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, extend, extensions, op, pt, unop, whisker, ι, CoconeMorphism, hom, equivalenceOfReindexing, eta, ext, extend, extendComp, extendId, extendIso, forget, functoriality, functorialityCompFunctoriality, functorialityEquivalence, precompose, precomposeComp, precomposeEquivalence, precomposeId, whiskering, whiskeringEquivalence, category, equiv, extend, extensions, op, pt, unop, whisker, π, ConeMorphism, hom, equivalenceOfReindexing, eta, ext, extend, extendComp, extendId, extendIso, forget, functoriality, functorialityCompFunctoriality, functorialityEquivalence, postcompose, postcomposeComp, postcomposeEquivalence, postcomposeId, whiskering, whiskeringEquivalence, coconeEquivalenceOpConeOp, coconeLeftOpOfCone, coconeOfConeLeftOp, coconeOfConeRightOp, coconeOfConeUnop, coconeRightOpOfCone, coconeUnopOfCone, coneLeftOpOfCocone, coneOfCoconeLeftOp, coneOfCoconeRightOp, coneOfCoconeUnop, coneRightOpOfCocone, coneUnopOfCocone, inhabitedCocone, inhabitedCoconeMorphism, inhabitedCone, inhabitedConeMorphism, cocones, cones	102
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, extend_pt, extend_ι, extensions_app, op_pt, op_π, unop_pt, unop_π, w, w_assoc, whisker_pt, whisker_ι, 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, cocone_iso_of_hom_iso, equivalenceOfReindexing_functor_obj, eta_hom_hom, eta_inv_hom, ext_hom_hom, ext_inv_hom, extendComp_hom_hom, extendComp_inv_hom, extendId_hom_hom, extendId_inv_hom, extendIso_hom_hom, extendIso_inv_hom, extend_hom, 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, instIsIsoCoconeExtend, precomposeEquivalence_counitIso, precomposeEquivalence_functor, precomposeEquivalence_inverse, precomposeEquivalence_unitIso, precompose_map_hom, precompose_obj_pt, precompose_obj_ι, reflects_cocone_isomorphism, whiskeringEquivalence_counitIso, whiskeringEquivalence_functor, whiskeringEquivalence_inverse, whiskeringEquivalence_unitIso, whiskering_map_hom, whiskering_obj, category_comp_hom, category_id_hom, equiv_hom_fst, equiv_hom_snd, equiv_inv_pt, equiv_inv_π, extend_pt, extend_π, extensions_app, op_pt, op_ι, unop_pt, unop_ι, w, w_assoc, whisker_pt, whisker_π, 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, equivalenceOfReindexing_counitIso, equivalenceOfReindexing_functor, equivalenceOfReindexing_inverse, equivalenceOfReindexing_unitIso, eta_hom_hom, eta_inv_hom, ext_hom_hom, ext_inv_hom, extendComp_hom_hom, extendComp_inv_hom, extendId_hom_hom, extendId_inv_hom, extendIso_hom_hom, extendIso_inv_hom, extend_hom, 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, instIsIsoConeExtend, 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, whiskeringEquivalence_counitIso, whiskeringEquivalence_functor, whiskeringEquivalence_inverse, whiskeringEquivalence_unitIso, whiskering_map_hom, whiskering_obj, coconeEquivalenceOpConeOp_counitIso, coconeEquivalenceOpConeOp_functor_map, coconeEquivalenceOpConeOp_functor_obj, coconeEquivalenceOpConeOp_inverse_map_hom, coconeEquivalenceOpConeOp_inverse_obj, coconeEquivalenceOpConeOp_unitIso, coconeLeftOpOfCone_pt, coconeLeftOpOfCone_ι_app, coconeOfConeLeftOp_pt, coconeOfConeLeftOp_ι_app, coconeOfConeRightOp_pt, coconeOfConeRightOp_ι, coconeOfConeUnop_pt, coconeOfConeUnop_ι, coconeRightOpOfCone_pt, coconeRightOpOfCone_ι, coconeUnopOfCone_pt, coconeUnopOfCone_ι, coneLeftOpOfCocone_pt, coneLeftOpOfCocone_π_app, coneOfCoconeLeftOp_pt, coneOfCoconeLeftOp_π_app, coneOfCoconeRightOp_pt, coneOfCoconeRightOp_π, coneOfCoconeUnop_pt, coneOfCoconeUnop_π, coneRightOpOfCocone_pt, coneRightOpOfCocone_π, 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	211
Total	313

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	7 math math: CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.Limits.yonedaCompLimIsoCocones_hom_app_app, cocones_obj, CategoryTheory.Limits.Cocone.extend_ι, cocones_map_app, CategoryTheory.Limits.Cocone.extensions_app
cones 📖	CompOp	11 math math: CategoryTheory.Limits.Cone.equiv_inv_pt, cones_map_app, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, CategoryTheory.Limits.Cone.extend_π, 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	46 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, 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	56 math math: mapConeMapCone_hom_hom, CategoryTheory.Monad.ForgetCreatesLimits.liftedConeIsLimit_lift_f, CategoryTheory.Limits.PreservesLimit.preserves, 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, 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.Cones.functoriality CategoryTheory.Limits.Cones.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.Cones.functoriality CategoryTheory.Limits.Cones.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.Cocones.functoriality CategoryTheory.Limits.Cocones.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.Cocones.functoriality CategoryTheory.Limits.Cocones.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.Cocones.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.Cocones.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.Cocones.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.Cocones.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.Cones.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.Cones.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.Cones.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.Cones.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.Cones.functoriality CategoryTheory.Limits.Cones.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.Cones.functoriality CategoryTheory.Limits.Cones.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.Cocones.functoriality CategoryTheory.Limits.Cocones.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.Cocones.functoriality CategoryTheory.Limits.Cocones.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	149 math math: Cocones.precompose_obj_ι, CategoryTheory.Functor.LeftExtension.coconeAtFunctor_map_hom, Cocone.category_id_hom, IsColimit.uniqueUpToIso_hom, coconeEquivalenceOpConeOp_unitIso, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, CategoryTheory.WithInitial.coconeEquiv_functor_obj_pt, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, Cocones.ext_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, PushoutCocone.unop_π_app, Cocones.cocone_iso_of_hom_iso, Types.isColimit_iff_coconeTypesIsColimit, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, Cocones.precomposeEquivalence_functor, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_right, CategoryTheory.Functor.Final.colimitCoconeOfComp_isColimit, CategoryTheory.Functor.Final.coconesEquiv_unitIso, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, Cocones.whiskeringEquivalence_unitIso, Cocones.eta_inv_hom, instIsIsoHomHomCocone, Cocones.whiskeringEquivalence_inverse, PushoutCocone.isoMk_inv_hom, colimit.map_desc, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, Cocones.precompose_obj_pt, CategoryTheory.Functor.Final.extendCocone_obj_ι_app, CategoryTheory.Functor.Final.coconesEquiv_functor, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, CoconeMorphism.hom_inv_id_assoc, Cocones.precomposeEquivalence_unitIso, Cocones.whiskering_obj, Cocones.equivalenceOfReindexing_functor_obj, CategoryTheory.Functor.coconeTypesEquiv_apply_pt, Cocone.category_comp_hom, CategoryTheory.IsUniversalColimit.precompose_isIso, HasColimit.isoOfNatIso_inv_desc_assoc, IsColimit.ofCoconeEquiv_symm_apply_desc, HasColimit.isoOfNatIso_hom_desc, Cocones.extendId_hom_hom, IsInitial.to_eq_descCoconeMorphism, DiagramOfCocones.coconePoints_map, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_pt, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, Cocones.functoriality_obj_pt, CategoryTheory.Adjunction.functorialityUnit_app_hom, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.Functor.mapCoconeMapCocone_hom_hom, Cocones.forget_obj, CategoryTheory.IsFiltered.cocone_nonempty, coconeEquivalenceOpConeOp_functor_obj, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, Cocone.toStructuredArrow_obj, CategoryTheory.IsCardinalFiltered.nonempty_cocone, CategoryTheory.IsVanKampenColimit.precompose_isIso, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, IsColimit.coconePointsIsoOfEquivalence_hom, DiagramOfCocones.comp, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_left_as, Cofork.