry_pt, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct'_hom, skyscraperPresheafCocone_pt, SimplicialObject.Splitting.ι_desc_assoc, CategoryTheory.Limits.colimit.desc_extend, CategoryTheory.Limits.colimit.homIso_hom, AddCommGrpCat.isColimit_iff_bijective_desc, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_map, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_pt, CategoryTheory.FinitaryExtensive.mono_ι, CategoryTheory.FinitaryExtensive.isPullback_initial_to_binaryCofan, CategoryTheory.Functor.Final.coconesEquiv_unitIso, CategoryTheory.Limits.IsColimit.homIso_hom, toCostructuredArrow_comp_toOver_comp_forget, underPost_ι_app, CategoryTheory.IsSplitCoequalizer.asCofork_pt, CategoryTheory.Limits.Types.pUnitCocone_pt, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_inv_homologyι_assoc, CategoryTheory.Limits.Cotrident.π_eq_app_one, CategoryTheory.Limits.PushoutCocone.condition_assoc, CategoryTheory.Limits.coconeOfConeLeftOp_pt, extendIso_inv_hom, CategoryTheory.Limits.Cofan.isColimit_iff_isIso_sigmaDesc, toCostructuredArrow_map, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, CategoryTheory.Limits.IsColimit.mono_ι_app_of_isFiltered, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux_assoc, CategoryTheory.Limits.PushoutCocone.op_snd, CategoryTheory.Limits.isColimitOfConeRightOpOfCocone_desc, HasCardinalLT.Set.cocone_pt, CategoryTheory.Limits.instIsIsoHomHomCocone, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.CokernelCofork.IsColimit.comp_π_eq_zero_iff_up_to_refinements, CategoryTheory.Limits.IsColimit.ι_map, CategoryTheory.BinaryCofan.isVanKampen_iff, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, Preorder.coconePt_mem_upperBounds, CategoryTheory.Functor.costructuredArrowMapCocone_pt, CategoryTheory.Presieve.isSheafFor_iff_preservesProduct, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', CategoryTheory.Limits.colimit.map_desc, CategoryTheory.Limits.PullbackCone.op_pt, w_assoc, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom, CategoryTheory.Limits.cokernel.zeroCokernelCofork_π, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage_ι, CategoryTheory.Limits.PushoutCocone.epi_inl_of_is_pushout_of_epi, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand_assoc, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, CategoryTheory.Limits.coneUnopOfCocone_pt, CategoryTheory.Limits.Cofork.unop_π_app_one, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, CategoryTheory.Comonad.ForgetCreatesColimits'.newCocone_ι_app, CategoryTheory.Limits.Cofork.IsColimit.epi, CategoryTheory.Presieve.firstMap_eq_secondMap, toCostructuredArrowCompProj_hom_app, CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff_aux, CategoryTheory.isPullback_of_cofan_isVanKampen, CategoryTheory.Limits.Types.binaryCoproductColimit_desc, CategoryTheory.Limits.opCoproductIsoProduct'_comp_self, CategoryTheory.Functor.Final.extendCocone_obj_ι_app, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, CategoryTheory.Limits.Cowedge.IsColimit.π_desc_assoc, CategoryTheory.Limits.CoconeMorphism.hom_inv_id_assoc, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit_pt, CategoryTheory.Limits.Cotrident.IsColimit.homIso_natural, CategoryTheory.Limits.IsColimit.nonempty_isColimit_iff_isIso_desc, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_right, HomotopicalAlgebra.AttachCells.ofArrowIso_g₂, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, CategoryTheory.Limits.coneOfCoconeRightOp_π, HomologicalComplex.coconeOfHasColimitEval_pt_d, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst_assoc, SSet.horn₃₁.desc.multicofork_pt, CategoryTheory.Limits.PushoutCocone.condition, CategoryTheory.Limits.Cofork.condition_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_pt, CategoryTheory.Limits.Bicone.toCocone_pt, CategoryTheory.Limits.coconeOfConeUnop_pt, CategoryTheory.Limits.FormalCoproduct.cofan_inj, functorialityEquivalence_counitIso, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingProperty_ι_app_bot, AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self_assoc, CategoryTheory.is_coprod_iff_isPushout, CategoryTheory.Limits.Types.FilteredColimit.jointly_surjective_of_isColimit₂, ModuleCat.HasColimit.colimitCocone_pt_isModule, CategoryTheory.Functor.mapCoconeOp_inv_hom, CategoryTheory.MorphismProperty.colimitsOfShape.of_isColimit, op_pt, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_isColimit_desc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, CategoryTheory.Limits.IsColimit.ι_map_assoc, CategoryTheory.Limits.CokernelCofork.IsColimit.isIso_π, CategoryTheory.Limits.Cofan.IsColimit.inj_desc, CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists, CompHausLike.sigmaComparison_eq_comp_isos, CategoryTheory.Functor.coconeTypesEquiv_apply_pt, CategoryTheory.Limits.Multicofork.toSigmaCofork_pt, tensor_ι_app, CategoryTheory.ObjectProperty.isStrongGenerator_iff_exists_extremalEpi, CategoryTheory.Limits.Cotrident.ofπ_pt, extendIso_hom_hom, functorialityEquivalence_unitIso, CategoryTheory.Limits.Multicofork.condition_assoc, CategoryTheory.ShortComplex.RightHomologyData.wι_assoc, CategoryTheory.preservesColimitIso_inv_comp_desc, category_comp_hom, CategoryTheory.Limits.IsColimit.homEquiv_apply, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc_assoc, CategoryTheory.Limits.IsColimit.desc_self, HomotopicalAlgebra.AttachCells.cell_def, CategoryTheory.IsUniversalColimit.isPullback_prod_of_isColimit, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.Limits.Cofan.ext_inv_hom, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc, CategoryTheory.FinitaryExtensive.mono_inl_of_isColimit, equivalenceOfReindexing_counitIso, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.Cowedge.IsColimit.π_desc, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit_under, CategoryTheory.Limits.IsColimit.isIso_colimMap_ι, CategoryTheory.Limits.FormalCoproduct.isColimitCofan_desc_f, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eq, functoriality_obj_ι_app, CategoryTheory.ObjectProperty.prop_of_isColimit_binaryCofan, CategoryTheory.Limits.CokernelCofork.condition, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc_assoc, CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork_Q, CategoryTheory.PreZeroHypercover.inj_sigmaOfIsColimit_f_assoc, PartOrdEmb.Limits.CoconePt.fac_apply, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inr, toCostructuredArrowCompToOverCompForget_inv_app, CategoryTheory.Monad.beckAlgebraCofork_pt, CategoryTheory.Limits.Cowedge.condition_assoc, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_left, CategoryTheory.Limits.cokernel.zeroCokernelCofork_pt, CategoryTheory.Limits.CompleteLattice.colimitCocone_cocone_pt, CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork_H, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, HomotopicalAlgebra.AttachCells.hm_assoc, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_hom_f, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.Limits.Cotrident.condition_assoc, CategoryTheory.Limits.coconeUnopOfConeEquiv_counitIso, CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer', CategoryTheory.Limits.CoconeMorphism.w_assoc, CategoryTheory.Limits.coneOfCoconeLeftOp_π_app, CategoryTheory.Limits.coneOfCoconeUnop_π, CategoryTheory.Limits.isColimitOfConeOfCoconeLeftOp_desc, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_pt, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.Limits.FormalCoproduct.cofan_inj_φ, HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff', CategoryTheory.Under.liftCocone_ι_app, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.Limits.Cofork.IsColimit.homIso_apply_coe, CategoryTheory.Limits.isLimitConeOfCoconeUnop_lift, CommAlgCat.binaryCofan_pt, SSet.horn₃₁.desc.multicofork_π_two_assoc, CategoryTheory.Limits.isColimitOfConeUnopOfCocone_desc, CategoryTheory.Limits.PushoutCocone.ofCocone_ι, CategoryTheory.Adjunction.functorialityUnit_app_hom, CategoryTheory.Limits.Multicofork.ext_hom_hom, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.isIso_f, CategoryTheory.Pairwise.cocone_pt, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.Limits.FormalCoproduct.cofan_inj_f_fst, CategoryTheory.Limits.Concrete.isColimit_exists_rep, CategoryTheory.Limits.opCoproductIsoProduct'_inv_comp_inj, SSet.horn₃₁.desc.multicofork_π_zero_assoc, ModuleCat.directLimitIsColimit_desc, SSet.finite_of_isColimit, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_inv, CategoryTheory.FunctorToTypes.binaryCoproductCocone_pt_map, CategoryTheory.Limits.Cofan.inj_injective_of_isColimit, Preorder.coconeOfUpperBound_pt, CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt, ModuleCat.directLimitCocone_pt_isAddCommGroup, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom, CategoryTheory.Functor.mapCoconeMapCocone_hom_hom, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Limits.PushoutCocone.eta_inv_hom, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, precomposeComp_hom_app_hom, CategoryTheory.Limits.Fork.op_pt, CategoryTheory.Limits.Multicofork.π_eq_app_right, functoriality_map_hom, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_inv_homologyι, HomologicalComplex.coconeOfHasColimitEval_pt_X, CommRingCat.FilteredColimits.nontrivial, SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero, SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero, extendId_inv_hom, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom_assoc, CategoryTheory.Limits.WidePushoutShape.mkCocone_pt, CategoryTheory.Limits.FormalCoproduct.cofan_inj_f_snd, CategoryTheory.FinitaryExtensive.mono_inr_of_isColimit, CategoryTheory.GrothendieckTopology.Point.presheafFiberMapCocone_pt, CategoryTheory.Limits.Cofork.op_π_app_zero, CategoryTheory.GrothendieckTopology.Point.presheafFiberOfIsCofilteredCocone_pt, AddCommGrpCat.Colimits.colimitCocone_pt, CategoryTheory.Limits.Cofork.IsColimit.π_desc_assoc, CategoryTheory.Limits.BinaryCofan.ext_hom_hom, CategoryTheory.PreOneHypercover.p₁_sigmaOfIsColimit, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, PartOrdEmb.Limits.cocone_ι_app, CategoryTheory.Limits.pushoutCoconeOfRightIso_x, CategoryTheory.Limits.PushoutCocone.condition_zero, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, CategoryTheory.Limits.pointwiseCocone_pt, Condensed.isColimitLocallyConstantPresheaf_desc_apply, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, CategoryTheory.Comma.colimitAuxiliaryCocone_pt, toStructuredArrow_obj, CategoryTheory.IsPushout.of_isColimit_binaryCofan_of_isInitial, AddCommGrpCat.Colimits.Quot.desc_toCocone_desc, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_obj, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inl, CategoryTheory.Limits.coconeUnopOfConeEquiv_inverse_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_pt, CategoryTheory.Comma.coconeOfPreserves_pt_right, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, CategoryTheory.Presheaf.final_toCostructuredArrow_comp_pre, CategoryTheory.Limits.PushoutCocone.ι_app_left, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_φ, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Abelian.AbelianStruct.imageι_π_assoc, CategoryTheory.FinitaryPreExtensive.hasPullbacks_of_is_coproduct, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_hom, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_hom, CategoryTheory.Limits.Multicofork.map_pt, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_left, AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f, CategoryTheory.Limits.opProductIsoCoproduct'_comp_self, CategoryTheory.Limits.IsColimit.OfNatIso.cocone_fac, precomposeId_hom_app_hom, CategoryTheory.Limits.PushoutCocone.ofCocone_pt, CategoryTheory.Limits.DiagramOfCocones.comp, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_left_as, CategoryTheory.Limits.Cofork.π_precompose, CategoryTheory.Limits.ReflexiveCofork.condition, CategoryTheory.SmallObject.coconeOfLE_pt, precomposeEquivalence_counitIso, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv_assoc, CategoryTheory.Limits.isLimitConeUnopOfCocone_lift, CategoryTheory.Limits.Cofan.ext_hom_hom, CategoryTheory.Limits.IndObjectPresentation.yoneda_isColimit_desc, CategoryTheory.Presheaf.tautologicalCocone'_pt, CategoryTheory.isPullback_initial_to_of_cofan_isVanKampen, CategoryTheory.Limits.Bicone.ofColimitCocone_ι, CategoryTheory.isSheaf_pointwiseColimit, CategoryTheory.Limits.MonoCoprod.mono_of_injective, CategoryTheory.Limits.PushoutCocone.isIso_inl_of_epi_of_isColimit, CategoryTheory.Limits.coneOfCoconeLeftOp_pt, CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inr, CategoryTheory.Limits.Cowedge.ext_hom_hom, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, precompose_map_hom, CategoryTheory.Mono.cofanInr_of_binaryCoproductDisjoint, CategoryTheory.Limits.PushoutCocone.ι_app_right, CategoryTheory.Functor.coconeOfIsLeftKanExtension_ι, CategoryTheory.Limits.coneRightOpOfCocone_π, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty, SSet.hasDimensionLT_of_isColimit, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_hom_app_f_f, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id, TopCat.isClosed_iff_of_isColimit, CategoryTheory.Comma.coconeOfPreserves_ι_app_right, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_Q, CategoryTheory.Limits.isIso_colimit_cocone_parallelPair_of_eq, CategoryTheory.Limits.Cowedge.mk_pt, CategoryTheory.Mono.cofanInl_of_binaryCoproductDisjoint, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, toOver_pt, fromStructuredArrow_obj_pt, HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff, CategoryTheory.Limits.Cofan.mk_pt, CategoryTheory.Comma.coconeOfPreserves_pt_hom, ofCofork_ι, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, CategoryTheory.Presieve.isSheafFor_of_preservesProduct, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_map_hom, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_snd, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_map_left, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, AddCommGrpCat.Colimits.Quot.desc_toCocone_desc_app, CategoryTheory.Limits.coneOpEquiv_counitIso, CategoryTheory.Limits.coneUnopOfCoconeEquiv_functor_map_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, CategoryTheory.Limits.colim.mapShortComplex_X₃, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_hom_hom, SimplicialObject.Split.cofan_inj_naturality_symm_assoc, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc_assoc, CommRingCat.coproductCocone_pt, CategoryTheory.Limits.PushoutCocone.IsColimit.inl_desc_assoc, CategoryTheory.Adjunction.functorialityCounit_app_hom, CategoryTheory.Limits.IsColimit.pullback_zero_ext, CategoryTheory.Limits.Multicofork.ofπ_pt, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_inv, CategoryTheory.isSeparator_iff_of_isColimit_cofan, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_of, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv_assoc, CategoryTheory.Limits.BinaryCofan.ι_app_right, PrincipalSeg.cocone_pt, CategoryTheory.Limits.Fork.π_comp_hom_assoc, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone.surjective, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_ι, CategoryTheory.MorphismProperty.PreIndSpreads.exists_isPushout, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_pt, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit_assoc, CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_pt, CategoryTheory.Limits.Multicofork.map_ι_app, TopCat.coinduced_of_isColimit, toCostructuredArrowCocone_ι_app, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.Limits.Cofork.coequalizer_ext, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, isColimit_iff_isIso_colimMap_ι, CategoryTheory.ShortComplex.RightHomologyData.wι, CategoryTheory.Functor.Final.extendCocone_obj_ι_app', CategoryTheory.PreZeroHypercover.presieve₀_sigmaOfIsColimit, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, CategoryTheory.Monad.beckCofork_pt, CategoryTheory.Limits.PushoutCocone.coequalizer_ext, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc, CategoryTheory.preservesColimitIso_inv_comp_desc_assoc, CategoryTheory.BinaryCofan.mono_inr_of_isVanKampen, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inl, precomposeId_inv_app_hom, CategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork_H, CategoryTheory.Limits.coconeRightOpOfConeEquiv_inverse_map, CategoryTheory.Limits.Cofork.condition, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right, CategoryTheory.IsGrothendieckAbelian.mono_of_isColimit_monoOver, HomotopicalAlgebra.AttachCells.reindex_cofan₂, CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone_to_top, CategoryTheory.Monad.ForgetCreatesColimits.coconePoint_A, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero, AddCommGrpCat.Colimits.Quot.ι_desc, CategoryTheory.Limits.IsColimit.pullback_hom_ext, CategoryTheory.Limits.coconeOfIsSplitEpi_pt, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit, CategoryTheory.Limits.coconeOfConeRightOp_pt, CategoryTheory.Comma.coconeOfPreserves_ι_app_left, CategoryTheory.Monad.ForgetCreatesColimits.newCocone_pt, CategoryTheory.Limits.coconeFiberwiseColimitOfCocone_ι_app, AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self, Algebra.codRestrictEqLocusPushoutCocone.surjective_of_isEffective, CategoryTheory.Limits.Cotrident.IsColimit.homIso_symm_apply, precompose_obj_ι, CategoryTheory.extendCofan_pt, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom_assoc, CategoryTheory.Limits.isLimitConeOfCoconeRightOp_lift, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, CategoryTheory.Limits.CokernelCofork.isColimitMapBifunctor.exists_desc, CategoryTheory.Limits.colimit.pre_desc_assoc, CategoryTheory.Limits.MonoCoprod.mono_binaryCofanSum_inl', SheafOfModules.Presentation.map_relations_I, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, CategoryTheory.Coyoneda.colimitCoconeIsColimit_desc, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc_assoc, CategoryTheory.Limits.colimit.pre_desc, CategoryTheory.FunctorToTypes.binaryCoproductColimit_desc, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_left, CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone, PresheafOfModules.colimitCocone_pt, SimplicialObject.Splitting.cofan_inj_comp_app, CategoryTheory.Sieve.yonedaFamily_fromCocone_compatible, CategoryTheory.Limits.coneOfCoconeRightOp_pt, CategoryTheory.Functor.leftAdjointObjIsDefined_of_isColimit, CategoryTheory.Limits.colimit.ι_desc_apply, CategoryTheory.Limits.IndObjectPresentation.ofCocone_I, CategoryTheory.Limits.Cofan.IsColimit.inj_desc_assoc, CategoryTheory.extendCofan_ι_app, CategoryTheory.Limits.reflexiveCoforkEquivCofork_inverse_obj_pt, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, CategoryTheory.Limits.coneLeftOpOfCocone_π_app, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_apply_eq, CategoryTheory.Coyoneda.colimitCocone_pt, TopCat.continuous_iff_of_isColimit, CategoryTheory.Limits.Multicofork.toSigmaCofork_π, CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq_pt, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt, CategoryTheory.Limits.Types.Colimit.ι_desc_apply, w, CategoryTheory.Limits.Multicofork.IsColimit.fac_assoc, eta_inv_hom, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right_assoc, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, CategoryTheory.Limits.Cofork.ext_inv, CategoryTheory.Limits.Types.pushoutCocone_inr_mono_of_isColimit, CategoryTheory.Limits.colimit.ι_desc, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_pt, CategoryTheory.Limits.MonoCoprod.mono_inl_iff, CategoryTheory.Limits.Cofork.IsColimit.homIso_natural, CategoryTheory.Limits.Types.jointly_surjective_of_isColimit, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, HomotopicalAlgebra.AttachCells.reindex_cofan₁, CategoryTheory.Limits.Multicofork.fst_app_right, AddCommGrpCat.Colimits.toCocone_pt_coe, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv, CategoryTheory.Limits.Fork.op_ι_app, Preorder.isLUB_of_isColimit, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc, CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_right, CategoryTheory.Limits.Bicone.toCocone_ι_app, fromCostructuredArrow_pt, CategoryTheory.Limits.coconeUnopOfCone_pt, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.Limits.IndObjectPresentation.ofCocone_isColimit, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit_assoc, CategoryTheory.Functor.coconeOfIsLeftKanExtension_pt, SSet.horn₃₂.desc.multicofork_π_zero_assoc, CategoryTheory.Limits.isColimitOfConeLeftOpOfCocone_desc, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inr, CategoryTheory.Limits.PushoutCocone.mk_pt, CategoryTheory.Limits.coneRightOpOfCocone_pt, CategoryTheory.PreOneHypercover.sigmaOfIsColimit_Y, CategoryTheory.Limits.colim.map_epi', CategoryTheory.Limits.PushoutCocone.IsColimit.inr_desc_assoc, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, w_apply, CategoryTheory.Functor.mapCocone₂_pt, CategoryTheory.Limits.splitEpiOfIdempotentOfIsColimitCofork_section_, CategoryTheory.Limits.MonoCoprod.mono_inj, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_none, CategoryTheory.Limits.PushoutCocone.IsColimit.inr_desc, SimplicialObject.Splitting.decomposition_id, CategoryTheory.Limits.coneLeftOpOfCocone_pt, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom, ext_hom_hom, CategoryTheory.Limits.CoconeMorphism.hom_inv_id, CategoryTheory.Limits.FintypeCat.finite_of_isColimit, CategoryTheory.Limits.Fork.op_ι_app_one, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_f, CategoryTheory.PreZeroHypercover.inj_sigmaOfIsColimit_f, CategoryTheory.Presheaf.imageSieve_cofanIsColimitDesc_shrinkYoneda_map, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, CategoryTheory.Presheaf.coconeOfRepresentable_naturality, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv, toCostructuredArrowCompToOverCompForget_hom_app, CategoryTheory.Functor.mapCocone₂_ι_app, CategoryTheory.Limits.Cofork.unop_π_app_zero, CategoryTheory.Limits.ReflexiveCofork.mk_pt, CategoryTheory.Limits.IsColimit.hom_desc, CategoryTheory.Functor.Final.colimit_cocone_comp_aux, CategoryTheory.Monad.MonadicityInternal.unitCofork_pt, CategoryTheory.FunctorToTypes.jointly_surjective, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_ι, CategoryTheory.Limits.Cofork.IsColimit.existsUnique, CategoryTheory.Limits.combineCocones_pt_obj, Algebra.codRestrictEqLocusPushoutCocone.injective_of_faithfulSMul, CommRingCat.coproductCoconeIsColimit_desc, CategoryTheory.Limits.Cotrident.app_one, CategoryTheory.Functor.Elements.shrinkYoneda_map_app_coconeπOpCompShrinkYonedaObj_ι_app, CategoryTheory.Limits.PushoutCocone.epi_inr_of_is_pushout_of_epi, ext_inv_hom_hom, CategoryTheory.Abelian.AbelianStruct.imageι_π, CategoryTheory.Limits.coconeFiberwiseColimitOfCocone_pt, functoriality_obj_pt, CategoryTheory.Limits.CokernelCofork.condition_assoc, CategoryTheory.Limits.Multicofork.ext_inv_hom, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand, CategoryTheory.Limits.isLimitConeLeftOpOfCocone_lift, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_obj, SSet.iSup_range_eq_top_of_isColimit, AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirected_pt, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv_assoc, CategoryTheory.Limits.CoproductDisjoint.nonempty_isInitial_of_ne, ModuleCat.FilteredColimits.ι_colimitDesc, CategoryTheory.Limits.colimit.existsUnique, CategoryTheory.Limits.MonoCoprod.mono_binaryCofanSum_inr', ofPushoutCocone_ι, forget_obj, SSet.horn₃₁.desc.multicofork_π_three_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, CategoryTheory.Limits.isLimitConeOfCoconeLeftOp_lift, CategoryTheory.ObjectProperty.prop_of_isColimit_cofan, CategoryTheory.Limits.Cotrident.coequalizer_ext, CategoryTheory.Limits.IndObjectPresentation.extend_isColimit_desc_app, CategoryTheory.Limits.IndObjectPresentation.ofCocone_ι, CategoryTheory.ObjectProperty.prop_of_isColimit, CategoryTheory.Limits.colimit.ι_coconeMorphism, CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, CategoryTheory.Presieve.isSheafFor_sigmaDesc_iff, CategoryTheory.Limits.Cowedge.ext_inv_hom, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, CategoryTheory.Limits.CokernelCofork.map_condition, CategoryTheory.Limits.CoproductDisjoint.mono_inj, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, CategoryTheory.Limits.PushoutCocone.IsColimit.inl_desc, LightProfinite.Extend.cocone_pt, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isColimit, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_functor_map_hom, CategoryTheory.Limits.colimit.ι_desc_assoc, CategoryTheory.IsPushout.of_is_coproduct, CategoryTheory.Abelian.mono_inl_of_isColimit, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj_assoc, CategoryTheory.Limits.Cofork.ext_hom, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.gluedCocone_pt, CategoryTheory.Limits.colimit.ι_desc_app_assoc, toCostructuredArrow_obj, CategoryTheory.Under.liftCocone_pt, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, CategoryTheory.Limits.coconePointwiseProduct_pt, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_hom_comp_ι_assoc, CategoryTheory.Preadditive.epi_iff_isZero_cokernel', CategoryTheory.Limits.Types.jointly_surjective, CategoryTheory.Limits.CokernelCofork.map_π, CategoryTheory.Over.liftCocone_ι_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.Limits.PullbackCone.unop_pt, CategoryTheory.Limits.coconeRightOpOfConeEquiv_counitIso, SimplicialObject.Splitting.ι_desc, mapCoconeToOver_inv_hom, CategoryTheory.Limits.wideCoequalizer.cotrident_ι_app_one, CategoryTheory.Limits.IndObjectPresentation.ofCocone_F, CategoryTheory.Limits.Cofan.cofanTypes_pt, CategoryTheory.Limits.IsColimit.ι_smul, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_cofanIsColimitDesc_shrinkYoneda_map, CategoryTheory.Functor.LeftExtension.coconeAt_pt, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty_assoc, CategoryTheory.Limits.colim.mapShortComplex_X₁, CategoryTheory.Limits.IndObjectPresentation.ofCocone_ℐ, CategoryTheory.Limits.pushoutCoconeOfLeftIso_x, CategoryTheory.Limits.BinaryCofan.