π_precompose, Cocone.equivStructuredArrow_unitIso, Cocones.extendComp_hom_hom, Cocones.reflects_cocone_isomorphism, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.IsFiltered.iff_cocone_nonempty, Cocone.fromStructuredArrow_obj_pt, DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, 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', Cocones.functoriality_obj_ι_app, CategoryTheory.IsVanKampenColimit.precompose_isIso_iff, CategoryTheory.Functor.LeftExtension.coconeAtFunctor_obj, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, SheafOfModules.Presentation.map_relations_I, reflexiveCoforkEquivCofork_inverse_obj_pt, Cocones.functorialityEquivalence_counitIso, Cocones.extendComp_inv_hom, Cocones.eta_hom_hom, IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.Functor.coconeTypesEquiv_apply_ι_app, Cocones.functoriality_faithful, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, Cocone.fromStructuredArrow_map_hom, CoconeMorphism.hom_inv_id, HasColimit.isoOfNatIso_hom_desc_assoc, Cocones.functoriality_full, Cocones.whiskeringEquivalence_functor, Cocone.equivStructuredArrow_inverse, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, Cocone.mapCoconeToOver_inv_hom, IsColimit.equivIsoColimit_symm_apply, colimit.map_desc_assoc, Cocones.extendIso_hom_hom, CategoryTheory.Functor.mapConeOp_inv_hom, CategoryTheory.Functor.Final.coconesEquiv_counitIso, IsColimit.hom_isIso, IsColimit.uniqueUpToIso_inv, Cocones.functoriality_map_hom, CoconeMorphism.inv_hom_id, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, DiagramOfCocones.id, IsColimit.ofIsoColimit_desc, Cocones.ext_hom_hom, coconeEquivalenceOpConeOp_inverse_obj, PushoutCocone.isoMk_hom_hom, coconeEquivalenceOpConeOp_counitIso, Cocones.precomposeEquivalence_inverse, Cocones.extendId_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, hasColimit_iff_hasInitial_cocone, CategoryTheory.Functor.mapConeOp_hom_hom, Cocones.functorialityEquivalence_inverse, Cocones.forget_map, Cocone.toStructuredArrow_map, CategoryTheory.Functor.Final.extendCocone_obj_pt, coconeEquivalenceOpConeOp_inverse_map_hom, instIsIsoHomInvCocone, CategoryTheory.Functor.Final.extendCocone_map_hom, Cocone.mapCoconeToOver_hom_hom, CoconeMorphism.inv_hom_id_assoc, coconeEquivalenceOpConeOp_functor_map, CategoryTheory.Functor.CoconeTypes.isColimit_iff, Cocones.precompose_map_hom, Cocone.equivStructuredArrow_functor, Cocone.fromStructuredArrow_obj_ι, Cocone.equivStructuredArrow_counitIso, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, Cocones.whiskering_map_hom, Cocones.functorialityEquivalence_functor, HasColimit.isoOfNatIso_inv_desc, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, Cocones.instIsIsoCoconeExtend, Cocones.whiskeringEquivalence_counitIso, Cocones.functorialityEquivalence_unitIso, CategoryTheory.Functor.Final.coconesEquiv_inverse, Cocones.extendIso_inv_hom, Cocones.precomposeEquivalence_counitIso, CategoryTheory.Functor.Final.colimitCoconeOfComp_cocone
CoconeMorphism 📖	CompData	—
ConeMorphism 📖	CompData	—
coconeEquivalenceOpConeOp 📖	CompOp	6 math math: coconeEquivalenceOpConeOp_unitIso, coconeEquivalenceOpConeOp_functor_obj, coconeEquivalenceOpConeOp_inverse_obj, coconeEquivalenceOpConeOp_counitIso, coconeEquivalenceOpConeOp_inverse_map_hom, coconeEquivalenceOpConeOp_functor_map
coconeLeftOpOfCone 📖	CompOp	5 math math: isColimitCoconeLeftOpOfCone_desc, isLimitOfCoconeLeftOpOfCone_lift, isLimitConeOfCoconeLeftOp_lift, coconeLeftOpOfCone_ι_app, coconeLeftOpOfCone_pt
coconeOfConeLeftOp 📖	CompOp	5 math math: coconeOfConeLeftOp_pt, isLimitOfCoconeOfConeLeftOp_lift, isLimitConeLeftOpOfCocone_lift, coconeOfConeLeftOp_ι_app, isColimitCoconeOfConeLeftOp_desc
coconeOfConeRightOp 📖	CompOp	5 math math: isLimitConeRightOpOfCocone_lift, isLimitOfCoconeOfConeRightOp_lift, coconeOfConeRightOp_ι, coconeOfConeRightOp_pt, isColimitCoconeOfConeRightOp_desc
coconeOfConeUnop 📖	CompOp	5 math math: coconeOfConeUnop_pt, isLimitConeUnopOfCocone_lift, isLimitOfCoconeOfConeUnop_lift, coconeOfConeUnop_ι, isColimitCoconeOfConeUnop_desc
coconeRightOpOfCone 📖	CompOp	6 math math: LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, isLimitOfCoconeRightOpOfCone_lift, isLimitConeOfCoconeRightOp_lift, isColimitCoconeRightOpOfCone_desc, coconeRightOpOfCone_ι, coconeRightOpOfCone_pt
coconeUnopOfCone 📖	CompOp	5 math math: isLimitConeOfCoconeUnop_lift, isColimitCoconeUnopOfCone_desc, coconeUnopOfCone_pt, isLimitOfCoconeUnopOfCone_lift, coconeUnopOfCone_ι
coneLeftOpOfCocone 📖	CompOp	5 math math: coneLeftOpOfCocone_π_app, isColimitOfConeLeftOpOfCocone_desc, coneLeftOpOfCocone_pt, isLimitConeLeftOpOfCocone_lift, isColimitCoconeOfConeLeftOp_desc
coneOfCoconeLeftOp 📖	CompOp	5 math math: isColimitCoconeLeftOpOfCone_desc, coneOfCoconeLeftOp_π_app, isColimitOfConeOfCoconeLeftOp_desc, coneOfCoconeLeftOp_pt, isLimitConeOfCoconeLeftOp_lift
coneOfCoconeRightOp 📖	CompOp	5 math math: coneOfCoconeRightOp_π, isLimitConeOfCoconeRightOp_lift, coneOfCoconeRightOp_pt, isColimitCoconeRightOpOfCone_desc, isColimitOfConeOfCoconeRightOp_desc
coneOfCoconeUnop 📖	CompOp	5 math math: coneOfCoconeUnop_π, isLimitConeOfCoconeUnop_lift, isColimitCoconeUnopOfCone_desc, isColimitOfConeOfCoconeUnop_desc, coneOfCoconeUnop_pt
coneRightOpOfCocone 📖	CompOp	5 math math: isLimitConeRightOpOfCocone_lift, isColimitOfConeRightOpOfCocone_desc, coneRightOpOfCocone_π, coneRightOpOfCocone_pt, isColimitCoconeOfConeRightOp_desc
coneUnopOfCocone 📖	CompOp	5 math math: coneUnopOfCocone_pt, isColimitOfConeUnopOfCocone_desc, isLimitConeUnopOfCocone_lift, coneUnopOfCocone_π, isColimitCoconeOfConeUnop_desc
inhabitedCocone 📖	CompOp	—
inhabitedCoconeMorphism 📖	CompOp	—
inhabitedCone 📖	CompOp	—
inhabitedConeMorphism 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coconeEquivalenceOpConeOp_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso Cocone Opposite Cone CategoryTheory.Category.opposite CategoryTheory.Functor.op Cocone.category Cone.category coconeEquivalenceOpConeOp CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.comp Cone.unop Opposite.unop Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cone.pt ConeMorphism.hom Opposite.op Cocone.op Quiver.Hom.op Cocone.pt CoconeMorphism.hom CategoryTheory.Functor.id CategoryTheory.Iso.op Cones.ext CategoryTheory.Iso.refl	—	—
coconeEquivalenceOpConeOp_functor_map 📖	mathematical	—	CategoryTheory.Functor.map Cocone Cocone.category Opposite Cone CategoryTheory.Category.opposite CategoryTheory.Functor.op Cone.category CategoryTheory.Equivalence.functor coconeEquivalenceOpConeOp Quiver.Hom.op CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cocone.op Cocone.pt CoconeMorphism.hom	—	—
coconeEquivalenceOpConeOp_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj Cocone Cocone.category Opposite Cone CategoryTheory.Category.opposite CategoryTheory.Functor.op Cone.category CategoryTheory.Equivalence.functor coconeEquivalenceOpConeOp Opposite.op Cocone.op	—	—
coconeEquivalenceOpConeOp_inverse_map_hom 📖	mathematical	—	CoconeMorphism.hom Cone.unop Opposite.unop Cone Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.Functor.map Cone.category Cocone Cocone.category CategoryTheory.Equivalence.inverse coconeEquivalenceOpConeOp Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cone.pt ConeMorphism.hom	—	—
coconeEquivalenceOpConeOp_inverse_obj 📖	mathematical	—	CategoryTheory.Functor.obj Opposite Cone CategoryTheory.Category.opposite CategoryTheory.Functor.op Cone.category Cocone Cocone.category CategoryTheory.Equivalence.inverse coconeEquivalenceOpConeOp Cone.unop Opposite.unop	—	—
coconeEquivalenceOpConeOp_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso Cocone Opposite Cone CategoryTheory.Category.opposite CategoryTheory.Functor.op Cocone.category Cone.category coconeEquivalenceOpConeOp CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.id CategoryTheory.Functor.comp Opposite.op Cocone.op Quiver.Hom.op CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cocone.pt CoconeMorphism.hom Cone.unop Opposite.unop Quiver.Hom.unop Cone.pt ConeMorphism.hom Cocones.ext CategoryTheory.Functor.obj CategoryTheory.Iso.refl	—	—
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 Cocone.pt coconeOfConeLeftOp Cocone.ι Quiver.Hom.op CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Cone.pt CategoryTheory.Functor.leftOp Opposite.op 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	—	—
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	—	—
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	—	—
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	—	—
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	—	—
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.hom Cocone Cocone.category	—	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.inv Cocone Cocone.category	—	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	180 math math: CategoryTheory.Limits.Cocones.precompose_obj_ι, CategoryTheory.Functor.LeftExtension.coconeAtFunctor_map_hom, category_id_hom, CategoryTheory.Limits.IsColimit.uniqueUpToIso_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, 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, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, CategoryTheory.Limits.Cocones.ext_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Limits.Cocones.cocone_iso_of_hom_iso, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_obj, CategoryTheory.Limits.Cocones.precomposeEquivalence_functor, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, CategoryTheory.Functor.Final.colimitCoconeOfComp_isColimit, CategoryTheory.Functor.Final.coconesEquiv_unitIso, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, CategoryTheory.Limits.Cocones.whiskeringEquivalence_unitIso, CategoryTheory.Limits.Cocones.eta_inv_hom, CategoryTheory.Limits.instIsIsoHomHomCocone, CategoryTheory.Limits.Cocones.whiskeringEquivalence_inverse, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.colimit.map_desc, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, CategoryTheory.Limits.Cocones.precompose_obj_pt, 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.Cocones.precomposeEquivalence_unitIso, CategoryTheory.Limits.Cocones.whiskering_obj, CategoryTheory.Limits.Cocones.equivalenceOfReindexing_functor_obj, 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, CategoryTheory.Limits.Cocones.extendId_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.IsInitial.to_eq_descCoconeMorphism, CategoryTheory.Limits.DiagramOfCocones.coconePoints_map, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, CategoryTheory.Limits.Cocones.functoriality_obj_pt, 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.Cocones.forget_obj, CategoryTheory.Limits.PushoutCocone.eta_inv_hom, CategoryTheory.Limits.BinaryCofan.ext_hom_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_obj, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, toStructuredArrow_obj, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_obj, CategoryTheory.IsVanKampenColimit.precompose_isIso, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_hom, CategoryTheory.Limits.DiagramOfCocones.comp, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_left_as, CategoryTheory.Limits.Cofork.π_precompose, equivStructuredArrow_unitIso, CategoryTheory.Limits.Cocones.extendComp_hom_hom, CategoryTheory.Limits.Cofan.ext_hom_hom, CategoryTheory.Limits.Cowedge.ext_hom_hom, CategoryTheory.Limits.Cocones.reflects_cocone_isomorphism, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, fromStructuredArrow_obj_pt, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_map_hom, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, 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', CategoryTheory.Limits.Cocones.functoriality_obj_ι_app, CategoryTheory.IsVanKampenColimit.precompose_isIso_iff, CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_π, CategoryTheory.Functor.LeftExtension.coconeAtFunctor_obj, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, SheafOfModules.Presentation.map_relations_I, CategoryTheory.Limits.reflexiveCoforkEquivCofork_inverse_obj_pt, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt, CategoryTheory.Limits.Cocones.functorialityEquivalence_counitIso, CategoryTheory.Limits.Cofork.ext_inv, CategoryTheory.Limits.Cocones.extendComp_inv_hom, CategoryTheory.Limits.Cocones.eta_hom_hom, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.Limits.Cocones.functoriality_faithful, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, fromStructuredArrow_map_hom, CategoryTheory.Limits.CoconeMorphism.hom_inv_id, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.Cocones.functoriality_full, CategoryTheory.Limits.Cocones.whiskeringEquivalence_functor, CategoryTheory.Limits.Multicofork.ext_inv_hom, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_obj, CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, CategoryTheory.Limits.Cowedge.ext_inv_hom, CategoryTheory.Limits.Cofork.ext_hom, equivStructuredArrow_inverse, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, mapCoconeToOver_inv_hom, CategoryTheory.Limits.IsColimit.equivIsoColimit_symm_apply, CategoryTheory.Limits.colimit.map_desc_assoc, CategoryTheory.Limits.Cocones.extendIso_hom_hom, 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.Cocones.functoriality_map_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_inverse, CategoryTheory.Limits.CoconeMorphism.inv_hom_id, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, CategoryTheory.Limits.DiagramOfCocones.id, CategoryTheory.Limits.IsColimit.ofIsoColimit_desc, CategoryTheory.Limits.Cocones.ext_hom_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_obj, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.Limits.Cocones.precomposeEquivalence_inverse, CategoryTheory.Limits.Cocones.extendId_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, CategoryTheory.Limits.hasColimit_iff_hasInitial_cocone, CategoryTheory.Functor.mapConeOp_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Cocones.functorialityEquivalence_inverse, CategoryTheory.Limits.Cocones.forget_map, toStructuredArrow_map, CategoryTheory.Functor.Final.extendCocone_obj_pt, CategoryTheory.Limits.PushoutCocone.eta_hom_hom, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_map_hom, 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.CoconeMorphism.inv_hom_id_assoc, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_map, CategoryTheory.Limits.Cocones.precompose_map_hom, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom, equivStructuredArrow_functor, fromStructuredArrow_obj_ι, equivStructuredArrow_counitIso, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.Limits.Cocones.whiskering_map_hom, CategoryTheory.Limits.Cocones.functorialityEquivalence_functor, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.Limits.Cocones.instIsIsoCoconeExtend, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_functor, CategoryTheory.Limits.Cocones.whiskeringEquivalence_counitIso, CategoryTheory.Limits.Cocones.functorialityEquivalence_unitIso, CategoryTheory.Functor.Final.coconesEquiv_inverse, CategoryTheory.Limits.Cocones.extendIso_inv_hom, CategoryTheory.Limits.Cocones.precomposeEquivalence_counitIso, CategoryTheory.Functor.Final.colimitCoconeOfComp_cocone
equiv 📖	CompOp	—
extend 📖	CompOp	17 math math: CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app, CategoryTheory.Limits.colimit.desc_extend, CategoryTheory.Limits.IsColimit.homIso_hom, CategoryTheory.Limits.IsColimit.homEquiv_apply, CategoryTheory.Limits.Cocones.extendId_hom_hom, CategoryTheory.Limits.IsColimit.OfNatIso.cocone_fac, CategoryTheory.Limits.Cocones.extendComp_hom_hom, CategoryTheory.Limits.Cocones.extend_hom, CategoryTheory.Limits.Cocones.extendComp_inv_hom, CategoryTheory.Limits.IndObjectPresentation.extend_isColimit_desc_app, CategoryTheory.Limits.Cocones.extendIso_hom_hom, CategoryTheory.Limits.Cocones.extendId_inv_hom, extend_ι, CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac, extend_pt, CategoryTheory.Limits.Cocones.instIsIsoCoconeExtend, CategoryTheory.Limits.Cocones.extendIso_inv_hom