ι_app_left, CategoryTheory.Limits.colimit.map_desc_assoc, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_left, ModuleCat.HasColimit.colimitCocone_pt_carrier, CategoryTheory.Limits.PushoutCocone.op_pt, CategoryTheory.Limits.PushoutCocone.mk_ι_app_right, CategoryTheory.Limits.Multicofork.snd_app_right, precomposeEquivalence_unitIso, CategoryTheory.Limits.Cotrident.condition, HomotopicalAlgebra.AttachCells.cell_def_assoc, CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCoconeIsColimit_desc_f, CategoryTheory.Functor.Final.coconesEquiv_counitIso, CategoryTheory.SmallObject.SuccStruct.iterationCocone_pt, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom_assoc, CategoryTheory.isCardinalPresentable_of_isColimit', CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation, CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer', CategoryTheory.Limits.BinaryCofan.IsColimit.desc'_coe, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.Limits.DiagramOfCocones.coconePoints_obj, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.Limits.coneOpEquiv_inverse_map, CategoryTheory.Limits.Types.binaryCoproductCocone_pt, CategoryTheory.Limits.Multicofork.sigma_condition, CategoryTheory.Comonad.ForgetCreatesColimits'.coconePoint_A, CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork_ι, CategoryTheory.Limits.colimit.cocone_x, TopCat.nonempty_isColimit_iff_eq_coinduced, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_inverse, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingPropertyFixedBot_ι_app_bot, CategoryTheory.Limits.isColimitOfConeOfCoconeRightOp_desc, CategoryTheory.Monad.ForgetCreatesColimits.liftedCocone_ι_app_f, CategoryTheory.Limits.CoconeMorphism.inv_hom_id, CategoryTheory.Limits.Cone.unop_pt, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, CategoryTheory.Functor.mapCoconeOp_hom_hom, CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer', CategoryTheory.Presieve.piComparison_fac, ext_inv_hom, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_pt, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, AddCommGrpCat.Colimits.Quot.desc_quotQuotUliftAddEquiv, TopCat.coconeOfCoconeForget_pt, AlgebraicGeometry.ofArrows_ι_mem_zariskiTopology_of_isColimit, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, CategoryTheory.Limits.DiagramOfCocones.id, CompleteLattice.MulticoequalizerDiagram.multicofork_pt, CategoryTheory.Limits.Multicofork.condition, CategoryTheory.Limits.IsColimit.ofIsoColimit_desc, CategoryTheory.Limits.CoconeMorphism.map_w_assoc, CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimit, CategoryTheory.MorphismProperty.colimitsOfShape.mk', CategoryTheory.Limits.IsColimit.isIso_ι_app_of_isTerminal, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_obj, whiskeringEquivalence_unitIso, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, op_π, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_counitIso, CategoryTheory.Limits.colimitCoconeOfUnique_cocone_pt, HomotopicalAlgebra.AttachCells.isPushout, CategoryTheory.Limits.epi_of_isColimit_parallelFamily, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom, CategoryTheory.Limits.coconeOfCoconeUncurry_pt, LightCondensed.isColimitLocallyConstantPresheaf_desc_apply, CategoryTheory.Limits.FintypeCat.jointly_surjective, CategoryTheory.Limits.Fork.op_ι_app_zero, CategoryTheory.Limits.coconeOfCoconeUncurry_ι_app, CategoryTheory.Limits.MonoCoprod.mono_binaryCofanSum_inr, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_none, CategoryTheory.Limits.colimit.post_desc, CategoryTheory.Limits.PushoutCocone.mk_ι_app_left, CategoryTheory.mono_of_cofan_isVanKampen, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, SSet.horn₃₂.desc.multicofork_pt, CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit_ι_app, CategoryTheory.Limits.Cofork.op_π_app_one, equivalenceOfReindexing_unitIso, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, CategoryTheory.Limits.Bicone.ofColimitCocone_pt, CategoryTheory.Limits.Cofork.IsColimit.π_desc, CategoryTheory.Limits.opProductIsoCoproduct'_inv_comp_lift, TopCat.isOpen_iff_of_isColimit_cofork, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_inv_φ, extendComp_hom_hom, toCostructuredArrowCompProj_inv_app, TopCat.isQuotientMap_of_isColimit_cofork, CategoryTheory.epi_iff_isIso_inl, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val_assoc, extend_ι, toStructuredArrow_map, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_pt, CategoryTheory.Limits.coconeOpEquiv_counitIso, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv, TopCat.isOpen_iff_of_isColimit, CategoryTheory.Limits.IndObjectPresentation.cocone_pt, CategoryTheory.Functor.Final.extendCocone_obj_pt, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom_assoc, CategoryTheory.Limits.proj_comp_opProductIsoCoproduct'_hom, CategoryTheory.Limits.colim.map_mono', CategoryTheory.Limits.Multicofork.sigma_condition_assoc, CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right, CategoryTheory.Limits.Multicofork.IsColimit.isPushout, CategoryTheory.Limits.PushoutCocone.unop_pt, CategoryTheory.Limits.PushoutCocone.eta_hom_hom, CategoryTheory.Comma.coconeOfPreserves_pt_left, ext_inv_inv_hom, CategoryTheory.isCardinalPresentable_of_isColimit, CategoryTheory.Limits.Cofan.nonempty_isColimit_iff_isIso_sigmaDesc, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id_assoc, CategoryTheory.Limits.Cofork.ofπ_pt, CategoryTheory.Limits.coconeOfDiagramInitial_pt, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_counitIso, CategoryTheory.Limits.BinaryBicone.toCocone_pt, TopCat.sigmaCofan_pt, CategoryTheory.Limits.Cone.op_pt, CategoryTheory.ShortComplex.exact_iff_of_forks, CategoryTheory.Limits.coequalizer.cofork_ι_app_one, CategoryTheory.Limits.Cofan.IsColimit.fac_assoc, CategoryTheory.Limits.coconeRightOpOfCone_pt, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, CategoryTheory.Limits.combineCocones_pt_map, toCostructuredArrowCocone_pt, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_pt, CategoryTheory.Monad.MonadicityInternal.counitCofork_pt, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.Limits.CokernelCofork.map_condition_assoc, CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_left, CategoryTheory.Abelian.mono_inl_of_factor_thru_epi_mono_factorization, CategoryTheory.Abelian.mono_inr_of_isColimit, skyscraperPresheafCoconeOfSpecializes_pt, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, CategoryTheory.Limits.Cofan.IsColimit.fac, CategoryTheory.Limits.Cofork.IsColimit.homIso_symm_apply, CategoryTheory.Limits.isColimitOfConeOfCoconeUnop_desc, CategoryTheory.MorphismProperty.IsStableUnderColimitsOfShape.condition, CategoryTheory.Limits.Cofork.IsColimit.π_desc', unop_pt, CategoryTheory.Limits.CokernelCofork.π_eq_zero, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac_assoc, CategoryTheory.Limits.instIsIsoHomInvCocone, CategoryTheory.Functor.Final.extendCocone_map_hom, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc, CategoryTheory.Limits.isIso_colimit_cocone_parallelPair_of_self, CategoryTheory.IsPushout.of_isColimit, CategoryTheory.Functor.mapCocone_pt, CategoryTheory.Limits.MonoCoprod.mono_binaryCofanSum_inl, ModuleCat.directLimitCocone_pt_isModule, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj_assoc, CategoryTheory.Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, mapCoconeToOver_hom_hom, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_map, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.Cofork.unop_ι, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj_assoc, CategoryTheory.preserves_desc_mapCocone, CategoryTheory.Limits.Multicofork.π_comp_hom, ofPushoutCocone_pt, CategoryTheory.Limits.CoconeMorphism.inv_hom_id_assoc, ModuleCat.FilteredColimits.ι_colimitDesc_assoc, CategoryTheory.Limits.CokernelCofork.IsColimit.isZero_of_epi, CategoryTheory.Limits.CompleteLattice.colimitCocone_isColimit_desc, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_isColimit_desc, SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁_hom_f_f, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand', eta_hom_hom, CategoryTheory.Limits.coneUnopOfCocone_π, CategoryTheory.Limits.Cotrident.app_one_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, extend_pt, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_cofanIsColimitDesc_uliftYoneda_map, CategoryTheory.Limits.coconeOfDiagramTerminal_pt, CategoryTheory.Limits.coconeOfCoconeCurry_ι_app, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.isSeparator_of_isColimit_cofan, precomposeComp_inv_app_hom, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac, CategoryTheory.FinitaryExtensive.isPullback_initial_to, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, SSet.horn₃₂.desc.multicofork_π_three_assoc, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd, CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCocone_ι_app_f, SSet.horn₃₂.desc.multicofork_π_one_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst, CategoryTheory.Limits.colimitCoconeOfUnique_isColimit_desc, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom, CategoryTheory.Limits.Cofork.IsColimit.π_desc'_assoc, CategoryTheory.Limits.PushoutCocone.isIso_inr_of_epi_of_isColimit, CategoryTheory.Limits.IsColimit.fac_assoc, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, CategoryTheory.PreOneHypercover.p₂_sigmaOfIsColimit, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_right, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_hom_φ, SimplicialObject.Split.cofan_inj_naturality_symm, CategoryTheory.Presheaf.tautologicalCocone_pt, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_obj, CategoryTheory.Limits.colimit.toOver_pt, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff', SimplicialObject.Splitting.cofan_inj_comp_app_assoc, CategoryTheory.Limits.colim.mapShortComplex_X₂, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_φ, HomotopicalAlgebra.AttachCells.ofArrowIso_g₁, CategoryTheory.FunctorToTypes.binaryCoproductCocone_pt_obj, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_hom_comp_ι, tensor_pt, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, TopCat.coconeOfCoconeForget_ι_app, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val, extendId_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.relativeGluingData_natTrans_app, CategoryTheory.Limits.PushoutCocone.unop_snd, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_obj, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit, CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_inverse_map, CategoryTheory.Limits.Cofork.app_one_eq_π, CategoryTheory.PreOneHypercover.p₂_sigmaOfIsColimit_assoc, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, CategoryTheory.Limits.HasColimitOfHasCoproductsOfHasCoequalizers.buildColimit_ι_app, CategoryTheory.Limits.Sigma.cocone_pt, CategoryTheory.epi_iff_isIso_inr, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.Limits.coconeOpEquiv_functor_map_hom, SimplicialObject.Splitting.cofan_inj_eq_assoc, CategoryTheory.Monad.ForgetCreatesColimits.liftedCoconeIsColimit_desc_f, underPost_pt, CategoryTheory.Limits.Cofork.op_ι, extensions_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_functor, CategoryTheory.Limits.Cotrident.IsColimit.homIso_apply_coe, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage_ι_assoc, CategoryTheory.Limits.coneOfCoconeUnop_pt, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'_assoc, CategoryTheory.Limits.colimit.pre_eq, CategoryTheory.IsPushout.isVanKampen_inl, CategoryTheory.Limits.CoconeMorphism.map_w, CategoryTheory.Limits.Multicofork.IsColimit.fac, CategoryTheory.Over.liftCocone_pt, CategoryTheory.Limits.constCocone_pt, AlgebraicGeometry.PresheafedSpace.colimitCocone_pt, CategoryTheory.BinaryCofan.isPullback_initial_to_of_isVanKampen, CategoryTheory.Limits.colimit.ι_desc_app, CategoryTheory.Limits.PushoutCocone.unop_fst, precompose_obj_pt, CategoryTheory.IsPushout.of_isColimit_cocone, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.epi_f, SimplicialObject.Splitting.cofan_inj_epi_naturality, CategoryTheory.Limits.PushoutCocone.op_fst, CategoryTheory.Limits.isCokernelEpiComp_desc, CategoryTheory.Limits.isIso_limit_cocone_parallelPair_of_epi, CategoryTheory.Limits.Types.pushoutCocone_inr_injective_of_isColimit, CategoryTheory.Limits.Cowedge.condition, SSet.range_eq_iSup_of_isColimit, Algebra.codRestrictEqLocusPushoutCocone.bijective_of_faithfullyFlat, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_counitIso, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, CategoryTheory.Preadditive.coforkOfCokernelCofork_pt, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_fst, CategoryTheory.Limits.coconeLeftOpOfCone_pt, HomotopicalAlgebra.AttachCells.hm, CategoryTheory.Limits.MonoCoprod.binaryCofan_inr, CategoryTheory.Limits.Types.Pushout.cocone_pt, CategoryTheory.Limits.epi_of_isColimit_cofork, CategoryTheory.GrothendieckTopology.Point.presheafFiberCocone_pt, CategoryTheory.Monad.ForgetCreatesColimits.newCocone_ι
unop 📖	CompOp	5 math math: unop_π, CategoryTheory.Limits.coneOpEquiv_inverse_obj, CategoryTheory.Limits.coneOpEquiv_counitIso, CategoryTheory.Limits.coneOpEquiv_inverse_map, unop_pt
whisker 📖	CompOp	22 math math: CategoryTheory.Functor.Final.colimitCoconeComp_cocone, whisker_pt, whisker_ι, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CategoryTheory.Functor.Final.colimitCoconeComp_isColimit, CategoryTheory.Limits.PullbackCone.op_ι_app, equivalenceOfReindexing_counitIso, whiskering_map_hom, CategoryTheory.IsUniversalColimit.whiskerEquivalence, CategoryTheory.Limits.coconeFiberwiseColimitOfCocone_ι_app, CategoryTheory.Limits.colimit.pre_desc_assoc, CategoryTheory.Limits.colimit.pre_desc, CategoryTheory.IsVanKampenColimit.whiskerEquivalence, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.IsVanKampenColimit.whiskerEquivalence_iff, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, whiskering_obj, equivalenceOfReindexing_unitIso, CategoryTheory.IsUniversalColimit.whiskerEquivalence_iff, CategoryTheory.Limits.colimit.pre_eq
whiskering 📖	CompOp	13 math math: whiskeringEquivalence_counitIso, equivalenceOfReindexing_inverse, CategoryTheory.Functor.Final.coconesEquiv_unitIso, equivalenceOfReindexing_functor, equivalenceOfReindexing_counitIso, whiskering_map_hom, whiskeringEquivalence_inverse, CategoryTheory.Functor.Final.coconesEquiv_counitIso, whiskeringEquivalence_unitIso, whiskering_obj, equivalenceOfReindexing_unitIso, CategoryTheory.Functor.Final.coconesEquiv_inverse, whiskeringEquivalence_functor
whiskeringEquivalence 📖	CompOp	4 math math: whiskeringEquivalence_counitIso, whiskeringEquivalence_inverse, whiskeringEquivalence_unitIso, whiskeringEquivalence_functor
ι 📖	CompOp	335 math math: CategoryTheory.MorphismProperty.exists_isPushout_of_isFiltered, CategoryTheory.Monad.ForgetCreatesColimits.commuting, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_right, CategoryTheory.Limits.Bicone.toCocone_ι_app_mk, CategoryTheory.Limits.Cotrident.ofCocone_ι, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv, CategoryTheory.Limits.IsColimit.fac, CategoryTheory.Limits.Cone.unop_ι, CategoryTheory.Functor.IsEventuallyConstantFrom.cocone_ι_app, CategoryTheory.Limits.ReflexiveCofork.app_one_eq_π, toOver_ι_app, CategoryTheory.Limits.Multicofork.ofπ_ι_app, CategoryTheory.Functor.mapCocone_ι_app, CategoryTheory.Limits.colimit.cocone_ι, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.hf, CategoryTheory.Limits.CoconeMorphism.w, CategoryTheory.MorphismProperty.exists_hom_of_isFinitelyPresentable, CategoryTheory.Functor.Elements.shrinkYoneda_map_app_coconeπOpCompShrinkYonedaObj_ι_app_assoc, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inl, CategoryTheory.Limits.PushoutCocone.mk_ι_app_zero, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.Functor.isColimitCoconeOfIsLeftKanExtension_desc, whisker_ι, CategoryTheory.Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit', CategoryTheory.Limits.PushoutCocone.unop_π_app, RingHom.EssFiniteType.exists_eq_comp_ι_app_of_isColimit, CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app, CategoryTheory.Limits.Fork.unop_ι_app_zero, ofCotrident_ι, unop_π, CategoryTheory.Limits.Cofork.ofCocone_ι, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLift, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_map, CategoryTheory.FinitaryExtensive.mono_ι, CategoryTheory.Limits.IsColimit.homIso_hom, underPost_ι_app, CategoryTheory.Limits.Cotrident.π_eq_app_one, toCostructuredArrow_map, CategoryTheory.Limits.Types.pUnitCocone_ι_app, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, CategoryTheory.Limits.IsColimit.mono_ι_app_of_isFiltered, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, LightProfinite.Extend.cocone_ι_app, CategoryTheory.Limits.IsColimit.ι_map, CategoryTheory.Limits.Types.binaryCoproductCocone_ι_app, w_assoc, ModuleCat.HasColimit.colimitCocone_ι_app, CategoryTheory.Limits.Cofork.unop_π_app_one, AddCommGrpCat.Colimits.colimitCocone_ι_app, TopCat.sigmaCofan_ι_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, CategoryTheory.Comonad.ForgetCreatesColimits'.newCocone_ι_app, fromCostructuredArrow_ι_app, CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff_aux, CategoryTheory.Functor.Final.extendCocone_obj_ι_app, CategoryTheory.GrothendieckTopology.Point.presheafFiberOfIsCofilteredCocone_ι_app, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_right, CategoryTheory.Limits.colimit.toOver_ι_app, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, CategoryTheory.Limits.coneOfCoconeRightOp_π, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingProperty_ι_app_bot, CategoryTheory.Limits.Types.FilteredColimit.jointly_surjective_of_isColimit₂, CategoryTheory.MorphismProperty.colimitsOfShape.of_isColimit, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_isColimit_desc, CategoryTheory.Limits.IsColimit.ι_map_assoc, CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists, tensor_ι_app, CategoryTheory.Limits.IsColimit.homEquiv_apply, AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirected_ι, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit_under, CategoryTheory.Limits.IsColimit.isIso_colimMap_ι, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.Limits.pointwiseCocone_ι_app_app, functoriality_obj_ι_app, PartOrdEmb.Limits.CoconePt.fac_apply, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_left, CategoryTheory.Coyoneda.colimitCocone_ι_app, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_base, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_ι_app, CategoryTheory.Limits.CoconeMorphism.w_assoc, CategoryTheory.Limits.coneOfCoconeLeftOp_π_app, CategoryTheory.Limits.coneOfCoconeUnop_π, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.Limits.CompleteLattice.colimitCocone_cocone_ι_app, CategoryTheory.Under.liftCocone_ι_app, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.Limits.PushoutCocone.ofCocone_ι, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.isIso_f, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_ι_app, PrincipalSeg.cocone_ι_app, CategoryTheory.Limits.Concrete.isColimit_exists_rep, ModuleCat.directLimitIsColimit_desc, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, CategoryTheory.Limits.Multicofork.π_eq_app_right, functoriality_map_hom, CategoryTheory.Limits.coconePointwiseProduct_ι_app, CategoryTheory.Limits.Cofork.op_π_app_zero, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, PartOrdEmb.Limits.cocone_ι_app, CategoryTheory.Limits.PushoutCocone.condition_zero, Condensed.isColimitLocallyConstantPresheaf_desc_apply, toStructuredArrow_obj, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, CategoryTheory.Limits.PushoutCocone.ι_app_left, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.FinitaryPreExtensive.hasPullbacks_of_is_coproduct, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_left, CategoryTheory.Limits.IndObjectPresentation.yoneda_isColimit_desc, CategoryTheory.isPullback_initial_to_of_cofan_isVanKampen, CategoryTheory.Limits.Bicone.ofColimitCocone_ι, CategoryTheory.Limits.Cofan.mk_ι_app, CategoryTheory.Limits.PushoutCocone.mk_ι_app, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, precompose_map_hom, CategoryTheory.Limits.PushoutCocone.ι_app_right, CategoryTheory.Functor.coconeOfIsLeftKanExtension_ι, CategoryTheory.Limits.coneRightOpOfCocone_π, TopCat.isClosed_iff_of_isColimit, CategoryTheory.Comma.coconeOfPreserves_ι_app_right, CategoryTheory.Limits.coconeOfConeRightOp_ι, ofCofork_ι, CategoryTheory.Pairwise.cocone_ι_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_of, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv_assoc, CategoryTheory.Limits.BinaryCofan.ι_app_right, CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone.surjective, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_ι, CategoryTheory.MorphismProperty.PreIndSpreads.exists_isPushout, CategoryTheory.Limits.Multicofork.map_ι_app, TopCat.coinduced_of_isColimit, toCostructuredArrowCocone_ι_app, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.Limits.Cofork.coequalizer_ext, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, isColimit_iff_isIso_colimMap_ι, CategoryTheory.Functor.Final.extendCocone_obj_ι_app', CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, CategoryTheory.Limits.PushoutCocone.coequalizer_ext, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone_to_top, AddCommGrpCat.Colimits.toCocone_ι_app, CategoryTheory.Limits.coconeOfDiagramTerminal_ι_app, AddCommGrpCat.Colimits.Quot.ι_desc, Preorder.coconeOfUpperBound_ι_app, CategoryTheory.Limits.asEmptyCocone_ι_app, skyscraperPresheafCocone_ι_app, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_hom, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit, CategoryTheory.Comma.coconeOfPreserves_ι_app_left, CategoryTheory.Limits.coconeOfDiagramInitial_ι_app, CategoryTheory.Limits.coconeFiberwiseColimitOfCocone_ι_app, precompose_obj_ι, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, CategoryTheory.Coyoneda.colimitCoconeIsColimit_desc, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_left, CategoryTheory.Limits.colimit.ι_desc_apply, CategoryTheory.extendCofan_ι_app, CategoryTheory.Limits.coneLeftOpOfCocone_π_app, TopCat.continuous_iff_of_isColimit, CategoryTheory.Limits.Types.Colimit.ι_desc_apply, w, eta_inv_hom, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right_assoc, CategoryTheory.Limits.WidePushoutShape.mkCocone_ι_app, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, CategoryTheory.Limits.colimit.ι_desc, CategoryTheory.Limits.Types.jointly_surjective_of_isColimit, CategoryTheory.Limits.Multicofork.fst_app_right, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.Limits.Bicone.toCocone_ι_app, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inr, CategoryTheory.SmallObject.SuccStruct.transfiniteCompositionOfShapeιIteration_incl, CategoryTheory.Functor.coconeTypesEquiv_apply_ι_app, w_apply, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_none, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom, HasCardinalLT.Set.cocone_ι_app, CategoryTheory.Limits.Fork.op_ι_app_one, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.Presheaf.coconeOfRepresentable_naturality, CategoryTheory.GrothendieckTopology.Point.presheafFiberMapCocone_ι_app, CategoryTheory.Functor.mapCocone₂_ι_app, CategoryTheory.Limits.Cofork.unop_π_app_zero, CategoryTheory.Limits.IsColimit.hom_desc, CategoryTheory.Functor.Final.colimit_cocone_comp_aux, CategoryTheory.FunctorToTypes.jointly_surjective, HomologicalComplex.coconeOfHasColimitEval_ι_app_f, CategoryTheory.Limits.Cotrident.app_one, CategoryTheory.Functor.Elements.shrinkYoneda_map_app_coconeπOpCompShrinkYonedaObj_ι_app, SSet.iSup_range_eq_top_of_isColimit, ModuleCat.FilteredColimits.ι_colimitDesc, ofPushoutCocone_ι, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, CategoryTheory.Limits.Cotrident.coequalizer_ext, CategoryTheory.Limits.IndObjectPresentation.ofCocone_ι, CategoryTheory.Limits.colimit.ι_coconeMorphism, CategoryTheory.Monad.beckAlgebraCofork_ι_app, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.Limits.coconeLeftOpOfCone_ι_app, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, CategoryTheory.Limits.colimit.ι_desc_assoc, CategoryTheory.Limits.coconeRightOpOfCone_ι, CategoryTheory.Limits.colimit.ι_desc_app_assoc, toCostructuredArrow_obj, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Limits.Types.jointly_surjective, CategoryTheory.Over.liftCocone_ι_app, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app, CategoryTheory.Limits.wideCoequalizer.cotrident_ι_app_one, ModuleCat.directLimitCocone_ι_app, CategoryTheory.Limits.IsColimit.ι_smul, Profinite.Extend.cocone_ι_app, CategoryTheory.Limits.BinaryCofan.ι_app_left, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_left, CategoryTheory.Limits.PushoutCocone.mk_ι_app_right, CategoryTheory.Limits.Multicofork.snd_app_right, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom_assoc, CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, TopCat.nonempty_isColimit_iff_eq_coinduced, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingPropertyFixedBot_ι_app_bot, CategoryTheory.Monad.ForgetCreatesColimits.liftedCocone_ι_app_f, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, CategoryTheory.FunctorToTypes.binaryCoproductCocone_ι_app, CategoryTheory.Limits.Sigma.cocone_ι, AlgebraicGeometry.ofArrows_ι_mem_zariskiTopology_of_isColimit, CategoryTheory.Limits.CoconeMorphism.map_w_assoc, CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimit, CategoryTheory.Limits.IsColimit.isIso_ι_app_of_isTerminal, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_obj, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_ι_app, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, op_π, CategoryTheory.Limits.coconeOfConeUnop_ι, CategoryTheory.Limits.epi_of_isColimit_parallelFamily, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, LightCondensed.isColimitLocallyConstantPresheaf_desc_apply, CategoryTheory.Limits.FintypeCat.jointly_surjective, CategoryTheory.Limits.Fork.op_ι_app_zero, CategoryTheory.Limits.coconeOfCoconeUncurry_ι_app, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_none, CategoryTheory.Presheaf.tautologicalCocone_ι_app, CategoryTheory.Presheaf.tautologicalCocone'_ι_app, CategoryTheory.Limits.PushoutCocone.mk_ι_app_left, CategoryTheory.mono_of_cofan_isVanKampen, CategoryTheory.Presheaf.coconeOfRepresentable_ι_app, CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit_ι_app, CategoryTheory.Limits.Cofork.op_π_app_one, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, skyscraperPresheafCoconeOfSpecializes_ι_app, CategoryTheory.Functor.Elements.coconeπOpCompShrinkYonedaObj_ι_app, CategoryTheory.Limits.Types.Pushout.cocone_ι_app, CategoryTheory.Over.forgetCocone_ι_app, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val_assoc, extend_ι, toStructuredArrow_map, TopCat.isOpen_iff_of_isColimit, CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right, CategoryTheory.GrothendieckTopology.Point.presheafFiberCocone_ι_app, CategoryTheory.Limits.coequalizer.cofork_ι_app_one, CategoryTheory.Limits.combineCocones_pt_map, CategoryTheory.Limits.Cotrident.ofπ_ι_app, CategoryTheory.Functor.LeftExtension.coconeAt_ι_app, CategoryTheory.Limits.coconeOfIsSplitEpi_ι_app, PresheafOfModules.colimitCocone_ι_app_app, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, CategoryTheory.SmallObject.coconeOfLE_ι_app, CategoryTheory.Limits.colimitCoconeOfUnique_cocone_ι, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Limits.CokernelCofork.π_eq_zero, CategoryTheory.Functor.Final.extendCocone_map_hom, CategoryTheory.Limits.coconeUnopOfCone_ι, CategoryTheory.Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac, CategoryTheory.Limits.Cofork.ofπ_ι_app, ModuleCat.FilteredColimits.ι_colimitDesc_assoc, eta_hom_hom, CategoryTheory.Limits.coneUnopOfCocone_π, CategoryTheory.Limits.Cotrident.app_one_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, CategoryTheory.Limits.coconeOfCoconeCurry_ι_app, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.FinitaryExtensive.isPullback_initial_to, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCocone_ι_app_f, CategoryTheory.Limits.colimitCoconeOfUnique_isColimit_desc, CategoryTheory.Limits.IsColimit.fac_assoc, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_right, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff', fromStructuredArrow_obj_ι, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv, TopCat.coconeOfCoconeForget_ι_app, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val, CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists, CategoryTheory.Limits.Cofork.app_one_eq_π, CategoryTheory.Limits.constCocone_ι, CategoryTheory.Limits.HasColimitOfHasCoproductsOfHasCoequalizers.buildColimit_ι_app, underPost_pt, CommRingCat.coproductCocone_ι, extensions_app, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_c, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, CategoryTheory.Limits.CoconeMorphism.map_w, CategoryTheory.Over.liftCocone_pt, CategoryTheory.Limits.colimit.ι_desc_app, CategoryTheory.IsPushout.of_isColimit_cocone, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.epi_f, CategoryTheory.Functor.costructuredArrowMapCocone_ι_app, SSet.range_eq_iSup_of_isColimit, CategoryTheory.Limits.Cone.op_ι, CategoryTheory.Monad.ForgetCreatesColimits.newCocone_ι