extensions 📖	CompOp	2 math math: extend_ι, extensions_app
op 📖	CompOp	22 math math: CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, 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.coconeEquivalenceOpConeOp_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.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.Presheaf.isLimit_iff_isSheafFor, TopCat.Presheaf.IsSheaf.isSheafOpensLeCover, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_map, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology
pt 📖	CompOp	837 math math: ModuleCat.HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.Limits.Cocones.precompose_obj_ι, TopCat.binaryCofan_isColimit_iff, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id_assoc, category_id_hom, 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.coconeEquivalenceOpConeOp_unitIso, 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, PartOrdEmb.Limits.cocone_pt_coe, toOver_ι_app, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit, CategoryTheory.Functor.mapCocone_ι_app, CategoryTheory.PreOneHypercover.forkOfIsColimit_pt, CategoryTheory.Limits.colimit.cocone_ι, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.hf, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, CategoryTheory.Limits.Fork.π_comp_hom, CategoryTheory.Limits.CoconeMorphism.w, CategoryTheory.WithInitial.coconeEquiv_functor_obj_pt, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, 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.PreZeroHypercover.sigmaOfIsColimit_X, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_f, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit', CategoryTheory.Limits.Cocones.ext_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, CategoryTheory.Limits.PushoutCocone.unop_π_app, 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.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.WithInitial.coconeEquiv_inverse_obj_pt_right, CategoryTheory.Monad.beckCoequalizer_desc, toCostructuredArrow_comp_proj, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt_assoc, CategoryTheory.Mono.of_coproductDisjoint, 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.Limits.Cotrident.π_eq_app_one, CategoryTheory.Limits.PushoutCocone.condition_assoc, CategoryTheory.Limits.coconeOfConeLeftOp_pt, CategoryTheory.Limits.Cofan.isColimit_iff_isIso_sigmaDesc, CategoryTheory.Limits.Cocones.whiskeringEquivalence_unitIso, toCostructuredArrow_map, CategoryTheory.Limits.Cocones.eta_inv_hom, 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.IsColimit.ι_map, CategoryTheory.BinaryCofan.isVanKampen_iff, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, Preorder.coconePt_mem_upperBounds, CategoryTheory.Functor.costructuredArrowMapCocone_pt, 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.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, toCostructuredArrowCompProj_hom_app, CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff_aux, CategoryTheory.isPullback_of_cofan_isVanKampen, CategoryTheory.Limits.Cocones.precompose_obj_pt, 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.Cocones.precomposeEquivalence_unitIso, 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, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingProperty_ι_app_bot, AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self_assoc, 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, CategoryTheory.ObjectProperty.isStrongGenerator_iff_exists_extremalEpi, CategoryTheory.Limits.Cotrident.ofπ_pt, 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.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, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.Cocones.extendId_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.Cowedge.IsColimit.π_desc, 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, CategoryTheory.Limits.Types.Colimit.ι_desc_apply', 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.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.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, CategoryTheory.Limits.Cocones.functoriality_obj_pt, 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.Cocones.forget_obj, CategoryTheory.Limits.PushoutCocone.eta_inv_hom, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, CategoryTheory.Limits.Fork.op_pt, CategoryTheory.Limits.Multicofork.π_eq_app_right, HomologicalComplex.coconeOfHasColimitEval_pt_X, CommRingCat.FilteredColimits.nontrivial, SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero, SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero, 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.Limits.Cofork.op_π_app_zero, AddCommGrpCat.Colimits.colimitCocone_pt, CategoryTheory.Limits.Cofork.IsColimit.π_desc_assoc, 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, 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.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, 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, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv_assoc, CategoryTheory.Limits.isLimitConeUnopOfCocone_lift, CategoryTheory.Limits.Cocones.extendComp_hom_hom, 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, 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.Functor.precomposeWhiskerLeftMapCocone_inv_hom, 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.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.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, 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.HasLiftingProperty.transfiniteComposition.SqStruct.w, CategoryTheory.Monad.beckCofork_pt, CategoryTheory.Limits.Cocones.functoriality_obj_ι_app, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc, CategoryTheory.preservesColimitIso_inv_comp_desc_assoc, CategoryTheory.BinaryCofan.mono_inr_of_isVanKampen, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inl, CategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork_H, CategoryTheory.Limits.Cofork.condition, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right, 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.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, CategoryTheory.Limits.Cotrident.IsColimit.homIso_symm_apply, CategoryTheory.extendCofan_pt, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom_assoc, CategoryTheory.Limits.isLimitConeOfCoconeRightOp_lift, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, CategoryTheory.Limits.colimit.pre_desc_assoc, 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, CategoryTheory.Limits.Cocones.functorialityEquivalence_counitIso, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right_assoc, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, CategoryTheory.Limits.Types.pushoutCocone_inr_mono_of_isColimit, CategoryTheory.Limits.Cocones.extendComp_inv_hom, 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, CategoryTheory.Limits.Cocones.eta_hom_hom, 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.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, 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.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, CommRingCat.coproductCoconeIsColimit_desc, CategoryTheory.Limits.Cotrident.app_one, CategoryTheory.Limits.PushoutCocone.epi_inr_of_is_pushout_of_epi, CategoryTheory.Limits.coconeFiberwiseColimitOfCocone_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, ofPushoutCocone_ι, SSet.horn₃₁.desc.multicofork_π_three_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, CategoryTheory.Limits.isLimitConeOfCoconeLeftOp_lift, 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.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.colimit.ι_desc_assoc, CategoryTheory.IsPushout.of_is_coproduct, CategoryTheory.Abelian.mono_inl_of_isColimit, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.gluedCocone_pt, CategoryTheory.Limits.colimit.