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
category_comp_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.Cocone CategoryTheory.Category.toCategoryStruct category pt	—	—
category_id_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.CategoryStruct.id CategoryTheory.Limits.Cocone CategoryTheory.Category.toCategoryStruct category pt	—	—
cocone_iso_of_hom_iso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cocone category	—	CategoryTheory.IsIso.mk' CategoryTheory.Limits.CoconeMorphism.w CategoryTheory.Limits.CoconeMorphism.ext CategoryTheory.IsIso.inv_hom_id CategoryTheory.IsIso.hom_inv_id
equivalenceOfReindexing_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cocone category equivalenceOfReindexing CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor precompose CategoryTheory.Iso.hom CategoryTheory.Equivalence.inverse whiskering CategoryTheory.Iso.inv CategoryTheory.Equivalence.invFunIdAssoc CategoryTheory.Functor.id CategoryTheory.Iso.symm CategoryTheory.Functor.associator CategoryTheory.Functor.isoWhiskerRight CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.NatIso.ofComponents' ext_inv whisker CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt CategoryTheory.Functor.rightUnitor	—	CategoryTheory.Functor.isoWhiskerRight_trans CategoryTheory.Iso.trans_assoc
equivalenceOfReindexing_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone category equivalenceOfReindexing CategoryTheory.Functor.comp whiskering precompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category	—	—
equivalenceOfReindexing_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cocone category equivalenceOfReindexing CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor precompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category whiskering CategoryTheory.Iso.inv CategoryTheory.Equivalence.invFunIdAssoc	—	—
equivalenceOfReindexing_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cocone category equivalenceOfReindexing CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor whiskering CategoryTheory.Equivalence.inverse precompose CategoryTheory.Iso.inv CategoryTheory.Equivalence.invFunIdAssoc CategoryTheory.Iso.hom CategoryTheory.NatIso.ofComponents' ext_inv CategoryTheory.Functor.obj whisker CategoryTheory.Iso.refl pt CategoryTheory.Functor.isoWhiskerRight CategoryTheory.Iso.symm CategoryTheory.Functor.rightUnitor CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Functor.associator	—	CategoryTheory.Functor.isoWhiskerRight_trans CategoryTheory.Iso.trans_assoc
eta_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom pt ι CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone category eta CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	—
eta_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom pt ι CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone category eta CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	—
ext_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone category ext pt	—	—
ext_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone category ext pt	—	—
ext_inv_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone category ext_inv pt	—	—
ext_inv_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone category ext_inv pt	—	—
extendComp_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom extend CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct pt CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone category extendComp CategoryTheory.CategoryStruct.id	—	—
extendComp_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom extend CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct pt CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone category extendComp CategoryTheory.CategoryStruct.id	—	—
extendHom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom extend extendHom	—	—
extendId_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom extend pt CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone category extendId	—	—
extendId_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom extend pt CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone category extendId	—	—
extendIso_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom extend CategoryTheory.Iso.hom pt CategoryTheory.Limits.Cocone category extendIso	—	—
extendIso_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom extend CategoryTheory.Iso.hom pt CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone category extendIso	—	—
extend_pt 📖	mathematical	—	pt extend	—	—
extend_ι 📖	mathematical	—	ι extend CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.obj CategoryTheory.Functor.const pt CategoryTheory.Functor.map	—	—
extensions_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.types CategoryTheory.Functor.comp CategoryTheory.Functor.obj Opposite CategoryTheory.Category.opposite CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.coyoneda Opposite.op pt CategoryTheory.uliftFunctor CategoryTheory.Functor.cocones extensions CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct Opposite.unop CategoryTheory.Functor.const ι CategoryTheory.Functor.map	—	—
forget_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Limits.Cocone category forget CategoryTheory.Limits.CoconeMorphism.hom	—	—
forget_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone category forget pt	—	—
functorialityEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category functorialityEquivalence CategoryTheory.NatIso.ofComponents' CategoryTheory.Equivalence.inverse functoriality precomposeEquivalence CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.associator CategoryTheory.Functor.id CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Iso.symm CategoryTheory.Equivalence.unitIso CategoryTheory.Functor.rightUnitor ext_inv CategoryTheory.Functor.obj CategoryTheory.Iso.app pt	—	—
functorialityEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp category functorialityEquivalence functoriality	—	—
functorialityEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category functorialityEquivalence functoriality precomposeEquivalence CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.associator CategoryTheory.Functor.id CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Iso.symm CategoryTheory.Equivalence.unitIso CategoryTheory.Functor.rightUnitor	—	—
functorialityEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category functorialityEquivalence CategoryTheory.NatIso.ofComponents' CategoryTheory.Functor.id functoriality CategoryTheory.Equivalence.inverse precomposeEquivalence CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.associator CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Iso.symm CategoryTheory.Functor.rightUnitor ext_inv CategoryTheory.Functor.obj CategoryTheory.Iso.app pt	—	—
functoriality_faithful 📖	mathematical	—	CategoryTheory.Functor.Faithful CategoryTheory.Limits.Cocone category CategoryTheory.Functor.comp functoriality	—	CategoryTheory.Limits.CoconeMorphism.ext CategoryTheory.Functor.map_injective
functoriality_full 📖	mathematical	—	CategoryTheory.Functor.Full CategoryTheory.Limits.Cocone category CategoryTheory.Functor.comp functoriality	—	CategoryTheory.Functor.map_injective CategoryTheory.Functor.map_comp CategoryTheory.Functor.map_preimage CategoryTheory.Limits.CoconeMorphism.w CategoryTheory.Limits.CoconeMorphism.ext
functoriality_map_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Functor.comp CategoryTheory.Functor.obj pt CategoryTheory.NatTrans.mk' CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Functor.map CategoryTheory.NatTrans.app ι CategoryTheory.Limits.Cocone category functoriality	—	—
functoriality_obj_pt 📖	mathematical	—	pt CategoryTheory.Functor.comp CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone category functoriality	—	—
functoriality_obj_ι_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Functor.comp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt ι CategoryTheory.Limits.Cocone category functoriality CategoryTheory.Functor.map	—	—
instIsIsoExtendHom 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cocone category extend extendHom	—	CategoryTheory.IsIso.mk' CategoryTheory.Limits.CoconeMorphism.ext CategoryTheory.IsIso.inv_hom_id CategoryTheory.IsIso.hom_inv_id
op_pt 📖	mathematical	—	CategoryTheory.Limits.Cone.pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op op Opposite.op pt	—	—
op_π 📖	mathematical	—	CategoryTheory.Limits.Cone.π Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op op CategoryTheory.NatTrans.op CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt ι	—	—
precomposeComp_hom_app_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone category precompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.comp CategoryTheory.NatTrans.app CategoryTheory.Iso.hom precomposeComp CategoryTheory.CategoryStruct.id pt	—	—
precomposeComp_inv_app_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone category CategoryTheory.Functor.comp precompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv precomposeComp CategoryTheory.CategoryStruct.id pt	—	—
precomposeEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cocone category precomposeEquivalence CategoryTheory.NatIso.ofComponents' CategoryTheory.Functor.comp precompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.Functor.id ext_inv CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt	—	—
precomposeEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone category precomposeEquivalence precompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category	—	—
precomposeEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cocone category precomposeEquivalence precompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category	—	—
precomposeEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cocone category precomposeEquivalence CategoryTheory.NatIso.ofComponents' CategoryTheory.Functor.id CategoryTheory.Functor.comp precompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom ext_inv CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt	—	—
precomposeId_hom_app_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone category precompose CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.hom precomposeId pt	—	—
precomposeId_inv_app_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone category CategoryTheory.Functor.id precompose CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv precomposeId pt	—	—
precompose_map_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom pt CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.obj CategoryTheory.Functor.const ι CategoryTheory.Functor.map CategoryTheory.Limits.Cocone category precompose	—	—
precompose_obj_pt 📖	mathematical	—	pt CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone category precompose	—	—
precompose_obj_ι 📖	mathematical	—	ι CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone category precompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.const pt	—	—
reflects_cocone_isomorphism 📖	mathematical	—	CategoryTheory.Functor.ReflectsIsomorphisms CategoryTheory.Limits.Cocone category CategoryTheory.Functor.comp functoriality	—	cocone_iso_of_hom_iso CategoryTheory.Functor.ReflectsIsomorphisms.reflects CategoryTheory.Functor.map_isIso
unop_pt 📖	mathematical	—	CategoryTheory.Limits.Cone.pt unop Opposite.unop pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op	—	—
unop_π 📖	mathematical	—	CategoryTheory.Limits.Cone.π unop CategoryTheory.NatTrans.removeOp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Opposite.unop pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op ι	—	—
w 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj pt CategoryTheory.Functor.map CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const ι	—	CategoryTheory.Category.comp_id CategoryTheory.NatTrans.naturality'
w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.map pt CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const ι	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' w
whisker_pt 📖	mathematical	—	pt CategoryTheory.Functor.comp whisker	—	—
whisker_ι 📖	mathematical	—	ι CategoryTheory.Functor.comp whisker CategoryTheory.Functor.whiskerLeft CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt	—	—
whiskeringEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category whiskeringEquivalence CategoryTheory.NatIso.ofComponents' CategoryTheory.Equivalence.inverse whiskering precompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.invFunIdAssoc CategoryTheory.Functor.id ext_inv CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt	—	—
whiskeringEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp category whiskeringEquivalence whiskering	—	—
whiskeringEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category whiskeringEquivalence whiskering precompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.invFunIdAssoc	—	—
whiskeringEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category whiskeringEquivalence CategoryTheory.NatIso.ofComponents' CategoryTheory.Functor.id whiskering CategoryTheory.Equivalence.inverse precompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.invFunIdAssoc ext_inv CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt	—	—
whiskering_map_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Functor.comp whisker CategoryTheory.Functor.map CategoryTheory.Limits.Cocone category whiskering	—	—
whiskering_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone category CategoryTheory.Functor.comp whiskering whisker	—	—