ι_desc_app_assoc, toCostructuredArrow_obj, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, CategoryTheory.Limits.coconePointwiseProduct_pt, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, 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, 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.Functor.LeftExtension.coconeAt_pt, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty_assoc, 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.Cocones.extendIso_hom_hom, CategoryTheory.Limits.PushoutCocone.mk_ι_app_right, CategoryTheory.Limits.Multicofork.snd_app_right, 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.Cocones.functoriality_map_hom, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.Limits.DiagramOfCocones.coconePoints_obj, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, 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.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, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_pt, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, AddCommGrpCat.Colimits.Quot.desc_quotQuotUliftAddEquiv, TopCat.coconeOfCoconeForget_pt, 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.Limits.Cocones.ext_hom_hom, CategoryTheory.Limits.IsColimit.isIso_ι_app_of_isTerminal, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_obj, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, op_π, 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.coconeEquivalenceOpConeOp_counitIso, 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.Limits.Cocones.extendId_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, SSet.horn₃₂.desc.multicofork_pt, CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit_ι_app, CategoryTheory.Limits.Cofork.op_π_app_one, 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, 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.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.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, 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.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.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.coconeEquivalenceOpConeOp_functor_map, 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', CategoryTheory.Limits.coneUnopOfCocone_π, CategoryTheory.Limits.Cotrident.app_one_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, extend_pt, CategoryTheory.Limits.coconeOfDiagramTerminal_pt, CategoryTheory.Limits.coconeOfCoconeCurry_ι_app, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.isSeparator_of_isColimit_cofan, 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.Cocones.precompose_map_hom, 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.FormalCoproduct.cofanHomEquiv_apply_φ, HomotopicalAlgebra.AttachCells.ofArrowIso_g₁, CategoryTheory.FunctorToTypes.binaryCoproductCocone_pt_obj, 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, 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.Cofork.app_one_eq_π, CategoryTheory.PreOneHypercover.p₂_sigmaOfIsColimit_assoc, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, CategoryTheory.Limits.Sigma.cocone_pt, CategoryTheory.epi_iff_isIso_inr, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, 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.Limits.Cocones.whiskeringEquivalence_counitIso, CategoryTheory.Limits.coneOfCoconeUnop_pt, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'_assoc, CategoryTheory.Limits.colimit.pre_eq, CategoryTheory.Limits.CoconeMorphism.map_w, CategoryTheory.Limits.Multicofork.IsColimit.fac, CategoryTheory.Limits.Cocones.extendIso_inv_hom, 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.Cocones.precomposeEquivalence_counitIso, CategoryTheory.Limits.PushoutCocone.unop_fst, 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, 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.Monad.ForgetCreatesColimits.newCocone_ι
unop 📖	CompOp	2 math math: unop_π, unop_pt
whisker 📖	CompOp	21 math math: CategoryTheory.Functor.Final.colimitCoconeComp_cocone, whisker_pt, whisker_ι, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CategoryTheory.Limits.Cocones.whiskering_obj, CategoryTheory.Limits.Cocones.equivalenceOfReindexing_functor_obj, CategoryTheory.Functor.Final.colimitCoconeComp_isColimit, CategoryTheory.Limits.PullbackCone.op_ι_app, 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, CategoryTheory.IsUniversalColimit.whiskerEquivalence_iff, CategoryTheory.Limits.Cocones.whiskering_map_hom, CategoryTheory.Limits.colimit.pre_eq
ι 📖	CompOp	321 math math: CategoryTheory.Limits.Cocones.precompose_obj_ι, 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.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, CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app, CategoryTheory.Limits.Fork.unop_ι_app_zero, ofCotrident_ι, unop_π, CategoryTheory.Limits.Cofork.ofCocone_ι, 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, CategoryTheory.Limits.Cocones.eta_inv_hom, 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.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, CategoryTheory.Limits.IsColimit.homEquiv_apply, AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirected_ι, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.Limits.IsColimit.isIso_colimMap_ι, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.Limits.pointwiseCocone_ι_app_app, CategoryTheory.Limits.Types.Colimit.ι_desc_apply', 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.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, 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, 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.Cocones.functoriality_obj_ι_app, 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, 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, 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.Cocones.eta_hom_hom, 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.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, 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.Cocones.functoriality_map_hom, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, TopCat.nonempty_isColimit_iff_eq_coinduced, 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, 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.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.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, 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.Cocones.precompose_map_hom, 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, 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	—	—
extend_pt 📖	mathematical	—	pt extend	—	—
extend_ι 📖	mathematical	—	ι extend 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	—	—
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	—	—
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	—	—
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 CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt CategoryTheory.Functor.map CategoryTheory.NatTrans.app ι	—	CategoryTheory.NatTrans.naturality CategoryTheory.Category.comp_id
w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.map CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt CategoryTheory.NatTrans.app 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	—	—

CategoryTheory.Limits.CoconeMorphism

Definitions

Name	Category	Theorems
hom 📖	CompOp	105 math math: CategoryTheory.Functor.LeftExtension.coconeAtFunctor_map_hom, CategoryTheory.Limits.Cocone.category_id_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, CategoryTheory.Limits.Fork.π_comp_hom, w, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, CategoryTheory.Limits.Cocones.ext_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, CategoryTheory.Limits.Multicofork.π_comp_hom_assoc, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, CategoryTheory.Limits.Cocones.eta_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.Cocone.category_comp_hom, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, CategoryTheory.Limits.Cofan.ext_inv_hom, CategoryTheory.Limits.Cocones.extendId_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.DiagramOfCocones.coconePoints_map, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, 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.BinaryCofan.ext_hom_hom, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Limits.DiagramOfCocones.comp, CategoryTheory.Limits.Cocones.extendComp_hom_hom, CategoryTheory.Limits.Cofan.ext_hom_hom, CategoryTheory.Limits.Cowedge.ext_hom_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.Limits.Cofork.mkHom_hom, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_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.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, CategoryTheory.Limits.Cocones.extend_hom, CategoryTheory.Limits.Cocones.extendComp_inv_hom, CategoryTheory.Limits.Cocones.eta_hom_hom, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, CategoryTheory.Limits.Cocone.fromStructuredArrow_map_hom, hom_inv_id, CategoryTheory.Limits.IsColimit.descCoconeMorphism_hom, CategoryTheory.Limits.Multicofork.ext_inv_hom, CategoryTheory.Limits.colimit.ι_coconeMorphism, CategoryTheory.Limits.Cowedge.ext_inv_hom, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, CategoryTheory.Limits.Cocone.mapCoconeToOver_inv_hom, CategoryTheory.Limits.Cocones.extendIso_hom_hom, CategoryTheory.Functor.mapConeOp_inv_hom, CategoryTheory.Limits.Cocones.functoriality_map_hom, CategoryTheory.Limits.colimit.coconeMorphism_hom, ext_iff, inv_hom_id, 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.Cocones.ext_hom_hom, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.Limits.Cotrident.mkHom_hom, CategoryTheory.Limits.Cocones.extendId_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, CategoryTheory.Functor.mapConeOp_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Cocones.forget_map, CategoryTheory.Limits.Cocone.toStructuredArrow_map, CategoryTheory.Limits.PushoutCocone.eta_hom_hom, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_map_hom, 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.coconeEquivalenceOpConeOp_functor_map, CategoryTheory.Limits.Cocones.precompose_map_hom, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.Limits.Cocones.whiskering_map_hom, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, map_w, CategoryTheory.Limits.Cocones.extendIso_inv_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.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.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.pt CategoryTheory.Functor.map CategoryTheory.NatTrans.app CategoryTheory.Limits.Cocone.ι hom	—	w
map_w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.pt CategoryTheory.Functor.map CategoryTheory.NatTrans.app 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.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.pt CategoryTheory.NatTrans.app CategoryTheory.Limits.Cocone.ι hom	—	—
w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.pt CategoryTheory.NatTrans.app CategoryTheory.Limits.Cocone.ι hom	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' w

CategoryTheory.Limits.Cocones

Definitions

Name	Category	Theorems
equivalenceOfReindexing 📖	CompOp	3 math math: equivalenceOfReindexing_functor_obj, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_hom, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_inv
eta 📖	CompOp	3 math math: eta_inv_hom, CategoryTheory.Limits.Cocone.equivStructuredArrow_unitIso, eta_hom_hom
ext 📖	CompOp	15 math math: CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, ext_inv_hom, CategoryTheory.Functor.Final.coconesEquiv_unitIso, whiskeringEquivalence_unitIso, precomposeEquivalence_unitIso, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, SheafOfModules.Presentation.map_relations_I, functorialityEquivalence_counitIso, CategoryTheory.Functor.Final.coconesEquiv_counitIso, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, ext_hom_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, whiskeringEquivalence_counitIso, functorialityEquivalence_unitIso, precomposeEquivalence_counitIso
extend 📖	CompOp	2 math math: extend_hom, instIsIsoCoconeExtend
extendComp 📖	CompOp	2 math math: extendComp_hom_hom, extendComp_inv_hom
extendId 📖	CompOp	2 math math: extendId_hom_hom, extendId_inv_hom
extendIso 📖	CompOp	2 math math: extendIso_hom_hom, extendIso_inv_hom
forget 📖	CompOp	2 math math: forget_obj, forget_map
functoriality 📖	CompOp	16 math math: functoriality_obj_pt, CategoryTheory.Adjunction.functorialityUnit_app_hom, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, reflects_cocone_isomorphism, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, CategoryTheory.Adjunction.functorialityCounit_app_hom, functoriality_obj_ι_app, functorialityEquivalence_counitIso, functoriality_faithful, functoriality_full, functoriality_map_hom, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, functorialityEquivalence_inverse, functorialityEquivalence_functor, functorialityEquivalence_unitIso
functorialityCompFunctoriality 📖	CompOp	—
functorialityEquivalence 📖	CompOp	4 math math: functorialityEquivalence_counitIso, functorialityEquivalence_inverse, functorialityEquivalence_functor, functorialityEquivalence_unitIso
precompose 📖	CompOp	35 math math: precompose_obj_ι, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, CategoryTheory.Limits.PushoutCocone.unop_π_app, precomposeEquivalence_functor, whiskeringEquivalence_unitIso, whiskeringEquivalence_inverse, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.colimit.map_desc, precompose_obj_pt, precomposeEquivalence_unitIso, equivalenceOfReindexing_functor_obj, CategoryTheory.IsUniversalColimit.precompose_isIso, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc, CategoryTheory.Limits.DiagramOfCocones.coconePoints_map, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, CategoryTheory.IsVanKampenColimit.precompose_isIso, CategoryTheory.Limits.DiagramOfCocones.comp, CategoryTheory.Limits.Cofork.π_precompose, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, CategoryTheory.IsVanKampenColimit.precompose_isIso_iff, SheafOfModules.Presentation.map_relations_I, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.colimit.map_desc_assoc, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, CategoryTheory.Limits.DiagramOfCocones.id, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, precomposeEquivalence_inverse, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, precompose_map_hom, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, whiskeringEquivalence_counitIso, precomposeEquivalence_counitIso
precomposeComp 📖	CompOp	—
precomposeEquivalence 📖	CompOp	9 math math: CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, precomposeEquivalence_functor, precomposeEquivalence_unitIso, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_hom_hom, functorialityEquivalence_counitIso, precomposeEquivalence_inverse, functorialityEquivalence_inverse, functorialityEquivalence_unitIso, precomposeEquivalence_counitIso
precomposeId 📖	CompOp	—
whiskering 📖	CompOp	9 math math: CategoryTheory.Functor.Final.coconesEquiv_unitIso, whiskeringEquivalence_unitIso, whiskeringEquivalence_inverse, whiskering_obj, whiskeringEquivalence_functor, CategoryTheory.Functor.Final.coconesEquiv_counitIso, whiskering_map_hom, whiskeringEquivalence_counitIso, CategoryTheory.Functor.Final.coconesEquiv_inverse
whiskeringEquivalence 📖	CompOp	4 math math: whiskeringEquivalence_unitIso, whiskeringEquivalence_inverse, whiskeringEquivalence_functor, whiskeringEquivalence_counitIso

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cocone_iso_of_hom_iso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category	—	CategoryTheory.Iso.comp_inv_eq CategoryTheory.Limits.CoconeMorphism.w CategoryTheory.Limits.CoconeMorphism.ext CategoryTheory.IsIso.hom_inv_id CategoryTheory.IsIso.inv_hom_id
equivalenceOfReindexing_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Equivalence.functor equivalenceOfReindexing CategoryTheory.Functor.comp precompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Limits.Cocone.whisker	—	—
eta_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.pt CategoryTheory.Limits.Cocone.ι CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category eta CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	—
eta_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.pt CategoryTheory.Limits.Cocone.ι CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone 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 CategoryTheory.Limits.Cocone.category ext CategoryTheory.Limits.Cocone.pt	—	—