CategoryTheory.Limits.CoconeMorphism

Definitions

Name	Category	Theorems
hom 📖	CompOp	127 math math: CategoryTheory.Functor.LeftExtension.coconeAtFunctor_map_hom, CategoryTheory.Limits.Cocone.category_id_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_functor_map_hom, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_functor_map_hom, CategoryTheory.Limits.coneUnopOfCoconeEquiv_counitIso, CategoryTheory.Limits.Fork.π_comp_hom, w, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, CategoryTheory.Limits.Multicofork.π_comp_hom_assoc, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, CategoryTheory.Limits.Cocone.extendComp_inv_hom, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, CategoryTheory.Limits.Cocone.extendIso_inv_hom, CategoryTheory.Limits.instIsIsoHomHomCocone, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, hom_inv_id_assoc, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CategoryTheory.Limits.IsColimit.mkCoconeMorphism_desc, CategoryTheory.Limits.coconeRightOpOfConeEquiv_functor_map_hom, CategoryTheory.Limits.Cocone.extendIso_hom_hom, CategoryTheory.Limits.Cocone.category_comp_hom, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, CategoryTheory.Limits.Cofan.ext_inv_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.DiagramOfCocones.coconePoints_map, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.Limits.coconeUnopOfConeEquiv_counitIso, w_assoc, CategoryTheory.Adjunction.functorialityUnit_app_hom, CategoryTheory.Limits.Multicofork.ext_hom_hom, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.Functor.mapCoconeMapCocone_hom_hom, CategoryTheory.Limits.PushoutCocone.eta_inv_hom, CategoryTheory.Limits.Cocone.precomposeComp_hom_app_hom, CategoryTheory.Limits.Cocone.functoriality_map_hom, CategoryTheory.Limits.coconeUnopOfConeEquiv_functor_map_hom, CategoryTheory.Limits.Cocone.extendId_inv_hom, CategoryTheory.Limits.BinaryCofan.ext_hom_hom, CategoryTheory.Limits.Cocone.whiskering_map_hom, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, CategoryTheory.Limits.coconeUnopOfConeEquiv_inverse_map, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Limits.Cocone.precomposeId_hom_app_hom, CategoryTheory.Limits.DiagramOfCocones.comp, CategoryTheory.Limits.Cofan.ext_hom_hom, CategoryTheory.Limits.Cowedge.ext_hom_hom, CategoryTheory.Limits.Cocone.precompose_map_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.Limits.Cofork.mkHom_hom, CategoryTheory.Limits.Cocone.forget_map, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_map_hom, CategoryTheory.Limits.coneOpEquiv_counitIso, CategoryTheory.Limits.coneUnopOfCoconeEquiv_functor_map_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_hom_hom, CategoryTheory.Adjunction.functorialityCounit_app_hom, CategoryTheory.Limits.Fork.π_comp_hom_assoc, CategoryTheory.Limits.Cocone.extendHom_hom, CategoryTheory.Limits.Cocone.precomposeId_inv_app_hom, CategoryTheory.Limits.coconeRightOpOfConeEquiv_inverse_map, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, CategoryTheory.Limits.Cocone.eta_inv_hom, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, CategoryTheory.Limits.Cocone.fromStructuredArrow_map_hom, CategoryTheory.Limits.Cocone.ext_hom_hom, hom_inv_id, CategoryTheory.Limits.IsColimit.descCoconeMorphism_hom, CategoryTheory.Limits.coneOpEquiv_functor_map_hom, CategoryTheory.Limits.Cocone.ext_inv_hom_hom, CategoryTheory.Limits.Multicofork.ext_inv_hom, CategoryTheory.Limits.colimit.ι_coconeMorphism, CategoryTheory.Limits.Cowedge.ext_inv_hom, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_functor_map_hom, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, CategoryTheory.Limits.coconeRightOpOfConeEquiv_counitIso, CategoryTheory.Limits.Cocone.mapCoconeToOver_inv_hom, CategoryTheory.Functor.mapConeOp_inv_hom, CategoryTheory.Limits.colimit.coconeMorphism_hom, CategoryTheory.Limits.coneOpEquiv_inverse_map, ext_iff, inv_hom_id, CategoryTheory.Limits.Cocone.ext_inv_hom, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, CategoryTheory.Limits.DiagramOfCocones.id, CategoryTheory.Limits.IsColimit.ofIsoColimit_desc, map_w_assoc, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_counitIso, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom, CategoryTheory.Limits.Cotrident.mkHom_hom, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, CategoryTheory.Limits.Cocone.extendComp_hom_hom, CategoryTheory.Functor.mapConeOp_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Cocone.toStructuredArrow_map, CategoryTheory.Limits.coconeOpEquiv_counitIso, CategoryTheory.Limits.PushoutCocone.eta_hom_hom, CategoryTheory.Limits.Cocone.ext_inv_inv_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_counitIso, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.Limits.instIsIsoHomInvCocone, CategoryTheory.Functor.Final.extendCocone_map_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.Limits.Cocone.mapCoconeToOver_hom_hom, CategoryTheory.Limits.Multicofork.π_comp_hom, inv_hom_id_assoc, CategoryTheory.Limits.Cocone.eta_hom_hom, CategoryTheory.Limits.Cocone.precomposeComp_inv_app_hom, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, CategoryTheory.Limits.Cocone.extendId_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_inverse_map, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.Limits.coconeOpEquiv_functor_map_hom, map_w, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_counitIso

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	hom	—	—	—
ext_iff 📖	mathematical	—	hom	—	ext
hom_inv_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt hom CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Iso.inv CategoryTheory.CategoryStruct.id	—	CategoryTheory.Iso.hom_inv_id
hom_inv_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt hom CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Iso.inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' hom_inv_id
inv_hom_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Iso.hom CategoryTheory.CategoryStruct.id	—	CategoryTheory.Iso.inv_hom_id
inv_hom_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Iso.hom	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' inv_hom_id
map_w 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone.pt CategoryTheory.Functor.map CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.ι hom	—	CategoryTheory.Functor.map_comp w
map_w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone.pt CategoryTheory.Functor.map CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.ι hom	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' map_w
w 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone.pt CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.ι hom	—	—
w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone.pt CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.ι hom	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' w

CategoryTheory.Limits.Cocones

Definitions

Name	Category	Theorems
equivalenceOfReindexing 📖	CompOp	—
eta 📖	CompOp	—
ext 📖	CompOp	—
extend 📖	CompOp	—
extendComp 📖	CompOp	—
extendId 📖	CompOp	—
extendIso 📖	CompOp	—
forget 📖	CompOp	—
functoriality 📖	CompOp	—
functorialityCompFunctoriality 📖	CompOp	—
functorialityEquivalence 📖	CompOp	—
postcompose 📖	CompOp	—
postcomposeComp 📖	CompOp	—
postcomposeEquivalence 📖	CompOp	—
postcomposeId 📖	CompOp	—
whiskering 📖	CompOp	—
whiskeringEquivalence 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cone_iso_of_hom_iso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category	—	CategoryTheory.Limits.Cocone.cocone_iso_of_hom_iso
functoriality_faithful 📖	mathematical	—	CategoryTheory.Functor.Faithful CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Functor.comp CategoryTheory.Limits.Cocone.functoriality	—	CategoryTheory.Limits.Cocone.functoriality_faithful
functoriality_full 📖	mathematical	—	CategoryTheory.Functor.Full CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Functor.comp CategoryTheory.Limits.Cocone.functoriality	—	CategoryTheory.Limits.Cocone.functoriality_full
reflects_cone_isomorphism 📖	mathematical	—	CategoryTheory.Functor.ReflectsIsomorphisms CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Functor.comp CategoryTheory.Limits.Cocone.functoriality	—	CategoryTheory.Limits.Cocone.reflects_cocone_isomorphism

CategoryTheory.Limits.Cone

Definitions

Name	Category	Theorems
category 📖	CompOp	281 math math: CategoryTheory.Limits.DiagramOfCones.id, CategoryTheory.Functor.Initial.extendCone_obj_pt, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, reflects_cone_isomorphism, CategoryTheory.Limits.ConeMorphism.hom_inv_id, CategoryTheory.Limits.hasLimit_iff_hasTerminal_cone, CategoryTheory.Functor.mapConeMapCone_hom_hom, CategoryTheory.Limits.coneOpEquiv_unitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, postcomposeComp_hom_app_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_functor_map_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_functor_obj, CategoryTheory.Mon.forgetMapConeLimitConeIso_inv_hom, CategoryTheory.Limits.IsLimit.liftConeMorphism_eq_isTerminal_from, CategoryTheory.Limits.ConeMorphism.inv_hom_id_assoc, functoriality_full, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_functor_map_hom, CategoryTheory.Limits.coneUnopOfCoconeEquiv_counitIso, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, CategoryTheory.Mon.forgetMapConeLimitConeIso_hom_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, postcomposeEquivalence_functor, CategoryTheory.Limits.Multifork.ext_hom_hom, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, whiskeringEquivalence_functor, functorialityEquivalence_inverse, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_π_app_left, postcomposeComp_inv_app_hom, ext_inv_inv_hom, CategoryTheory.Limits.Fork.isoForkOfι_hom_hom, eta_hom_hom, fromCostructuredArrow_map_hom, toCostructuredArrow_obj, CategoryTheory.Functor.mapConePostcompose_inv_hom, extendIso_hom_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.Limits.coconeUnopOfConeEquiv_unitIso, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, extendId_hom_hom, CategoryTheory.Limits.IsLimit.uniqueUpToIso_inv, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, CategoryTheory.Over.conePost_obj_π_app, cone_iso_of_hom_iso, CategoryTheory.Over.ConstructProducts.conesEquiv_unitIso, forget_obj, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, fromCostructuredArrow_obj_π, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, postcomposeEquivalence_unitIso, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_inverse_obj, CategoryTheory.Functor.Initial.conesEquiv_counitIso, postcompose_obj_pt, CategoryTheory.Limits.Fork.ι_postcompose, CategoryTheory.Limits.Fork.equivOfIsos_functor_obj_ι, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_star, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, CategoryTheory.Limits.coconeRightOpOfConeEquiv_functor_map_hom, CategoryTheory.Functor.mapCoconeOp_inv_hom, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_inverse_obj, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_counitIso, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_map_hom, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_functor, CategoryTheory.Limits.Wedge.ext_hom_hom, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_inverse_obj_ι, equivCostructuredArrow_inverse, CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctor_lift_left, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.Limits.IsLimit.ofIsoLimit_lift, CategoryTheory.Functor.Initial.extendCone_obj_π_app', CategoryTheory.Limits.coneOpEquiv_inverse_obj, functorialityEquivalence_counitIso, CategoryTheory.Limits.coconeUnopOfConeEquiv_counitIso, CategoryTheory.Limits.coconeUnopOfConeEquiv_functor_obj, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_of, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.Functor.RightExtension.coneAtFunctor_obj, CategoryTheory.Limits.coconeUnopOfConeEquiv_functor_map_hom, category_id_hom, CategoryTheory.Limits.coconeOpEquiv_inverse_map, CategoryTheory.Limits.IsLimit.equivIsoLimit_symm_apply, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_map_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, CategoryTheory.Limits.coconeOpEquiv_functor_obj, FundamentalGroupoidFunctor.instIsIsoFanGrpdObjTopCatFundamentalGroupoidFunctorPiTopToPiCone, whiskeringEquivalence_unitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, postcompose_obj_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_pt, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, CategoryTheory.Limits.coconeUnopOfConeEquiv_inverse_map, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_left, whiskering_map_hom, CategoryTheory.Limits.IsLimit.uniqueUpToIso_hom, CategoryTheory.Over.conePost_map_hom, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_inv_hom, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_obj, postcomposeEquivalence_counitIso, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_obj, CategoryTheory.Limits.Trident.ext_hom, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_inverse, CategoryTheory.Functor.Initial.conesEquiv_unitIso, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_inverse_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.Limits.Fork.ext_hom, CategoryTheory.Limits.DiagramOfCones.conePoints_map, mapConeToUnder_inv_hom, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.Limits.Cones.functoriality_faithful, CategoryTheory.Limits.coconeRightOpOfConeEquiv_inverse_obj, extendId_inv_hom, CategoryTheory.Limits.coneOpEquiv_functor_obj, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_hom, CategoryTheory.Limits.Fan.ext_inv_hom, CategoryTheory.Limits.coconeRightOpOfConeEquiv_unitIso, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.Limits.coneOpEquiv_counitIso, CategoryTheory.Limits.coneUnopOfCoconeEquiv_functor_map_hom, extendComp_inv_hom, CategoryTheory.Limits.Fan.ext_hom_hom, CategoryTheory.Functor.Initial.extendCone_map_hom, toCostructuredArrow_map, CategoryTheory.Limits.PullbackCone.eta_inv_hom, CategoryTheory.Functor.Initial.conesEquiv_inverse, CategoryTheory.Over.ConstructProducts.conesEquiv_counitIso, CategoryTheory.Limits.Fork.ext_inv, CategoryTheory.Limits.instIsIsoHomInvCone, CategoryTheory.Limits.coconeRightOpOfConeEquiv_inverse_map, functoriality_obj_π_app, CategoryTheory.Limits.PullbackCone.unop_ι_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_inverse_map, CategoryTheory.Limits.Cones.functoriality_full, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Limits.coneUnopOfCoconeEquiv_functor_obj, CategoryTheory.Limits.colimitLimitToLimitColimitCone_iso, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Limits.coneUnopOfCoconeEquiv_inverse_obj, equivalenceOfReindexing_functor, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_hom_hom, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_obj, equivCostructuredArrow_functor, whiskeringEquivalence_counitIso, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CategoryTheory.Over.conePostIso_inv_app_hom, CategoryTheory.Limits.Fork.equivOfIsos_inverse_obj_ι, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, functoriality_obj_pt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_inverse, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isLimit, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_map_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_unitIso, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_pt, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.Limits.PullbackCone.eta_hom_hom, ext_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Over.conePost_obj_pt, CategoryTheory.Limits.coconeOpEquiv_inverse_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_pt, CategoryTheory.Limits.Trident.ext_inv, CategoryTheory.Over.ConstructProducts.conesEquiv_functor, CategoryTheory.Functor.mapConeWhisker_hom_hom, equivCostructuredArrow_counitIso, CategoryTheory.Limits.coneOpEquiv_functor_map_hom, ext_inv_hom_hom, CategoryTheory.Limits.Wedge.ext_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_map_hom, category_comp_hom, CategoryTheory.Limits.coconeOpEquiv_unitIso, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Limits.ConeMorphism.hom_inv_id_assoc, ext_hom_hom, functorialityEquivalence_functor, fromCostructuredArrow_obj_pt, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_functor_map_hom, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_functor_obj, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_unitIso, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_inverse_map, CategoryTheory.Limits.coconeRightOpOfConeEquiv_counitIso, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, CategoryTheory.Limits.limit.lift_map, CategoryTheory.Limits.coconeRightOpOfConeEquiv_functor_obj, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.Functor.RightExtension.coneAtFunctor_map_hom, whiskering_obj, CategoryTheory.Functor.mapConePostcompose_hom_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_inv, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_pt, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_hom_hom, CategoryTheory.Limits.coneOpEquiv_inverse_map, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_obj, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.Limits.coconeUnopOfConeEquiv_inverse_obj, CategoryTheory.Limits.DiagramOfCones.comp, CategoryTheory.Functor.mapCoconeOp_hom_hom, equivalenceOfReindexing_counitIso, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_counitIso, equivalenceOfReindexing_unitIso, mapConeToUnder_hom_hom, functoriality_map_hom, CategoryTheory.Over.ConstructProducts.conesEquivInverse_obj, postcomposeId_inv_app_hom, CategoryTheory.Limits.coneUnopOfCoconeEquiv_inverse_map, CategoryTheory.Functor.Initial.limitConeOfComp_cone, equivCostructuredArrow_unitIso, instIsIsoExtendHom, equivalenceOfReindexing_inverse, CategoryTheory.Limits.coconeOpEquiv_counitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, extendComp_hom_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_counitIso, CategoryTheory.Limits.Multifork.ext_inv_hom, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, CategoryTheory.Functor.mapConeMapCone_inv_hom, CategoryTheory.Limits.BinaryFan.ext_hom_hom, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Functor.Initial.extendCone_obj_π_app, extendIso_inv_hom, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, CategoryTheory.Limits.Fork.isoForkOfι_inv_hom, postcomposeId_hom_app_hom, CategoryTheory.Functor.mapConeWhisker_inv_hom, forget_map, CategoryTheory.WithTerminal.coneEquiv_functor_obj_pt, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_unitIso, CategoryTheory.Over.ConstructProducts.conesEquiv_inverse, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, whiskeringEquivalence_inverse, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_functor, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_unitIso, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_functor_obj_ι, CategoryTheory.Limits.limit.lift_map_assoc, CategoryTheory.Limits.Cones.reflects_cone_isomorphism, CategoryTheory.Functor.Initial.conesEquiv_functor, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, postcomposeEquivalence_inverse, CategoryTheory.Limits.Cones.cone_iso_of_hom_iso, postcompose_map_hom, eta_inv_hom, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_inverse_map, functoriality_faithful, CategoryTheory.Limits.coconeOpEquiv_functor_map_hom, CategoryTheory.Limits.IsTerminal.from_eq_liftConeMorphism, FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone, CategoryTheory.Limits.coneUnopOfCoconeEquiv_unitIso, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_functor_obj, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_π_app, CategoryTheory.Limits.IsLimit.hom_isIso, CategoryTheory.Functor.Initial.limitConeOfComp_isLimit, CategoryTheory.Limits.instIsIsoHomHomCone, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Over.ConstructProducts.conesEquivInverse_map_hom, CategoryTheory.Adjunction.functorialityCounit'_app_hom, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_right_as, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_counitIso, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_map_hom, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv_assoc, CategoryTheory.Limits.ConeMorphism.inv_hom_id, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, functorialityEquivalence_unitIso
equiv 📖	CompOp	4 math math: equiv_inv_pt, equiv_hom_fst, equiv_inv_π, equiv_hom_snd
equivalenceOfReindexing 📖	CompOp	6 math math: equivalenceOfReindexing_functor, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_inv, equivalenceOfReindexing_counitIso, equivalenceOfReindexing_unitIso, equivalenceOfReindexing_inverse
eta 📖	CompOp	3 math math: eta_hom_hom, equivCostructuredArrow_unitIso, eta_inv_hom
ext 📖	CompOp	14 math math: postcomposeEquivalence_unitIso, CategoryTheory.Functor.Initial.conesEquiv_counitIso, functorialityEquivalence_counitIso, whiskeringEquivalence_unitIso, postcomposeEquivalence_counitIso, CategoryTheory.Functor.Initial.conesEquiv_unitIso, whiskeringEquivalence_counitIso, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isLimit, ext_inv_hom, ext_hom_hom, equivalenceOfReindexing_counitIso, equivalenceOfReindexing_unitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, functorialityEquivalence_unitIso
ext_inv 📖	CompOp	2 math math: ext_inv_inv_hom, ext_inv_hom_hom
extend 📖	CompOp	15 math math: extendIso_hom_hom, extendId_hom_hom, extend_π, extend_pt, CategoryTheory.Limits.IsLimit.OfNatIso.cone_fac, extendHom_hom, extendId_inv_hom, extendComp_inv_hom, CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_fac, instIsIsoExtendHom, extendComp_hom_hom, extendIso_inv_hom, CategoryTheory.Limits.IsLimit.homIso_hom, CategoryTheory.Limits.limit.lift_extend, CategoryTheory.Limits.IsLimit.homEquiv_apply
extendComp 📖	CompOp	2 math math: extendComp_inv_hom, extendComp_hom_hom
extendHom 📖	CompOp	2 math math: extendHom_hom, instIsIsoExtendHom
extendId 📖	CompOp	2 math math: extendId_hom_hom, extendId_inv_hom
extendIso 📖	CompOp	2 math math: extendIso_hom_hom, extendIso_inv_hom
extensions 📖	CompOp	1 math math: extensions_app
forget 📖	CompOp	2 math math: forget_obj, forget_map
functoriality 📖	CompOp	21 math math: reflects_cone_isomorphism, functoriality_full, functorialityEquivalence_inverse, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, functorialityEquivalence_counitIso, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.Limits.Cones.functoriality_faithful, functoriality_obj_π_app, CategoryTheory.Limits.Cones.functoriality_full, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.Over.conePostIso_inv_app_hom, functoriality_obj_pt, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, functorialityEquivalence_functor, functoriality_map_hom, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, CategoryTheory.Limits.Cones.reflects_cone_isomorphism, functoriality_faithful, CategoryTheory.Adjunction.functorialityCounit'_app_hom, functorialityEquivalence_unitIso
functorialityCompFunctoriality 📖	CompOp	—
functorialityEquivalence 📖	CompOp	4 math math: functorialityEquivalence_inverse, functorialityEquivalence_counitIso, functorialityEquivalence_functor, functorialityEquivalence_unitIso
op 📖	CompOp	13 math math: CategoryTheory.Limits.PullbackCone.op_ι_app, Condensed.isColimitLocallyConstantPresheaf_desc_apply, CategoryTheory.Limits.coneOpEquiv_functor_obj, CategoryTheory.Limits.coneOpEquiv_counitIso, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.Limits.coneOpEquiv_functor_map_hom, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Functor.mapConeOp_inv_hom, LightCondensed.isColimitLocallyConstantPresheaf_desc_apply, CategoryTheory.Functor.mapConeOp_hom_hom, op_pt, AlgebraicGeometry.nonempty_isColimit_Γ_mapCocone, op_ι
postcompose 📖	CompOp	39 math math: CategoryTheory.Limits.DiagramOfCones.id, postcomposeComp_hom_app_hom, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, postcomposeEquivalence_functor, postcomposeComp_inv_app_hom, CategoryTheory.Functor.mapConePostcompose_inv_hom, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, postcomposeEquivalence_unitIso, postcompose_obj_pt, CategoryTheory.Limits.Fork.ι_postcompose, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_map_hom, whiskeringEquivalence_unitIso, postcompose_obj_π, postcomposeEquivalence_counitIso, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.Limits.DiagramOfCones.conePoints_map, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, equivalenceOfReindexing_functor, whiskeringEquivalence_counitIso, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isLimit, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Limits.limit.lift_map, CategoryTheory.Functor.mapConePostcompose_hom_hom, CategoryTheory.Limits.DiagramOfCones.comp, equivalenceOfReindexing_counitIso, equivalenceOfReindexing_unitIso, postcomposeId_inv_app_hom, equivalenceOfReindexing_inverse, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, postcomposeId_hom_app_hom, whiskeringEquivalence_inverse, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv, CategoryTheory.Limits.limit.lift_map_assoc, postcomposeEquivalence_inverse, postcompose_map_hom, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv_assoc
postcomposeComp 📖	CompOp	2 math math: postcomposeComp_hom_app_hom, postcomposeComp_inv_app_hom
postcomposeEquivalence 📖	CompOp	9 math math: postcomposeEquivalence_functor, functorialityEquivalence_inverse, postcomposeEquivalence_unitIso, functorialityEquivalence_counitIso, postcomposeEquivalence_counitIso, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_hom_hom, postcomposeEquivalence_inverse, functorialityEquivalence_unitIso
postcomposeId 📖	CompOp	2 math math: postcomposeId_inv_app_hom, postcomposeId_hom_app_hom
pt 📖	CompOp	904 math math: AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_snd, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_pt, CategoryTheory.Limits.Trident.condition_assoc, CategoryTheory.Limits.Fork.IsLimit.homIso_natural, CategoryTheory.Limits.DiagramOfCones.id, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj_assoc, CategoryTheory.Functor.Initial.extendCone_obj_pt, toUnder_pt, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, CategoryTheory.Functor.coneOfIsRightKanExtension_pt, CategoryTheory.Limits.BinaryFan.rightUnitor_hom, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, AddCommGrpCat.binaryProductLimitCone_cone_pt, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac, LightProfinite.Extend.functorOp_obj, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback', CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_pt, CategoryTheory.Limits.ConeMorphism.hom_inv_id, CategoryTheory.extendFan_pt, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_snd_assoc, CategoryTheory.Functor.mapConeMapCone_hom_hom, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_comp_assoc, CategoryTheory.Limits.Wedge.mk_pt, CategoryTheory.Limits.Trident.app_zero, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, AlgebraicGeometry.opensCone_pt, postcomposeComp_hom_app_hom, unop_ι, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, ofTrident_π, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_functor_map_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, CategoryTheory.Mon.forgetMapConeLimitConeIso_inv_hom, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_apply_val, CategoryTheory.Monad.ForgetCreatesLimits.liftedConeIsLimit_lift_f, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_snd, CategoryTheory.Limits.Fork.IsLimit.lift_ι'_assoc, CategoryTheory.Limits.ConeMorphism.inv_hom_id_assoc, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_left, CategoryTheory.PreOneHypercover.forkOfIsColimit_pt, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, CategoryTheory.Functor.isLimitConeOfIsRightKanExtension_lift, Profinite.Extend.functorOp_map, CategoryTheory.Functor.isCardinalAccessible_of_isLimit, CategoryTheory.Abelian.epi_fst_of_factor_thru_epi_mono_factorization, AlgebraicGeometry.exists_isAffineOpen_preimage_eq, CategoryTheory.biconeMk_obj, CategoryTheory.Limits.coneUnopOfCoconeEquiv_counitIso, HomologicalComplex.coneOfHasLimitEval_pt_d, CategoryTheory.ObjectProperty.prop_of_isLimit_kernelFork, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_φ, CategoryTheory.Limits.BinaryBicone.toCone_π_app_right, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map', CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj, equiv_inv_pt, CategoryTheory.Limits.Types.limitCone_pt, CategoryTheory.Limits.BinaryFan.braiding_hom_snd_assoc, CategoryTheory.Comonad.beckCoalgebraFork_pt, CategoryTheory.Limits.IsLimit.map_π, CategoryTheory.Mon.forgetMapConeLimitConeIso_hom_hom, CategoryTheory.Comonad.ComonadicityInternal.unitFork_pt, CategoryTheory.Limits.mono_of_isLimit_parallelFamily, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.IsPullback.of_isLimit_binaryFan_of_isTerminal, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedCone_π_app_f, CategoryTheory.Limits.PullbackCone.π_app_right, Preorder.conePt_mem_lowerBounds, CategoryTheory.Limits.Multifork.ext_hom_hom, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, CategoryTheory.Limits.Fork.unop_ι_app_zero, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos_assoc, CategoryTheory.isCoseparator_of_isLimit_fan, CategoryTheory.Limits.KernelFork.condition_assoc, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_π_app_left, postcomposeComp_inv_app_hom, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, CategoryTheory.Limits.FormalCoproduct.pullbackCone_fst_φ, ext_inv_inv_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom, CategoryTheory.Limits.Fork.isoForkOfι_hom_hom, CategoryTheory.Functor.RightExtension.coneAt_pt, CategoryTheory.Limits.PullbackCone.condition, CategoryTheory.Limits.BinaryFan.braiding_hom_fst_assoc, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles_assoc, CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.fac, CategoryTheory.Limits.Fork.IsLimit.mono, eta_hom_hom, toCostructuredArrow_obj, CategoryTheory.Limits.kernel.zeroKernelFork_ι, CategoryTheory.Limits.KernelFork.IsLimit.isZero_of_mono, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct'_hom, CategoryTheory.Limits.WidePullbackCone.reindex_pt, CategoryTheory.Functor.mapConePostcompose_inv_hom, CategoryTheory.Comma.coneOfPreserves_π_app_right, CategoryTheory.Comma.limitAuxiliaryCone_pt, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, CategoryTheory.Limits.isColimitCoconeLeftOpOfCone_desc, extendIso_hom_hom, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyData_K, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.FunctorToTypes.binaryProductCone_pt_obj, CategoryTheory.Limits.coconeOfConeLeftOp_pt, CategoryTheory.Limits.constCone_pt, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, whisker_π, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, extendId_hom_hom, CompHausLike.pullback.isLimit_lift, CategoryTheory.Under.liftCone_pt, CategoryTheory.Limits.PullbackCone.unop_inl, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_isTerminalTensorUnit_lift_hom, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom, CategoryTheory.Limits.isLimitOfCoconeOfConeRightOp_lift, CategoryTheory.ObjectProperty.prop_of_isLimit, toStructuredArrowCompProj_inv_app, AlgebraicGeometry.Scheme.Pullback.gluedLift_p1, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp, CategoryTheory.Limits.BinaryFan.IsLimit.lift'_coe, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, CategoryTheory.Limits.PullbackCone.IsLimit.lift_fst, CategoryTheory.Limits.Trident.ofι_pt, CategoryTheory.Limits.Fork.ofι_pt, CategoryTheory.Over.conePost_obj_π_app, CategoryTheory.Limits.PullbackCone.op_pt, CategoryTheory.Limits.Types.binaryProductCone_pt, CategoryTheory.Limits.coneUnopOfCocone_pt, CategoryTheory.Limits.Cofork.unop_π_app_one, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inl, CategoryTheory.Limits.isLimitOfCoconeOfConeLeftOp_lift, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_right, forget_obj, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom_assoc, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, Profinite.exists_locallyConstant_finite_aux, CategoryTheory.Mon.limitConeIsLimit_lift_hom, CategoryTheory.Limits.IsLimit.nonempty_isLimit_iff_isIso_lift, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_apply_fst, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp, CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_pt, GrpCat.binaryProductLimitCone_cone_pt, CategoryTheory.Limits.opCoproductIsoProduct'_comp_self, CategoryTheory.Limits.pullbackConeOfLeftIso_snd, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.Limits.ConeMorphism.w, CategoryTheory.Limits.limit.lift_post, postcomposeEquivalence_unitIso, lightDiagramToLightProfinite_obj, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv, extend_π, CategoryTheory.Functor.Initial.conesEquiv_counitIso, Profinite.isIso_indexCone_lift, CategoryTheory.Limits.Bicone.toCone_π_app_mk, CategoryTheory.Limits.Multifork.ofι_pt, CategoryTheory.Limits.PullbackCone.condition_assoc, CategoryTheory.Limits.Trident.condition, CategoryTheory.Limits.PullbackCone.unop_inr, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom, postcompose_obj_pt, CategoryTheory.Limits.Fork.ι_postcompose, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.homologyπ_isoHomology_inv_assoc, CategoryTheory.Limits.BinaryBicone.toCone_π_app_left, CategoryTheory.Limits.coconeOfConeUnop_pt, CategoryTheory.Limits.Fork.equivOfIsos_functor_obj_ι, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_star, Profinite.Extend.functorOp_obj, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_H, CategoryTheory.Limits.coconeRightOpOfConeEquiv_functor_map_hom, CategoryTheory.Monad.ForgetCreatesLimits.newCone_π_app, ModuleCat.binaryProductLimitCone_cone_π_app_right, CategoryTheory.Limits.Fork.IsLimit.existsUnique, toStructuredArrowCompToUnderCompForget_hom_app, CategoryTheory.Limits.PullbackCone.combine_π_app, CategoryTheory.Limits.Cocone.op_pt, LightProfinite.lightToProfinite_map_proj_eq, CompHausLike.sigmaComparison_eq_comp_isos, CategoryTheory.Limits.Fork.hom_comp_ι, CategoryTheory.Limits.asEmptyCone_pt, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.associator_naturality, CategoryTheory.Limits.Multiequalizer.multifork_π_app_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_map_hom, CategoryTheory.Limits.ConeMorphism.map_w_assoc, CategoryTheory.Limits.coneOfDiagramTerminal_pt, CategoryTheory.Cat.HasLimits.limitCone_pt, CategoryTheory.Limits.BinaryFan.braiding_hom_snd, CategoryTheory.Limits.limit.isoLimitCone_hom_π_assoc, CategoryTheory.Limits.Multifork.toPiFork_pt, CategoryTheory.Limits.PullbackCone.op_inr, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, AlgebraicGeometry.isBasis_preimage_isAffineOpen, CategoryTheory.Limits.coneOfDiagramInitial_pt, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_functor, CategoryTheory.Limits.coneOfConeCurry_pt, CategoryTheory.Limits.Wedge.IsLimit.lift_ι, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.Limits.Wedge.ext_hom_hom, CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctor_lift_left, AlgebraicGeometry.Scheme.Pullback.gluedLift_p2, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_epi, CategoryTheory.Limits.IsLimit.ofIsoLimit_lift, CategoryTheory.Limits.IsLimit.pushout_zero_ext, CategoryTheory.Functor.Initial.extendCone_obj_π_app', CategoryTheory.Limits.Fork.IsLimit.homIso_symm_apply, functorialityEquivalence_counitIso, CategoryTheory.Limits.WidePullbackCone.IsLimit.lift_base, AddCommGrpCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Limits.Types.Small.limitCone_pt, fromStructuredArrow_pt, toStructuredArrow_comp_toUnder_comp_forget, CategoryTheory.Mon.limit_mon_mul, CategoryTheory.Limits.BinaryFan.braiding_inv_snd, CategoryTheory.Limits.PullbackCone.mono_fst_of_is_pullback_of_mono, CategoryTheory.Limits.coconeUnopOfConeEquiv_counitIso, AddCommGrpCat.binaryProductLimitCone_cone_π_app_left, CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer', CategoryTheory.Limits.Types.isLimitEquivSections_apply, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg_assoc, extend_pt, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_of, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, CategoryTheory.Comma.coneOfPreserves_pt_right, CategoryTheory.Limits.opCoproductIsoProduct'_inv_comp_inj, ofPullbackCone_pt, ProfiniteAddGrp.instIsTopologicalAddGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂ContinuousAddMonoidHomToProfiniteContinuousMap, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj, GrpCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac, CategoryTheory.Preadditive.forkOfKernelFork_pt, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Limits.IsLimit.OfNatIso.cone_fac, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, TopCat.nonempty_isLimit_iff_eq_induced, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, AddCommGrpCat.HasLimit.productLimitCone_cone_pt_coe, CategoryTheory.Limits.Fork.op_pt, CategoryTheory.Limits.PullbackCone.isIso_fst_of_mono_of_isLimit, ofPullbackCone_π, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, CategoryTheory.Limits.ConeMorphism.map_w, ProfiniteGrp.cone_pt, TopCat.piFan_pt, CategoryTheory.Limits.limit.isoLimitCone_hom_π, CategoryTheory.Limits.coconeUnopOfConeEquiv_functor_map_hom, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_right, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_K, category_id_hom, CategoryTheory.Functor.rightAdjointObjIsDefined_of_isLimit, CategoryTheory.Limits.IsLimit.hom_lift, CategoryTheory.Limits.coconeOpEquiv_inverse_map, CategoryTheory.Limits.PullbackCone.mk_π_app_right, CategoryTheory.Limits.Cofork.op_π_app_zero, CategoryTheory.Limits.coneOfConeCurry_π_app, CategoryTheory.Sheaf.isSheaf_of_isLimit, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, CategoryTheory.Limits.isColimitCoconeUnopOfCone_desc, CategoryTheory.Monad.ForgetCreatesLimits.liftedCone_pt, AddGrpCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Limits.pullbackConeOfRightIso_fst, CategoryTheory.lift_comp_preservesLimitIso_hom_assoc, whiskeringEquivalence_unitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, postcompose_obj_π, equiv_hom_fst, CategoryTheory.ObjectProperty.prop_of_isLimit_fan, toStructuredArrowCone_π_app, Condensed.isColimitLocallyConstantPresheaf_desc_apply, CategoryTheory.Limits.Fork.hom_comp_ι_assoc, Profinite.instEpiAppDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceπAsLimitCone, Preorder.coneOfLowerBound_pt, CategoryTheory.Limits.isLimitOfCoconeLeftOpOfCone_lift, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_pt, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_inv, CategoryTheory.Under.forgetCone_pt, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp_assoc, CategoryTheory.Limits.BinaryFan.rightUnitor_inv, CategoryTheory.Limits.pullbackConeOfRightIso_x, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.PullbackCone.mk_π_app_one, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_left, TopCat.Sheaf.interUnionPullbackConeLift_right, LightProfinite.Extend.functor_map, CategoryTheory.Limits.CompleteLattice.limitCone_isLimit_lift, CategoryTheory.Over.conePost_map_hom, CategoryTheory.Limits.HasLimitOfHasProductsOfHasEqualizers.buildLimit_pt, CategoryTheory.IsPullback.of_isLimit, CategoryTheory.Limits.Fork.ofCone_π, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_isLimit_lift, CategoryTheory.Limits.opProductIsoCoproduct'_comp_self, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_obj, postcomposeEquivalence_counitIso, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_obj, AlgebraicGeometry.exists_preimage_eq, CategoryTheory.Limits.KernelFork.IsLimit.isIso_ι, CategoryTheory.Limits.Trident.ext_hom, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.Abelian.epi_snd_of_isLimit, CategoryTheory.Limits.coneOfSectionCompYoneda_pt, CategoryTheory.Limits.Types.limitConeIsLimit_lift_coe, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom, CategoryTheory.Limits.coneOfAdj_pt, CategoryTheory.Functor.Initial.conesEquiv_unitIso, CategoryTheory.Limits.WidePullbackShape.mkCone_pt, CategoryTheory.lift_comp_preservesLimitIso_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', CategoryTheory.Limits.KernelFork.condition, Profinite.exists_isClopen_of_cofiltered, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, TopCat.nonempty_limitCone_of_compact_t2_cofiltered_system, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_map, CategoryTheory.Limits.Fork.IsLimit.homIso_apply_coe, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_apply_snd, CategoryTheory.Limits.coneOfCoconeLeftOp_pt, CategoryTheory.Limits.limit.cone_x, CategoryTheory.Limits.Fork.IsLimit.lift_ι, CategoryTheory.Limits.Fork.ext_hom, CategoryTheory.ShortComplex.LeftHomologyData.wπ_assoc, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, mapConeToUnder_inv_hom, CategoryTheory.Limits.PullbackCone.π_app_left, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_pt, CategoryTheory.Limits.Wedge.condition, CategoryTheory.FunctorToTypes.binaryProductLimit_lift, CategoryTheory.Limits.limit.existsUnique, CategoryTheory.regularTopology.parallelPair_pullback_initial, CategoryTheory.Limits.biproduct.conePointUniqueUpToIso_inv, CategoryTheory.Limits.Multifork.app_left_eq_ι, CategoryTheory.Limits.Multifork.condition, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.leftUnitor_naturality, CategoryTheory.Limits.coconeOfConeRightOp_ι, CategoryTheory.Limits.limitConeOfUnique_cone_pt, CategoryTheory.Limits.Fork.op_π, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.Under.liftCone_π_app, CategoryTheory.Limits.Wedge.IsLimit.lift_ι_assoc, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_left, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Mon.limitCone_π_app_hom, CategoryTheory.Comma.limitAuxiliaryCone_π_app, extendId_inv_hom, CategoryTheory.Limits.Trident.IsLimit.homIso_apply_coe, CategoryTheory.Limits.WidePullbackCone.mk_pt, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_hom, CategoryTheory.Limits.Fan.ext_inv_hom, CategoryTheory.Limits.Bicone.toCone_pt, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.Limits.coneOpEquiv_counitIso, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, extendComp_inv_hom, CategoryTheory.Limits.Multifork.IsLimit.fac_assoc, Profinite.Extend.functor_obj, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_f_coe, CategoryTheory.Limits.Fan.ext_hom_hom, CategoryTheory.Limits.WidePullbackCone.IsLimit.lift_π_assoc, CategoryTheory.Functor.Initial.extendCone_map_hom, toCostructuredArrow_map, CategoryTheory.Limits.BinaryFan.π_app_right, AlgebraicGeometry.opensCone_π_app, CategoryTheory.Limits.PullbackCone.eta_inv_hom, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_fst, CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone.surjective, CategoryTheory.Limits.Fan.IsLimit.fac_assoc, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_π, CategoryTheory.Limits.limit.lift_π_app, CategoryTheory.biconeMk_map, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone_pt, CategoryTheory.Limits.WidePullbackCone.condition_assoc, PresheafOfModules.isSheaf_of_isLimit, CategoryTheory.Limits.Fork.ext_inv, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right_assoc, CategoryTheory.Limits.WidePullbackCone.IsLimit.lift_base_assoc, CategoryTheory.Limits.instIsIsoHomInvCone, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv, overPost_pt, CategoryTheory.IsUniversalColimit.nonempty_isColimit_of_pullbackCone_left, CategoryTheory.Functor.Initial.limit_cone_comp_aux, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.triangle, CategoryTheory.Sheaf.coneΓ_pt, CategoryTheory.Preadditive.mono_iff_isZero_kernel', CategoryTheory.Limits.coneOfSectionCompCoyoneda_pt, CategoryTheory.Over.liftCone_π_app, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_π, Condensed.instFinalOppositeDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceCostructuredArrowFintypeCatProfiniteOpToProfiniteOpPtAsLimitConeFunctorOp, CategoryTheory.Limits.isLimitConeOfAdj_lift, CategoryTheory.Limits.Types.Limit.lift_π_apply, CategoryTheory.Limits.BinaryFan.braiding_inv_fst_assoc, functoriality_obj_π_app, CategoryTheory.Limits.isLimitOfCoconeRightOpOfCone_lift, CategoryTheory.Limits.ConeMorphism.w_assoc, CategoryTheory.Limits.PullbackCone.unop_ι_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, CategoryTheory.IsUniversalColimit.nonempty_isColimit_prod_of_pullbackCone, CategoryTheory.Limits.BinaryBicone.toCone_pt, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.Multifork.ofPiFork_pt, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_none, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_symm_apply_val, CategoryTheory.Limits.biprod.conePointUniqueUpToIso_hom, CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit, CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_eq, CategoryTheory.Limits.Fan.IsLimit.fac, CategoryTheory.Functor.mapCone_pt, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Limits.coconeOfConeRightOp_pt, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_inverse_map, CategoryTheory.Functor.mapCone₂_pt, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_pt, CategoryTheory.Limits.kernel.zeroKernelFork_pt, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, CategoryTheory.Limits.BinaryFan.braiding_hom_fst, Algebra.codRestrictEqLocusPushoutCocone.surjective_of_isEffective, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.Limits.Fan.mk_pt, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.Limits.WidePullbackCone.IsLimit.lift_π, CategoryTheory.Functor.mapCone₂_π_app, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv_assoc, LightProfinite.Extend.functorOp_map, TopCat.Sheaf.interUnionPullbackConeLift_left, CategoryTheory.Limits.coneOfCoconeRightOp_pt, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_symm_apply_fst, Alexandrov.lowerCone_π_app, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac', CategoryTheory.Limits.Fork.condition, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, CategoryTheory.ShortComplex.LeftHomologyData.wπ, ModuleCat.binaryProductLimitCone_cone_π_app_left, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Limits.KernelFork.app_one, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc, CategoryTheory.Functor.coneOfIsRightKanExtension_π, CategoryTheory.Limits.Fork.app_zero_eq_ι, CategoryTheory.Limits.limit.cone_π, CategoryTheory.Limits.IsLimit.isIso_limMap_π, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_inv_hom, CategoryTheory.Limits.limit.lift_π_apply, CategoryTheory.Limits.DiagramOfCones.conePoints_obj, CategoryTheory.Limits.isLimitOfCoconeOfConeUnop_lift, CategoryTheory.Limits.isKernelCompMono_lift, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_left, CategoryTheory.Limits.pullbackConeOfLeftIso_x, toStructuredArrowCompProj_hom_app, CategoryTheory.Limits.Trident.ofCone_π, CategoryTheory.Limits.Types.Small.limitConeIsLimit_lift, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_hom_hom, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp, CategoryTheory.IsSplitEqualizer.asFork_pt, CategoryTheory.Functor.mapCone_π_app, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_obj, whiskeringEquivalence_counitIso, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CategoryTheory.Over.conePostIso_inv_app_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeSndIsOpenImmersion, CategoryTheory.Sheaf.coneΓ_π_app, CategoryTheory.Limits.Fork.equivOfIsos_inverse_obj_ι, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.Limits.coneOfConeUncurry_π_app, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_pt, CategoryTheory.Abelian.AbelianStruct.