ext_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category ext CategoryTheory.Limits.Cocone.pt	—	—
extendComp_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.extend CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category extendComp CategoryTheory.CategoryStruct.id	—	—
extendComp_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.extend CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cocone.pt CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category extendComp CategoryTheory.CategoryStruct.id	—	—
extendId_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.extend CategoryTheory.Limits.Cocone.pt CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category extendId	—	—
extendId_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.extend CategoryTheory.Limits.Cocone.pt CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category extendId	—	—
extendIso_hom_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.extend CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone.pt CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category extendIso	—	—
extendIso_inv_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.extend CategoryTheory.Iso.hom CategoryTheory.Limits.Cocone.pt CategoryTheory.Iso.inv CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category extendIso	—	—
extend_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.extend extend	—	—
forget_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category forget CategoryTheory.Limits.CoconeMorphism.hom	—	—
forget_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category forget CategoryTheory.Limits.Cocone.pt	—	—
functorialityEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone.category functorialityEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Equivalence.inverse functoriality precomposeEquivalence CategoryTheory.Iso.symm CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.trans CategoryTheory.Functor.associator CategoryTheory.Functor.id CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Equivalence.unitIso CategoryTheory.Functor.rightUnitor ext CategoryTheory.Functor.obj CategoryTheory.Iso.app CategoryTheory.Limits.Cocone.pt	—	—
functorialityEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Limits.Cocone.category functorialityEquivalence functoriality	—	—
functorialityEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone.category functorialityEquivalence functoriality precomposeEquivalence CategoryTheory.Iso.symm CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.trans CategoryTheory.Functor.associator CategoryTheory.Functor.id CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Equivalence.unitIso CategoryTheory.Functor.rightUnitor	—	—
functorialityEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone.category functorialityEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.id functoriality CategoryTheory.Equivalence.inverse precomposeEquivalence CategoryTheory.Iso.symm CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.trans CategoryTheory.Functor.associator CategoryTheory.Functor.isoWhiskerLeft CategoryTheory.Functor.rightUnitor ext CategoryTheory.Functor.obj CategoryTheory.Iso.app	—	—
functoriality_faithful 📖	mathematical	—	CategoryTheory.Functor.Faithful CategoryTheory.Limits.Cocone 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 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 CategoryTheory.Limits.Cocone.pt CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Functor.map CategoryTheory.NatTrans.app CategoryTheory.Limits.Cocone.ι CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category functoriality	—	—
functoriality_obj_pt 📖	mathematical	—	CategoryTheory.Limits.Cocone.pt CategoryTheory.Functor.comp CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone 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 CategoryTheory.Limits.Cocone.pt CategoryTheory.Limits.Cocone.ι CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category functoriality CategoryTheory.Functor.map	—	—
instIsIsoCoconeExtend 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Limits.Cocone.extend extend	—	CategoryTheory.Limits.CoconeMorphism.ext CategoryTheory.IsIso.hom_inv_id CategoryTheory.IsIso.inv_hom_id
precomposeEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category precomposeEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.comp precompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.Functor.id ext CategoryTheory.Functor.obj CategoryTheory.Iso.refl CategoryTheory.Limits.Cocone.pt	—	—
precomposeEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category precomposeEquivalence precompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category	—	—
precomposeEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category precomposeEquivalence precompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category	—	—
precomposeEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category precomposeEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.id CategoryTheory.Functor.comp precompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv ext CategoryTheory.Functor.obj CategoryTheory.Iso.refl CategoryTheory.Limits.Cocone.pt	—	—
precompose_map_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Limits.Cocone.pt CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.obj CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.ι CategoryTheory.Functor.map CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category precompose	—	—
precompose_obj_pt 📖	mathematical	—	CategoryTheory.Limits.Cocone.pt CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category precompose	—	—
precompose_obj_ι 📖	mathematical	—	CategoryTheory.Limits.Cocone.ι CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category precompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cocone.pt	—	—
reflects_cocone_isomorphism 📖	mathematical	—	CategoryTheory.Functor.ReflectsIsomorphisms CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Functor.comp functoriality	—	cocone_iso_of_hom_iso CategoryTheory.Functor.ReflectsIsomorphisms.reflects CategoryTheory.Functor.map_isIso
whiskeringEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone.category whiskeringEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Equivalence.inverse whiskering precompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.Iso.inv CategoryTheory.Functor.leftUnitor CategoryTheory.Functor.whiskerRight CategoryTheory.Functor.associator ext CategoryTheory.Functor.obj CategoryTheory.Iso.refl CategoryTheory.Limits.Cocone.pt	—	—
whiskeringEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Limits.Cocone.category whiskeringEquivalence whiskering	—	—
whiskeringEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone.category whiskeringEquivalence whiskering precompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.Iso.inv CategoryTheory.Functor.leftUnitor CategoryTheory.Functor.whiskerRight CategoryTheory.Equivalence.counitIso CategoryTheory.Functor.associator	—	—
whiskeringEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cocone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cocone.category whiskeringEquivalence CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.id whiskering CategoryTheory.Equivalence.inverse precompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.Functor.leftUnitor CategoryTheory.Functor.whiskerRight CategoryTheory.Equivalence.counitIso CategoryTheory.Functor.associator ext CategoryTheory.Functor.obj CategoryTheory.Iso.refl CategoryTheory.Limits.Cocone.pt	—	—
whiskering_map_hom 📖	mathematical	—	CategoryTheory.Limits.CoconeMorphism.hom CategoryTheory.Functor.comp CategoryTheory.Limits.Cocone.whisker CategoryTheory.Functor.map CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category whiskering	—	—
whiskering_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Limits.Cocone CategoryTheory.Limits.Cocone.category CategoryTheory.Functor.comp whiskering CategoryTheory.Limits.Cocone.whisker	—	—

CategoryTheory.Limits.Cone