ι_imageπ_assoc, functoriality_obj_pt, AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'_f, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_pt, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_inverse, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isLimit, CategoryTheory.Functor.IsEventuallyConstantTo.isIso_π_of_isLimit, CategoryTheory.Functor.IsEventuallyConstantTo.cone_pt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Limits.Pi.map_eq_prod_map, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac_assoc, CategoryTheory.Limits.coconeUnopOfCone_pt, CategoryTheory.Limits.Concrete.surjective_π_app_zero_of_surjective_map, LightProfinite.instTotallyDisconnectedSpaceCarrierToTopTruePtCompHausLimitConeCompLightProfiniteToCompHaus, Profinite.exists_locallyConstant, CategoryTheory.Limits.Trident.equalizer_ext, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_pt, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.Limits.Multifork.IsLimit.fac, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp, CategoryTheory.extendFan_π_app, CategoryTheory.Limits.coneRightOpOfCocone_pt, CommGrpCat.binaryProductLimitCone_cone_pt, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.Limits.PullbackCone.eta_hom_hom, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_snd, CategoryTheory.Limits.BinaryBicone.ofLimitCone_snd, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst_assoc, ext_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Limits.PullbackCone.mk_pt, CategoryTheory.Over.conePost_obj_pt, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_pt, CategoryTheory.Limits.limitConeOfUnique_isLimit_lift, CategoryTheory.coherentTopology.epi_π_app_zero_of_epi, CategoryTheory.Limits.coneLeftOpOfCocone_pt, CategoryTheory.Limits.Trident.ι_eq_app_zero, CategoryTheory.Limits.limit.lift_pre, CategoryTheory.Limits.Fork.op_ι_app_one, w, CategoryTheory.Limits.mono_of_isLimit_fork, CategoryTheory.Limits.PullbackCone.ofCone_π, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_pt, CategoryTheory.Limits.Trident.ext_inv, CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_fst, CategoryTheory.Limits.PullbackCone.op_inl, CategoryTheory.Limits.PullbackCone.IsLimit.lift_snd, CategoryTheory.Functor.mapConeWhisker_hom_hom, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hab, ModuleCat.HasLimit.productLimitCone_cone_pt_isModule, CategoryTheory.Limits.Cofork.unop_π_app_zero, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι_assoc, CategoryTheory.Limits.coneOpEquiv_functor_map_hom, toStructuredArrow_obj, Algebra.codRestrictEqLocusPushoutCocone.injective_of_faithfulSMul, ext_inv_hom_hom, CategoryTheory.Over.isPullback_of_binaryFan_isLimit, CategoryTheory.Limits.biprod.conePointUniqueUpToIso_inv, CategoryTheory.Limits.IsLimit.fac_assoc, CategoryTheory.Limits.PullbackCone.flip_pt, CategoryTheory.Limits.BinaryFan.braiding_inv_fst, CategoryTheory.Limits.Wedge.ext_inv_hom, CategoryTheory.Limits.BinaryFan.assoc_snd, CategoryTheory.Limits.Pi.cone_pt, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, Profinite.Extend.functorOp_final, category_comp_hom, CategoryTheory.Limits.CoproductDisjoint.nonempty_isInitial_of_ne, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.pentagon, CategoryTheory.Limits.FormalCoproduct.pullbackCone_fst_f, CategoryTheory.Monad.ForgetCreatesLimits.conePoint_A, CategoryTheory.Comma.coneOfPreserves_pt_hom, ModuleCat.HasLimit.productLimitCone_cone_pt_carrier, CategoryTheory.Limits.Trident.IsLimit.homIso_symm_apply, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Enriched.FunctorCategory.coneFunctorEnrichedHom_pt, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.ConeMorphism.hom_inv_id_assoc, TopCat.coneOfConeForget_π_app, CategoryTheory.Limits.BinaryFan.braiding_inv_snd_assoc, CategoryTheory.Limits.Bicone.ofLimitCone_π, ext_hom_hom, CategoryTheory.Limits.Fan.IsLimit.lift_proj, ofFork_π, CategoryTheory.Limits.isColimitCoconeRightOpOfCone_desc, CategoryTheory.Limits.isColimitCoconeOfConeRightOp_desc, CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_K, TopCat.induced_of_isLimit, CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map, CategoryTheory.Limits.coconeLeftOpOfCone_ι_app, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty', fromCostructuredArrow_obj_pt, isLimit_iff_isIso_limMap_π, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_pt, CategoryTheory.MorphismProperty.limitsOfShape.mk', CategoryTheory.Limits.coconeRightOpOfCone_ι, CategoryTheory.Limits.PullbackCone.combine_pt_map, CategoryTheory.Limits.Fork.IsLimit.lift_ι_assoc, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_inverse_map, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Limits.PullbackCone.equalizer_ext, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, CategoryTheory.Limits.PullbackCone.unop_pt, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_id, CategoryTheory.Limits.coconeRightOpOfConeEquiv_counitIso, CategoryTheory.Limits.limit.lift_π_assoc, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, CategoryTheory.Limits.Fork.IsLimit.lift_ι', CategoryTheory.Mon.limit_X, CategoryTheory.Limits.limit.pre_eq, CategoryTheory.Limits.limit.lift_map, AddCommGrpCat.HasLimit.lift_hom_apply, CategoryTheory.Limits.PullbackCone.combine_pt_obj, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, CategoryTheory.Limits.Fan.IsLimit.lift_proj_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.Limits.PushoutCocone.op_pt, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, LightCondensed.epi_π_app_zero_of_epi, CategoryTheory.Functor.mapConeOp_inv_hom, CategoryTheory.Limits.FormalCoproduct.pullbackCone_condition, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, CategoryTheory.regularTopology.equalizerCondition_w, CategoryTheory.Functor.mapConePostcompose_hom_hom, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles, CategoryTheory.Subfunctor.equalizer.fork_pt, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_inv, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, TopCat.Presheaf.isGluing_iff_pairwise, Alexandrov.lowerCone_pt, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_pt, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_none, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_fst, HomologicalComplex.quasiIsoAt_π_of_isLimit_of_isEventuallyConstantTo, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv_assoc, HomologicalComplex.coneOfHasLimitEval_pt_X, whisker_pt, CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer', ModuleCat.HasLimit.lift_hom_apply, ModuleCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Comonad.beckEqualizer_lift, CategoryTheory.Comonad.ForgetCreatesLimits'.conePoint_A, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_obj, Profinite.Extend.cone_pt, CategoryTheory.isCoseparator_iff_of_isLimit_fan, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, lightDiagramToLightProfinite_map, CategoryTheory.IsUniversalColimit.nonempty_isColimit_of_pullbackCone_right, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, CategoryTheory.Limits.limit.isoLimitCone_inv_π, CategoryTheory.Limits.Bicone.toCone_π_app, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_hom, CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_π, CategoryTheory.Limits.BinaryFan.leftUnitor_hom, CategoryTheory.Subobject.leInfCone_π_app_none, CategoryTheory.Limits.Fan.nonempty_isLimit_iff_isIso_piLift, unop_pt, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom_assoc, CategoryTheory.Limits.DiagramOfCones.comp, CategoryTheory.Limits.PullbackCone.condition_one, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, equivalenceOfReindexing_counitIso, CategoryTheory.MorphismProperty.IsStableUnderLimitsOfShape.condition, CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer', CategoryTheory.Presieve.piComparison_fac, CategoryTheory.Limits.BinaryBicone.ofLimitCone_fst, toUnder_π_app, CategoryTheory.Limits.IsLimit.assoc_lift, CategoryTheory.Comonad.beckFork_pt, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_obj, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, AlgebraicGeometry.Scheme.nonempty_of_isLimit, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, CategoryTheory.Limits.limit.coneMorphism_π, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_counitIso, CategoryTheory.Limits.KernelFork.map_condition, AlgebraicGeometry.Scheme.compactSpace_of_isLimit, CategoryTheory.Limits.coconeOfConeUnop_ι, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.homologyπ_isoHomology_inv, CategoryTheory.Limits.IsLimit.lift_self, CategoryTheory.Mon.limitCone_pt, equivalenceOfReindexing_unitIso, LightCondensed.isColimitLocallyConstantPresheaf_desc_apply, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty, CommRingCat.piFan_pt, CategoryTheory.Limits.Fork.op_ι_app_zero, AlgebraicGeometry.Scheme.exists_π_app_comp_eq_of_locallyOfFinitePresentation, CategoryTheory.Cat.HasLimits.limitConeLift_toFunctor, CategoryTheory.Limits.Trident.app_zero_assoc, CategoryTheory.Limits.PullbackCone.isIso_snd_of_mono_of_isLimit, CategoryTheory.Limits.combineCones_pt_map, toStructuredArrow_comp_proj, CategoryTheory.Abelian.epi_fst_of_isLimit, CategoryTheory.Mon.limit_mon_one, CategoryTheory.Limits.Cofork.op_π_app_one, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp, CategoryTheory.Limits.IsLimit.map_π_assoc, mapConeToUnder_hom_hom, LightProfinite.Extend.functor_initial, functoriality_map_hom, CategoryTheory.Limits.opProductIsoCoproduct'_inv_comp_lift, ModuleCat.HasLimit.productLimitCone_cone_pt_isAddCommGroup, CategoryTheory.Limits.BinaryFan.leftUnitor_inv, postcomposeId_inv_app_hom, CategoryTheory.Limits.isColimitCoconeOfConeLeftOp_desc, CategoryTheory.Functor.mapConeOp_hom_hom, CategoryTheory.coherentTopology.isLocallySurjective_π_app_zero_of_isLocallySurjective_map, CategoryTheory.Limits.PullbackCone.IsLimit.lift_fst_assoc, LightCondensed.instFinalNatCostructuredArrowOppositeFintypeCatLightProfiniteOpToLightProfiniteOpPtAsLimitConeFunctorOp, CategoryTheory.Limits.KernelFork.map_ι, ModuleCat.binaryProductLimitCone_cone_pt, CategoryTheory.Limits.coneUnopOfCoconeEquiv_inverse_map, CategoryTheory.Limits.equalizer.fork_π_app_zero, CategoryTheory.Comma.coneOfPreserves_pt_left, CategoryTheory.Functor.structuredArrowMapCone_pt, CommGrpCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Limits.coneOfConeUncurry_pt, CategoryTheory.Limits.splitMonoOfIdempotentOfIsLimitFork_retraction, CategoryTheory.Limits.Multifork.hom_comp_ι, CategoryTheory.Limits.coconeOpEquiv_counitIso, w_apply, CategoryTheory.Limits.isLimitOfCoconeUnopOfCone_lift, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, overPost_π_app, toStructuredArrow_map, CategoryTheory.Limits.proj_comp_opProductIsoCoproduct'_hom, CategoryTheory.Limits.PushoutCocone.unop_pt, CategoryTheory.Limits.Multifork.pi_condition_assoc, CategoryTheory.Limits.SequentialProduct.cone_π_app, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, CategoryTheory.Limits.limit.lift_π_app_assoc, w_assoc, extendComp_hom_hom, AlgebraicGeometry.isAffineHom_π_app, LightProfinite.Extend.functor_obj, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_counitIso, CategoryTheory.Limits.Multifork.ext_inv_hom, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, op_pt, CategoryTheory.ShortComplex.exact_iff_of_forks, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.f'_eq, HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff, CategoryTheory.Monad.ForgetCreatesLimits.liftedCone_π_app_f, CategoryTheory.Limits.combineCones_pt_obj, CategoryTheory.Limits.coconeRightOpOfCone_pt, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_pt_snd, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.Functor.mapConeMapCone_inv_hom, CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff', CategoryTheory.Limits.BinaryFan.ext_hom_hom, CategoryTheory.Functor.IsEventuallyConstantTo.isIso_π_of_isLimit', LightProfinite.instEpiAppOppositeNatπAsLimitCone, CategoryTheory.FunctorToTypes.binaryProductCone_pt_map, CategoryTheory.Limits.IsLimit.pushout_hom_ext, CategoryTheory.Limits.PullbackCone.IsLimit.lift_snd_assoc, CategoryTheory.Limits.IsLimit.isZero_pt, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.π_comp_isoHomology_hom, CategoryTheory.Limits.BinaryFan.assocInv_snd, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_tensorProductIsBinaryProduct_lift_hom, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, CategoryTheory.Limits.Multifork.ofPiFork_ι, CategoryTheory.Functor.Initial.extendCone_obj_π_app, CategoryTheory.Limits.Fork.condition_assoc, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp, CategoryTheory.Limits.Cocone.unop_pt, CategoryTheory.preserves_lift_mapCone, instSecondCountableTopologyCarrierToTopTotallyDisconnectedSpacePtOppositeNatProfiniteCone, extendIso_inv_hom, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac_assoc, CategoryTheory.Limits.coconeUnopOfCone_ι, CategoryTheory.Limits.BinaryFan.assocInv_fst, CategoryTheory.Limits.Fork.isoForkOfι_inv_hom, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj_assoc, postcomposeId_hom_app_hom, CategoryTheory.Limits.BinaryFan.π_app_left, CategoryTheory.Functor.mapConeWhisker_inv_hom, CategoryTheory.Limits.IsLimit.existsUnique, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, toStructuredArrowCompToUnderCompForget_inv_app, CategoryTheory.ShortComplex.RightHomologyData.ofIsLimitKernelFork_H, CategoryTheory.mono_iff_isIso_fst, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_zero, CategoryTheory.WithTerminal.coneEquiv_functor_obj_pt, CategoryTheory.Limits.IsLimit.homIso_hom, CategoryTheory.Limits.PullbackCone.ofCone_pt, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.rightUnitor_naturality, CategoryTheory.Limits.PullbackCone.mk_π_app_left, CategoryTheory.CategoryOfElements.CreatesLimitsAux.map_lift_mapCone, TopCat.isSheaf_of_isLimit, CategoryTheory.Comonad.ComonadicityInternal.counitFork_pt, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_apply_coe, extensions_app, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.Limits.HasLimitOfHasProductsOfHasEqualizers.buildLimit_π_app, CategoryTheory.Limits.isColimitCoconeOfConeUnop_desc, AddGrpCat.binaryProductLimitCone_cone_pt, CategoryTheory.Limits.coneOfIsSplitMono_pt, CommRingCat.prodFan_pt, TopCat.Sheaf.interUnionPullbackCone_pt, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv, Profinite.exists_locallyConstant_finite_nonempty, CategoryTheory.Limits.BinaryFan.assoc_fst, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_comp, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac, CategoryTheory.Limits.limit.lift_map_assoc, CategoryTheory.Limits.Types.Limit.lift_π_apply', CategoryTheory.mono_iff_isIso_snd, AddCommGrpCat.binaryProductLimitCone_cone_π_app_right, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_pt, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj, CategoryTheory.PreservesFiniteLimitsOfFlat.fac, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_symm_apply_snd, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedConeIsLimit_lift_f, CategoryTheory.Limits.PullbackCone.mono_snd_of_is_pullback_of_mono, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg, CategoryTheory.IsPullback.of_isLimit_cone, CategoryTheory.Limits.limit.lift_π, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CategoryTheory.Limits.wideEqualizer.trident_π_app_zero, CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_snd, CategoryTheory.Limits.Multifork.hom_comp_ι_assoc, CategoryTheory.Limits.Bicone.ofLimitCone_pt, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.π_comp_isoHomology_hom_assoc, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, Profinite.exists_locallyConstant_fin_two, PresheafOfModules.limitCone_pt, Profinite.Extend.functor_initial, CategoryTheory.Over.liftCone_pt, toStructuredArrowCone_pt, CategoryTheory.Abelian.AbelianStruct.ι_imageπ, CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, CommRingCat.instIsLocalHomCarrierPtWalkingParallelPairEqualizerForkRingHomHomι, HomologicalComplex.isIso_π_f_of_isLimit_of_isEventuallyConstantTo, postcompose_map_hom, ProfiniteGrp.instIsTopologicalGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂ContinuousMonoidHomToProfiniteContinuousMap, eta_inv_hom, CategoryTheory.Limits.BinaryFan.mk_pt, Profinite.Extend.functor_map, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, CategoryTheory.Limits.BinaryBicone.ofLimitCone_pt, CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_self, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map, AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffine, CategoryTheory.Limits.Trident.IsLimit.homIso_natural, CategoryTheory.ObjectProperty.prop_of_isLimit_binaryFan, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, CategoryTheory.Limits.Multifork.toPiFork_π_app_zero, CategoryTheory.Limits.biproduct.conePointUniqueUpToIso_hom, CategoryTheory.Limits.Types.isLimit_iff_bijective_sectionOfCone, CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map_aux, CategoryTheory.Limits.FormalCoproduct.pullbackCone_snd_f, CategoryTheory.Limits.IsLimit.isIso_π_app_of_isInitial, CategoryTheory.Limits.coneOfCoconeUnop_pt, CategoryTheory.Limits.Multifork.toSections_fac, Profinite.isIso_asLimitCone_lift, TopCat.coneOfConeForget_pt, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_pt_fst, CategoryTheory.Limits.Fork.unop_π, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, LightProfinite.Extend.functorOp_final, CategoryTheory.Limits.limit.lift_extend, TopCat.isTopologicalBasis_cofiltered_limit, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inr, CategoryTheory.IsPullback.of_is_product, CategoryTheory.Limits.Multifork.isLimit_types_iff, CategoryTheory.Limits.IsLimit.fac, CategoryTheory.Limits.Types.isLimit_iff, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_π_app, CategoryTheory.Limits.combineCones_π_app_app, CategoryTheory.Limits.instIsIsoHomHomCone, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.instSndPullbackConeOfLeft, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, CategoryTheory.Limits.Multifork.condition_assoc, Preorder.isGLB_of_isLimit, CategoryTheory.Over.ConstructProducts.conesEquivInverse_map_hom, Algebra.codRestrictEqLocusPushoutCocone.bijective_of_faithfullyFlat, CategoryTheory.Limits.FormalCoproduct.pullbackCone_snd_φ, CategoryTheory.Limits.WidePullbackCone.condition, CategoryTheory.Adjunction.functorialityCounit'_app_hom, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_right_as, CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone.injective, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right, Profinite.exists_hom, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.liftAux_fac, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_counitIso, AlgebraicGeometry.Scheme.isAffine_of_isLimit, CategoryTheory.Limits.FormalCoproduct.isPullback, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedCone_pt, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_map_hom, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv_assoc, CompHausLike.pullback.cone_pt, CategoryTheory.Limits.coconeLeftOpOfCone_pt, CategoryTheory.Limits.ConeMorphism.inv_hom_id, CategoryTheory.Limits.Fork.equalizer_ext, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι, CategoryTheory.Limits.Types.isLimitEquivSections_symm_apply, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac, op_ι, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst, CategoryTheory.Limits.IsLimit.homEquiv_apply, CategoryTheory.Limits.CompleteLattice.limitCone_cone_pt, CategoryTheory.Limits.Multifork.pi_condition, CategoryTheory.Limits.KernelFork.map_condition_assoc, CategoryTheory.Comma.coneOfPreserves_π_app_left
unop 📖	CompOp	5 math math: unop_ι, CategoryTheory.Limits.coconeOpEquiv_inverse_map, CategoryTheory.Limits.coconeOpEquiv_inverse_obj, unop_pt, CategoryTheory.Limits.coconeOpEquiv_counitIso
whisker 📖	CompOp	16 math math: whisker_π, CategoryTheory.Functor.Initial.limitConeComp_isLimit, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, whiskering_map_hom, CategoryTheory.Functor.Initial.limitConeComp_cone, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.Limits.PullbackCone.unop_ι_app, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.Limits.limit.lift_pre, CategoryTheory.Functor.mapConeWhisker_hom_hom, CategoryTheory.Limits.limit.pre_eq, whiskering_obj, whisker_pt, equivalenceOfReindexing_counitIso, equivalenceOfReindexing_unitIso, CategoryTheory.Functor.mapConeWhisker_inv_hom
whiskering 📖	CompOp	15 math math: whiskeringEquivalence_functor, CategoryTheory.Functor.Initial.conesEquiv_counitIso, CategoryTheory.Over.conePostIso_hom_app_hom, whiskeringEquivalence_unitIso, whiskering_map_hom, CategoryTheory.Functor.Initial.conesEquiv_unitIso, CategoryTheory.Functor.Initial.conesEquiv_inverse, equivalenceOfReindexing_functor, whiskeringEquivalence_counitIso, CategoryTheory.Over.conePostIso_inv_app_hom, whiskering_obj, equivalenceOfReindexing_counitIso, equivalenceOfReindexing_unitIso, equivalenceOfReindexing_inverse, whiskeringEquivalence_inverse
whiskeringEquivalence 📖	CompOp	4 math math: whiskeringEquivalence_functor, whiskeringEquivalence_unitIso, whiskeringEquivalence_counitIso, whiskeringEquivalence_inverse
π 📖	CompOp	329 math math: CategoryTheory.Limits.limitConeOfUnique_cone_π, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac, LightProfinite.Extend.functorOp_obj, CategoryTheory.Limits.Trident.app_zero, AlgebraicGeometry.opensCone_pt, unop_ι, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, ofTrident_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_left, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, CategoryTheory.Functor.isLimitConeOfIsRightKanExtension_lift, CategoryTheory.Limits.Pi.cone_π, Profinite.Extend.functorOp_map, AlgebraicGeometry.exists_isAffineOpen_preimage_eq, CategoryTheory.Limits.BinaryBicone.toCone_π_app_right, CategoryTheory.Limits.IsLimit.map_π, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedCone_π_app_f, CategoryTheory.Limits.PullbackCone.π_app_right, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Limits.Fork.unop_ι_app_zero, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos_assoc, Profinite.Extend.cone_π_app, CategoryTheory.Limits.Cocone.unop_π, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_π_app_left, CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.fac, eta_hom_hom, toCostructuredArrow_obj, CategoryTheory.Functor.IsEventuallyConstantTo.cone_π_app, CategoryTheory.Comma.coneOfPreserves_π_app_right, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, CategoryTheory.Functor.RightExtension.coneAt_π_app, CategoryTheory.Limits.coneOfDiagramTerminal_π_app, whisker_π, CategoryTheory.Under.liftCone_pt, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, CategoryTheory.Limits.PullbackCone.mk_π_app, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp, CategoryTheory.Over.conePost_obj_π_app, ModuleCat.HasLimit.productLimitCone_cone_π, CategoryTheory.Limits.Cofork.unop_π_app_one, fromStructuredArrow_π_app, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_right, Profinite.exists_locallyConstant_finite_aux, fromCostructuredArrow_obj_π, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.Limits.ConeMorphism.w, extend_π, CategoryTheory.Limits.Bicone.toCone_π_app_mk, CategoryTheory.Limits.coneOfCoconeRightOp_π, CategoryTheory.Limits.BinaryBicone.toCone_π_app_left, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_star, Profinite.Extend.functorOp_obj, CategoryTheory.Limits.coneOfDiagramInitial_π_app, CategoryTheory.Limits.WidePullbackShape.mkCone_π_app, CategoryTheory.Monad.ForgetCreatesLimits.newCone_π_app, ModuleCat.binaryProductLimitCone_cone_π_app_right, CategoryTheory.Limits.PullbackCone.combine_π_app, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, LightProfinite.lightToProfinite_map_proj_eq, CategoryTheory.Limits.Multiequalizer.multifork_π_app_left, CategoryTheory.Cat.HasLimits.limitCone_π_app, CategoryTheory.Limits.ConeMorphism.map_w_assoc, CategoryTheory.Limits.limit.isoLimitCone_hom_π_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, AlgebraicGeometry.isBasis_preimage_isAffineOpen, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.Functor.Initial.extendCone_obj_π_app', CategoryTheory.Enriched.FunctorCategory.coneFunctorEnrichedHom_π_app, CategoryTheory.Mon.limit_mon_mul, AddCommGrpCat.binaryProductLimitCone_cone_π_app_left, CategoryTheory.Limits.coneOfCoconeLeftOp_π_app, CategoryTheory.Limits.coneOfCoconeUnop_π, PresheafOfModules.limitCone_π_app_app, CategoryTheory.Limits.Types.isLimitEquivSections_apply, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg_assoc, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, CategoryTheory.Limits.coneOfIsSplitMono_π_app, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_of, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, TopCat.nonempty_isLimit_iff_eq_induced, ofPullbackCone_π, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, CategoryTheory.Limits.ConeMorphism.map_w, CategoryTheory.Limits.limit.isoLimitCone_hom_π, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_right, CategoryTheory.Limits.Fork.ofι_π_app, CategoryTheory.Limits.IsLimit.hom_lift, CategoryTheory.Limits.PullbackCone.mk_π_app_right, CategoryTheory.Limits.Cofork.op_π_app_zero, CategoryTheory.Limits.coneOfConeCurry_π_app, CategoryTheory.Limits.Types.limitCone_π_app, postcompose_obj_π, toStructuredArrowCone_π_app, Condensed.isColimitLocallyConstantPresheaf_desc_apply, Profinite.instEpiAppDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceπAsLimitCone, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp_assoc, CategoryTheory.Limits.PullbackCone.mk_π_app_one, LightProfinite.Extend.functor_map, CategoryTheory.Over.conePost_map_hom, CategoryTheory.Limits.Fork.ofCone_π, AlgebraicGeometry.exists_preimage_eq, CategoryTheory.Limits.Types.limitConeIsLimit_lift_coe, Profinite.exists_isClopen_of_cofiltered, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Limits.coneRightOpOfCocone_π, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.PullbackCone.π_app_left, CategoryTheory.Limits.Multifork.app_left_eq_ι, CategoryTheory.Limits.coconeOfConeRightOp_ι, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Under.liftCone_π_app, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_left, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Mon.limitCone_π_app_hom, CategoryTheory.Comma.limitAuxiliaryCone_π_app, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_hom, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, Profinite.Extend.functor_obj, CategoryTheory.Functor.Initial.extendCone_map_hom, toCostructuredArrow_map, CategoryTheory.Limits.BinaryFan.π_app_right, AlgebraicGeometry.opensCone_π_app, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_π, CategoryTheory.Limits.limit.lift_π_app, equiv_inv_π, CategoryTheory.biconeMk_map, CategoryTheory.Limits.Types.Small.limitCone_π_app, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right_assoc, overPost_pt, CategoryTheory.Functor.Initial.limit_cone_comp_aux, CategoryTheory.Over.liftCone_π_app, CategoryTheory.Limits.isLimitConeOfAdj_lift, CategoryTheory.Limits.Types.Limit.lift_π_apply, equiv_hom_snd, functoriality_obj_π_app, CategoryTheory.Limits.ConeMorphism.w_assoc, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_none, CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, AddCommGrpCat.HasLimit.productLimitCone_cone_π, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.Functor.mapCone₂_π_app, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, LightProfinite.Extend.functorOp_map, Alexandrov.lowerCone_π_app, CategoryTheory.Limits.coneLeftOpOfCocone_π_app, ModuleCat.binaryProductLimitCone_cone_π_app_left, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Limits.KernelFork.app_one, CategoryTheory.Functor.coneOfIsRightKanExtension_π, CategoryTheory.Limits.Fork.app_zero_eq_ι, CategoryTheory.Limits.limit.cone_π, CategoryTheory.Limits.IsLimit.isIso_limMap_π, CategoryTheory.Limits.limit.lift_π_apply, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_left, ProfiniteGrp.cone_π_app, CategoryTheory.Limits.Trident.ofCone_π, CompHausLike.pullback.cone_π, CategoryTheory.Limits.Types.Small.limitConeIsLimit_lift, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp, CategoryTheory.Functor.mapCone_π_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CategoryTheory.Sheaf.coneΓ_π_app, CategoryTheory.Limits.coneOfConeUncurry_π_app, CategoryTheory.Limits.asEmptyCone_π_app, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.Functor.IsEventuallyConstantTo.isIso_π_of_isLimit, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Limits.Trident.ofι_π_app, CategoryTheory.Limits.coneOfSectionCompYoneda_π, CategoryTheory.Limits.Concrete.surjective_π_app_zero_of_surjective_map, Profinite.exists_locallyConstant, CategoryTheory.Limits.Trident.equalizer_ext, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp, CategoryTheory.extendFan_π_app, CategoryTheory.Limits.BinaryBicone.ofLimitCone_snd, CategoryTheory.Over.conePost_obj_pt, CategoryTheory.Limits.limitConeOfUnique_isLimit_lift, CategoryTheory.coherentTopology.epi_π_app_zero_of_epi, CategoryTheory.Limits.Trident.ι_eq_app_zero, CategoryTheory.Limits.Fork.op_ι_app_one, w, CategoryTheory.Limits.PullbackCone.ofCone_π, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hab, CategoryTheory.Limits.Cofork.unop_π_app_zero, toStructuredArrow_obj, CategoryTheory.Limits.IsLimit.fac_assoc, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, CategoryTheory.Limits.limit.homIso_hom, TopCat.coneOfConeForget_π_app, CategoryTheory.Limits.Bicone.ofLimitCone_π, ofFork_π, TopCat.induced_of_isLimit, CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map, CategoryTheory.Limits.coconeLeftOpOfCone_ι_app, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty', isLimit_iff_isIso_limMap_π, CategoryTheory.Limits.coconeRightOpOfCone_ι, CategoryTheory.Limits.PullbackCone.combine_pt_map, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Limits.PullbackCone.equalizer_ext, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, Preorder.coneOfLowerBound_π_app, CategoryTheory.Limits.limit.lift_π_assoc, AddCommGrpCat.HasLimit.lift_hom_apply, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone_π_app, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, LightCondensed.epi_π_app_zero_of_epi, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, TopCat.Presheaf.isGluing_iff_pairwise, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_pt, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_π_app, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_none, HomologicalComplex.quasiIsoAt_π_of_isLimit_of_isEventuallyConstantTo, ModuleCat.HasLimit.lift_hom_apply, CategoryTheory.FunctorToTypes.binaryProductCone_π_app, ModuleCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Limits.Multifork.ofι_π_app, CategoryTheory.Limits.limit.isoLimitCone_inv_π, CategoryTheory.Limits.Bicone.toCone_π_app, HomologicalComplex.coneOfHasLimitEval_π_app_f, CategoryTheory.Subobject.leInfCone_π_app_none, CategoryTheory.Limits.PullbackCone.condition_one, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, CategoryTheory.Limits.BinaryBicone.ofLimitCone_fst, toUnder_π_app, CategoryTheory.Limits.coneOfSectionCompCoyoneda_π, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, CategoryTheory.Limits.limit.coneMorphism_π, CategoryTheory.Limits.Cocone.op_π, CategoryTheory.Limits.coconeOfConeUnop_ι, LightCondensed.isColimitLocallyConstantPresheaf_desc_apply, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty, CategoryTheory.Limits.Fork.op_ι_app_zero, AlgebraicGeometry.Scheme.exists_π_app_comp_eq_of_locallyOfFinitePresentation, CategoryTheory.Cat.HasLimits.limitConeLift_toFunctor, CategoryTheory.Limits.Trident.app_zero_assoc, CategoryTheory.Limits.combineCones_pt_map, CategoryTheory.Limits.Cofork.op_π_app_one, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp, CategoryTheory.Limits.IsLimit.map_π_assoc, functoriality_map_hom, CategoryTheory.coherentTopology.isLocallySurjective_π_app_zero_of_isLocallySurjective_map, CategoryTheory.Limits.equalizer.fork_π_app_zero, w_apply, overPost_π_app, toStructuredArrow_map, CategoryTheory.Limits.SequentialProduct.cone_π_app, CategoryTheory.Limits.limit.lift_π_app_assoc, w_assoc, AlgebraicGeometry.isAffineHom_π_app, LightProfinite.Extend.functor_obj, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, CategoryTheory.Monad.ForgetCreatesLimits.liftedCone_π_app_f, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac, CategoryTheory.Limits.CompleteLattice.limitCone_cone_π_app, CategoryTheory.Functor.IsEventuallyConstantTo.isIso_π_of_isLimit', LightProfinite.instEpiAppOppositeNatπAsLimitCone, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, CategoryTheory.Functor.Initial.extendCone_obj_π_app, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp, CategoryTheory.Limits.coconeUnopOfCone_ι, CategoryTheory.Limits.BinaryFan.π_app_left, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_zero, CategoryTheory.Limits.IsLimit.homIso_hom, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.Limits.PullbackCone.mk_π_app_left, extensions_app, CategoryTheory.Limits.HasLimitOfHasProductsOfHasEqualizers.buildLimit_π_app, CategoryTheory.Limits.coneUnopOfCocone_π, Profinite.exists_locallyConstant_finite_nonempty, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_π_app, CategoryTheory.Limits.Types.Limit.lift_π_apply', AddCommGrpCat.binaryProductLimitCone_cone_π_app_right, CategoryTheory.PreservesFiniteLimitsOfFlat.fac, CategoryTheory.Limits.constCone_π, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg, CategoryTheory.IsPullback.of_isLimit_cone, CategoryTheory.Limits.limit.lift_π, CategoryTheory.Limits.wideEqualizer.trident_π_app_zero, Profinite.exists_locallyConstant_fin_two, CategoryTheory.Comonad.beckCoalgebraFork_π_app, TopCat.piFan_π_app, CategoryTheory.Limits.Fan.mk_π_app, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, HomologicalComplex.isIso_π_f_of_isLimit_of_isEventuallyConstantTo, postcompose_map_hom, eta_inv_hom, Profinite.Extend.functor_map, CategoryTheory.Limits.coneOfAdj_π, AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffine, CategoryTheory.Under.forgetCone_π_app, CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map_aux, CategoryTheory.Limits.IsLimit.isIso_π_app_of_isInitial, TopCat.isTopologicalBasis_cofiltered_limit, CategoryTheory.Limits.IsLimit.fac, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_π_app, CategoryTheory.Limits.combineCones_π_app_app, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right, Profinite.exists_hom, CategoryTheory.Limits.Fork.equalizer_ext, CategoryTheory.Limits.Types.isLimitEquivSections_symm_apply, op_ι, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.Functor.structuredArrowMapCone_π_app, CategoryTheory.Limits.IsLimit.homEquiv_apply, CategoryTheory.Comma.coneOfPreserves_π_app_left

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
category_comp_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.Cone CategoryTheory.Category.toCategoryStruct category pt	—	—
category_id_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.CategoryStruct.id CategoryTheory.Limits.Cone CategoryTheory.Category.toCategoryStruct category pt	—	—
cone_iso_of_hom_iso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cone category	—	CategoryTheory.Iso.inv_comp_eq CategoryTheory.Limits.ConeMorphism.w CategoryTheory.Limits.ConeMorphism.ext CategoryTheory.IsIso.hom_inv_id CategoryTheory.IsIso.inv_hom_id
equiv_hom_fst 📖	mathematical	—	Opposite CategoryTheory.Functor.obj CategoryTheory.Category.opposite CategoryTheory.types CategoryTheory.Functor.cones CategoryTheory.Iso.hom CategoryTheory.Limits.Cone equiv Opposite.op pt	—	—
equiv_hom_snd 📖	mathematical	—	Opposite CategoryTheory.Functor.obj CategoryTheory.Category.opposite CategoryTheory.types CategoryTheory.Functor.cones CategoryTheory.Iso.hom CategoryTheory.Limits.Cone equiv π	—	—
equiv_inv_pt 📖	mathematical	—	pt CategoryTheory.Iso.inv CategoryTheory.types CategoryTheory.Limits.Cone Opposite CategoryTheory.Functor.obj CategoryTheory.Category.opposite CategoryTheory.Functor.cones equiv Opposite.unop Quiver.Hom CategoryTheory.Functor CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.const	—	—
equiv_inv_π 📖	mathematical	—	π CategoryTheory.Iso.inv CategoryTheory.types CategoryTheory.Limits.Cone Opposite CategoryTheory.Functor.obj CategoryTheory.Category.opposite CategoryTheory.Functor.cones equiv Quiver.Hom CategoryTheory.Functor CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.const Opposite.unop	—	—
equivalenceOfReindexing_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cone category equivalenceOfReindexing CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor postcompose CategoryTheory.Iso.inv CategoryTheory.Equivalence.inverse whiskering CategoryTheory.Iso.hom CategoryTheory.Equivalence.invFunIdAssoc CategoryTheory.Functor.id CategoryTheory.Iso.symm CategoryTheory.Functor.associator CategoryTheory.Functor.isoWhiskerRight CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.NatIso.ofComponents ext whisker CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt CategoryTheory.Functor.rightUnitor	—	CategoryTheory.Functor.isoWhiskerRight_trans CategoryTheory.Iso.trans_assoc
equivalenceOfReindexing_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone category equivalenceOfReindexing CategoryTheory.Functor.comp whiskering postcompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category	—	—
equivalenceOfReindexing_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cone category equivalenceOfReindexing CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor postcompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category whiskering CategoryTheory.Iso.hom CategoryTheory.Equivalence.invFunIdAssoc	—	—
equivalenceOfReindexing_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cone category equivalenceOfReindexing CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor whiskering CategoryTheory.Equivalence.inverse postcompose CategoryTheory.Iso.hom CategoryTheory.Equivalence.invFunIdAssoc CategoryTheory.Iso.inv CategoryTheory.NatIso.ofComponents ext CategoryTheory.Functor.obj whisker CategoryTheory.Iso.refl pt CategoryTheory.Functor.isoWhiskerRight CategoryTheory.Iso.symm CategoryTheory.Functor.rightUnitor CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Functor.associator	—	CategoryTheory.Functor.isoWhiskerRight_trans CategoryTheory.Iso.trans_assoc
eta_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom pt π CategoryTheory.Iso.hom CategoryTheory.Limits.Cone category eta CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	—
eta_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom pt π CategoryTheory.Iso.inv CategoryTheory.Limits.Cone category eta CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	—
ext_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Iso.hom CategoryTheory.Limits.Cone category ext pt	—	—
ext_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cone category ext pt	—	—
ext_inv_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Iso.hom CategoryTheory.Limits.Cone category ext_inv pt	—	—
ext_inv_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cone category ext_inv pt	—	—
extendComp_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom extend CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct pt CategoryTheory.Iso.hom CategoryTheory.Limits.Cone category extendComp CategoryTheory.CategoryStruct.id	—	—
extendComp_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom extend CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct pt CategoryTheory.Iso.inv CategoryTheory.Limits.Cone category extendComp CategoryTheory.CategoryStruct.id	—	—
extendHom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom extend extendHom	—	—
extendId_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom extend pt CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Iso.hom CategoryTheory.Limits.Cone category extendId	—	—
extendId_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom extend pt CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Iso.inv CategoryTheory.Limits.Cone category extendId	—	—
extendIso_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom extend CategoryTheory.Iso.inv pt CategoryTheory.Iso.hom CategoryTheory.Limits.Cone category extendIso	—	—
extendIso_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom extend CategoryTheory.Iso.inv pt CategoryTheory.Limits.Cone category extendIso	—	—
extend_pt 📖	mathematical	—	pt extend	—	—
extend_π 📖	mathematical	—	π extend CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.obj CategoryTheory.Functor.const pt CategoryTheory.Functor.map	—	—
extensions_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite CategoryTheory.Category.opposite CategoryTheory.types CategoryTheory.Functor.comp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.yoneda pt CategoryTheory.uliftFunctor CategoryTheory.Functor.cones extensions CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct Opposite.unop CategoryTheory.Functor.op CategoryTheory.Functor.const CategoryTheory.Functor.map π	—	—
forget_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Limits.Cone category forget CategoryTheory.Limits.ConeMorphism.hom	—	—
forget_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Limits.Cone category forget pt	—	—
functorialityEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category functorialityEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Equivalence.inverse functoriality postcomposeEquivalence CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.associator CategoryTheory.Functor.id CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Iso.symm CategoryTheory.Equivalence.unitIso CategoryTheory.Functor.rightUnitor ext CategoryTheory.Functor.obj CategoryTheory.Iso.app pt	—	—
functorialityEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone CategoryTheory.Functor.comp category functorialityEquivalence functoriality	—	—
functorialityEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category functorialityEquivalence functoriality postcomposeEquivalence CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.associator CategoryTheory.Functor.id CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Iso.symm CategoryTheory.Equivalence.unitIso CategoryTheory.Functor.rightUnitor	—	—
functorialityEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category functorialityEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.id functoriality CategoryTheory.Equivalence.inverse postcomposeEquivalence CategoryTheory.Iso.trans CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.associator CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Iso.symm CategoryTheory.Functor.rightUnitor ext CategoryTheory.Functor.obj CategoryTheory.Iso.app	—	—
functoriality_faithful 📖	mathematical	—	CategoryTheory.Functor.Faithful CategoryTheory.Limits.Cone category CategoryTheory.Functor.comp functoriality	—	CategoryTheory.Limits.ConeMorphism.ext CategoryTheory.Functor.map_injective
functoriality_full 📖	mathematical	—	CategoryTheory.Functor.Full CategoryTheory.Limits.Cone category CategoryTheory.Functor.comp functoriality	—	CategoryTheory.Functor.map_injective CategoryTheory.Functor.map_comp CategoryTheory.Functor.map_preimage CategoryTheory.Limits.ConeMorphism.w CategoryTheory.Limits.ConeMorphism.ext
functoriality_map_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.comp CategoryTheory.Functor.obj pt CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Functor.map CategoryTheory.NatTrans.app π CategoryTheory.Limits.Cone category functoriality	—	—
functoriality_obj_pt 📖	mathematical	—	pt CategoryTheory.Functor.comp CategoryTheory.Functor.obj CategoryTheory.Limits.Cone category functoriality	—	—
functoriality_obj_π_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt CategoryTheory.Functor.comp π CategoryTheory.Limits.Cone category functoriality CategoryTheory.Functor.map	—	—
instIsIsoExtendHom 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cone category extend extendHom	—	CategoryTheory.Limits.ConeMorphism.ext CategoryTheory.IsIso.hom_inv_id CategoryTheory.IsIso.inv_hom_id
op_pt 📖	mathematical	—	CategoryTheory.Limits.Cocone.pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op op Opposite.op pt	—	—
op_ι 📖	mathematical	—	CategoryTheory.Limits.Cocone.ι Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op op CategoryTheory.NatTrans.op CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt π	—	—
postcomposeComp_hom_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cone category postcompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.comp CategoryTheory.NatTrans.app CategoryTheory.Iso.hom postcomposeComp CategoryTheory.CategoryStruct.id pt	—	—
postcomposeComp_inv_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cone category CategoryTheory.Functor.comp postcompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv postcomposeComp CategoryTheory.CategoryStruct.id pt	—	—
postcomposeEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cone category postcomposeEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.comp postcompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.Functor.id ext CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt	—	—
postcomposeEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone category postcomposeEquivalence postcompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category	—	—
postcomposeEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cone category postcomposeEquivalence postcompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category	—	—
postcomposeEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cone category postcomposeEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.id CategoryTheory.Functor.comp postcompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv ext CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt	—	—
postcomposeId_hom_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cone category postcompose CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.hom postcomposeId pt	—	—
postcomposeId_inv_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cone category CategoryTheory.Functor.id postcompose CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv postcomposeId pt	—	—
postcompose_map_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom pt CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.obj CategoryTheory.Functor.const π CategoryTheory.Functor.map CategoryTheory.Limits.Cone category postcompose	—	—
postcompose_obj_pt 📖	mathematical	—	pt CategoryTheory.Functor.obj CategoryTheory.Limits.Cone category postcompose	—	—
postcompose_obj_π 📖	mathematical	—	π CategoryTheory.Functor.obj CategoryTheory.Limits.Cone category postcompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.const pt	—	—
reflects_cone_isomorphism 📖	mathematical	—	CategoryTheory.Functor.ReflectsIsomorphisms CategoryTheory.Limits.Cone category CategoryTheory.Functor.comp functoriality	—	cone_iso_of_hom_iso CategoryTheory.Functor.ReflectsIsomorphisms.reflects CategoryTheory.Functor.map_isIso
unop_pt 📖	mathematical	—	CategoryTheory.Limits.Cocone.pt unop Opposite.unop pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op	—	—
unop_ι 📖	mathematical	—	CategoryTheory.Limits.Cocone.ι unop CategoryTheory.NatTrans.removeOp CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const Opposite.unop pt Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op π	—	—
w 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct pt CategoryTheory.Functor.obj CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const π CategoryTheory.Functor.map	—	CategoryTheory.Category.id_comp CategoryTheory.NatTrans.naturality
w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct pt CategoryTheory.Functor.obj CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const π CategoryTheory.Functor.map	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' w
whisker_pt 📖	mathematical	—	pt CategoryTheory.Functor.comp whisker	—	—
whisker_π 📖	mathematical	—	π CategoryTheory.Functor.comp whisker CategoryTheory.Functor.whiskerLeft CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt	—	—
whiskeringEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category whiskeringEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Equivalence.inverse whiskering postcompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.invFunIdAssoc CategoryTheory.Functor.id ext CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt	—	—
whiskeringEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone CategoryTheory.Functor.comp category whiskeringEquivalence whiskering	—	—
whiskeringEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category whiskeringEquivalence whiskering postcompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.invFunIdAssoc	—	—
whiskeringEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor category whiskeringEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.id whiskering CategoryTheory.Equivalence.inverse postcompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.invFunIdAssoc ext CategoryTheory.Functor.obj CategoryTheory.Iso.refl pt	—	—
whiskering_map_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.comp whisker CategoryTheory.Functor.map CategoryTheory.Limits.Cone category whiskering	—	—
whiskering_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Limits.Cone category CategoryTheory.Functor.comp whiskering whisker	—	—

CategoryTheory.Limits.ConeMorphism

Definitions

Name	Category	Theorems
hom 📖	CompOp	153 math math: CategoryTheory.Limits.DiagramOfCones.id, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, hom_inv_id, CategoryTheory.Functor.mapConeMapCone_hom_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Limits.Cone.postcomposeComp_hom_app_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_functor_map_hom, CategoryTheory.Mon.forgetMapConeLimitConeIso_inv_hom, inv_hom_id_assoc, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_functor_map_hom, CategoryTheory.Limits.coneUnopOfCoconeEquiv_counitIso, CategoryTheory.Mon.forgetMapConeLimitConeIso_hom_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, CategoryTheory.Limits.Multifork.ext_hom_hom, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, CategoryTheory.Limits.Cone.postcomposeComp_inv_app_hom, CategoryTheory.Limits.Cone.ext_inv_inv_hom, CategoryTheory.Limits.Fork.isoForkOfι_hom_hom, CategoryTheory.Limits.Cone.eta_hom_hom, CategoryTheory.Limits.Cone.fromCostructuredArrow_map_hom, CategoryTheory.Functor.mapConePostcompose_inv_hom, CategoryTheory.Limits.Cone.extendIso_hom_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, CategoryTheory.Limits.Cone.extendId_hom_hom, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, CategoryTheory.Limits.IsLimit.liftConeMorphism_hom, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, w, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, CategoryTheory.Limits.coconeRightOpOfConeEquiv_functor_map_hom, CategoryTheory.Functor.mapCoconeOp_inv_hom, CategoryTheory.Limits.Fork.hom_comp_ι, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_map_hom, map_w_assoc, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.Limits.Wedge.ext_hom_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.Limits.IsLimit.ofIsoLimit_lift, CategoryTheory.Limits.coconeUnopOfConeEquiv_counitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, map_w, CategoryTheory.Limits.coconeUnopOfConeEquiv_functor_map_hom, CategoryTheory.Limits.Cone.category_id_hom, CategoryTheory.Limits.coconeOpEquiv_inverse_map, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_map_hom, CategoryTheory.Limits.Fork.hom_comp_ι_assoc, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, CategoryTheory.Limits.Cone.whiskering_map_hom, CategoryTheory.Over.conePost_map_hom, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_inv_hom, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.Limits.DiagramOfCones.conePoints_map, CategoryTheory.Limits.Cone.mapConeToUnder_inv_hom, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, CategoryTheory.Limits.Cone.extendHom_hom, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.Limits.Cone.extendId_inv_hom, CategoryTheory.Limits.Fan.ext_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.Limits.coneOpEquiv_counitIso, CategoryTheory.Limits.coneUnopOfCoconeEquiv_functor_map_hom, CategoryTheory.Limits.Cone.extendComp_inv_hom, CategoryTheory.Limits.Fan.ext_hom_hom, CategoryTheory.Functor.Initial.extendCone_map_hom, CategoryTheory.Limits.Cone.toCostructuredArrow_map, CategoryTheory.Limits.PullbackCone.eta_inv_hom, CategoryTheory.Limits.instIsIsoHomInvCone, w_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_inverse_map, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_hom_hom, ext_iff, CategoryTheory.Over.conePostIso_inv_app_hom, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.Limits.Fork.mkHom_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_map_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.Limits.PullbackCone.eta_hom_hom, CategoryTheory.Limits.Cone.ext_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Limits.IsLimit.mkConeMorphism_lift, CategoryTheory.Functor.mapConeWhisker_hom_hom, CategoryTheory.Limits.coneOpEquiv_functor_map_hom, CategoryTheory.Limits.Cone.ext_inv_hom_hom, CategoryTheory.Limits.Wedge.ext_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_map_hom, CategoryTheory.Limits.Cone.category_comp_hom, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, hom_inv_id_assoc, CategoryTheory.Limits.Cone.ext_hom_hom, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_functor_map_hom, CategoryTheory.Limits.limit.coneMorphism_hom, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_inverse_map, CategoryTheory.Limits.coconeRightOpOfConeEquiv_counitIso, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.Functor.RightExtension.coneAtFunctor_map_hom, CategoryTheory.Functor.mapConePostcompose_hom_hom, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_hom_hom, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.Limits.DiagramOfCones.comp, CategoryTheory.Functor.mapCoconeOp_hom_hom, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, CategoryTheory.Limits.limit.coneMorphism_π, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_counitIso, CategoryTheory.Limits.Cone.mapConeToUnder_hom_hom, CategoryTheory.Limits.Cone.functoriality_map_hom, CategoryTheory.Limits.Cone.postcomposeId_inv_app_hom, CategoryTheory.Limits.coneUnopOfCoconeEquiv_inverse_map, CategoryTheory.Limits.Multifork.hom_comp_ι, CategoryTheory.Limits.coconeOpEquiv_counitIso, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, CategoryTheory.Limits.Cone.extendComp_hom_hom, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_counitIso, CategoryTheory.Limits.Multifork.ext_inv_hom, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, CategoryTheory.Functor.mapConeMapCone_inv_hom, CategoryTheory.Limits.BinaryFan.ext_hom_hom, CategoryTheory.Limits.Trident.mkHom_hom, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Limits.Cone.extendIso_inv_hom, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, CategoryTheory.Limits.Fork.isoForkOfι_inv_hom, CategoryTheory.Limits.Cone.postcomposeId_hom_app_hom, CategoryTheory.Functor.mapConeWhisker_inv_hom, CategoryTheory.Limits.Cone.forget_map, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.Limits.Multifork.hom_comp_ι_assoc, CategoryTheory.Limits.Cone.postcompose_map_hom, CategoryTheory.Limits.Cone.eta_inv_hom, CategoryTheory.Limits.coconeOpEquiv_functor_map_hom, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, CategoryTheory.Limits.instIsIsoHomHomCone, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Over.ConstructProducts.conesEquivInverse_map_hom, CategoryTheory.Adjunction.functorialityCounit'_app_hom, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_counitIso, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_map_hom, inv_hom_id, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	hom	—	—	—
ext_iff 📖	mathematical	—	hom	—	ext
hom_inv_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt hom CategoryTheory.Iso.hom CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Iso.inv CategoryTheory.CategoryStruct.id	—	CategoryTheory.Iso.hom_inv_id
hom_inv_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt hom CategoryTheory.Iso.hom CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Iso.inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' hom_inv_id
inv_hom_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Iso.hom CategoryTheory.CategoryStruct.id	—	CategoryTheory.Iso.inv_hom_id
inv_hom_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Iso.hom	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' inv_hom_id
map_w 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Limits.Cone.pt CategoryTheory.Functor.map hom CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cone.π	—	w
map_w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Limits.Cone.pt CategoryTheory.Functor.map hom CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cone.π	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' map_w
w 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt CategoryTheory.Functor.obj hom CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cone.π	—	—
w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt hom CategoryTheory.Functor.obj CategoryTheory.NatTrans.app CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cone.π	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' w

CategoryTheory.Limits.Cones

Definitions

Name	Category	Theorems
equivalenceOfReindexing 📖	CompOp	—
eta 📖	CompOp	—
ext 📖	CompOp	—
extend 📖	CompOp	—
extendComp 📖	CompOp	—
extendId 📖	CompOp	—
extendIso 📖	CompOp	—
forget 📖	CompOp	—
functoriality 📖	CompOp	—
functorialityCompFunctoriality 📖	CompOp	—
functorialityEquivalence 📖	CompOp	—
postcompose 📖	CompOp	—
postcomposeComp 📖	CompOp	—
postcomposeEquivalence 📖	CompOp	—
postcomposeId 📖	CompOp	—
whiskering 📖	CompOp	—
whiskeringEquivalence 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cone_iso_of_hom_iso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category	—	CategoryTheory.Limits.Cone.cone_iso_of_hom_iso
functoriality_faithful 📖	mathematical	—	CategoryTheory.Functor.Faithful CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Functor.comp CategoryTheory.Limits.Cone.functoriality	—	CategoryTheory.Limits.Cone.functoriality_faithful
functoriality_full 📖	mathematical	—	CategoryTheory.Functor.Full CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Functor.comp CategoryTheory.Limits.Cone.functoriality	—	CategoryTheory.Limits.Cone.functoriality_full
reflects_cone_isomorphism 📖	mathematical	—	CategoryTheory.Functor.ReflectsIsomorphisms CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Functor.comp CategoryTheory.Limits.Cone.functoriality	—	CategoryTheory.Limits.Cone.reflects_cone_isomorphism

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