Definitions

Name	Category	Theorems
category 📖	CompOp	230 math math: CategoryTheory.Limits.Cones.postcomposeId_hom_app_hom, 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, CategoryTheory.Limits.ConeMorphism.hom_inv_id, CategoryTheory.Limits.hasLimit_iff_hasTerminal_cone, CategoryTheory.Functor.mapConeMapCone_hom_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Limits.Cones.equivalenceOfReindexing_inverse, CategoryTheory.Limits.Cones.whiskeringEquivalence_functor, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, CategoryTheory.Limits.IsLimit.liftConeMorphism_eq_isTerminal_from, CategoryTheory.Limits.ConeMorphism.inv_hom_id_assoc, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, CategoryTheory.Limits.Cones.postcompose_obj_pt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, CategoryTheory.Limits.Cones.ext_hom_hom, CategoryTheory.Limits.Multifork.ext_hom_hom, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_π_app_left, CategoryTheory.Limits.Fork.isoForkOfι_hom_hom, CategoryTheory.Limits.Cones.functorialityEquivalence_functor, fromCostructuredArrow_map_hom, toCostructuredArrow_obj, CategoryTheory.Functor.mapConePostcompose_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.Limits.Cones.extendId_inv_hom, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, CategoryTheory.Limits.IsLimit.uniqueUpToIso_inv, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, CategoryTheory.Over.conePost_obj_π_app, CategoryTheory.Over.ConstructProducts.conesEquiv_unitIso, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, fromCostructuredArrow_obj_π, CategoryTheory.Limits.Cones.forget_map, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, CategoryTheory.Functor.Initial.conesEquiv_counitIso, 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.Cones.whiskering_map_hom, CategoryTheory.Functor.mapCoconeOp_inv_hom, 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.Cones.whiskeringEquivalence_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.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.Limits.Cones.functoriality_obj_π_app, CategoryTheory.Functor.RightExtension.coneAtFunctor_obj, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, category_id_hom, CategoryTheory.Limits.IsLimit.equivIsoLimit_symm_apply, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_map_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, FundamentalGroupoidFunctor.instIsIsoFanGrpdObjTopCatFundamentalGroupoidFunctorPiTopToPiCone, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, CategoryTheory.Limits.Cones.whiskeringEquivalence_unitIso, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_pt, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_left, CategoryTheory.Limits.IsLimit.uniqueUpToIso_hom, CategoryTheory.Over.conePost_map_hom, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_inv_hom, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_obj, CategoryTheory.Limits.Cones.postcomposeEquivalence_unitIso, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_obj, CategoryTheory.Limits.Trident.ext_hom, CategoryTheory.Limits.Cones.postcomposeEquivalence_counitIso, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_inverse, CategoryTheory.Limits.Cones.functorialityEquivalence_unitIso, CategoryTheory.Functor.Initial.conesEquiv_unitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.Limits.Cones.functoriality_obj_pt, CategoryTheory.Limits.Fork.ext_hom, CategoryTheory.Limits.DiagramOfCones.conePoints_map, mapConeToUnder_inv_hom, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, CategoryTheory.Limits.Cones.extendComp_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.Limits.Cones.postcomposeEquivalence_functor, CategoryTheory.Limits.Cones.extendIso_inv_hom, CategoryTheory.Limits.Cones.functoriality_faithful, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_hom, CategoryTheory.Limits.Fan.ext_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.Limits.Fan.ext_hom_hom, CategoryTheory.Functor.Initial.extendCone_map_hom, toCostructuredArrow_map, CategoryTheory.Limits.PullbackCone.eta_inv_hom, CategoryTheory.Limits.Cones.eta_inv_hom, CategoryTheory.Functor.Initial.conesEquiv_inverse, CategoryTheory.Over.ConstructProducts.conesEquiv_counitIso, CategoryTheory.Limits.Cones.whiskeringEquivalence_counitIso, CategoryTheory.Limits.Cones.extendIso_hom_hom, CategoryTheory.Limits.Fork.ext_inv, CategoryTheory.Limits.instIsIsoHomInvCone, CategoryTheory.Limits.PullbackCone.unop_ι_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, CategoryTheory.Limits.Cones.eta_hom_hom, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Limits.Cones.functoriality_full, CategoryTheory.Limits.Cones.postcompose_obj_π, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.Limits.Cones.functoriality_map_hom, CategoryTheory.Limits.Cones.extendId_hom_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Limits.colimitLimitToLimitColimitCone_iso, CategoryTheory.Limits.Cones.functorialityEquivalence_inverse, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Limits.Cones.postcomposeComp_inv_app_hom, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_hom_hom, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_obj, equivCostructuredArrow_functor, 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, CategoryTheory.Limits.Cones.forget_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_inverse, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_map_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_pt, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.Limits.PullbackCone.eta_hom_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Over.conePost_obj_pt, CategoryTheory.Limits.Cones.functorialityEquivalence_counitIso, 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.Wedge.ext_inv_hom, CategoryTheory.Limits.Cones.ext_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_map_hom, category_comp_hom, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Limits.ConeMorphism.hom_inv_id_assoc, fromCostructuredArrow_obj_pt, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, CategoryTheory.Limits.limit.lift_map, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.Functor.RightExtension.coneAtFunctor_map_hom, CategoryTheory.Functor.mapConePostcompose_hom_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_inv, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_pt, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_hom_hom, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_obj, CategoryTheory.Limits.Cones.instIsIsoConeExtend, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.Limits.DiagramOfCones.comp, CategoryTheory.Functor.mapCoconeOp_hom_hom, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_obj, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, mapConeToUnder_hom_hom, CategoryTheory.Over.ConstructProducts.conesEquivInverse_obj, CategoryTheory.Functor.Initial.limitConeOfComp_cone, equivCostructuredArrow_unitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, 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.Cones.equivalenceOfReindexing_functor, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_map_hom, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Functor.Initial.extendCone_obj_π_app, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, CategoryTheory.Limits.Fork.isoForkOfι_inv_hom, CategoryTheory.Functor.mapConeWhisker_inv_hom, CategoryTheory.WithTerminal.coneEquiv_functor_obj_pt, CategoryTheory.Over.ConstructProducts.conesEquiv_inverse, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_map, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, 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.Limits.Cones.extendComp_hom_hom, CategoryTheory.Functor.Initial.conesEquiv_functor, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.Limits.Cones.cone_iso_of_hom_iso, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, CategoryTheory.Limits.Cones.whiskering_obj, CategoryTheory.Limits.IsTerminal.from_eq_liftConeMorphism, CategoryTheory.Limits.Cones.postcomposeComp_hom_app_hom, CategoryTheory.Limits.Cones.postcompose_map_hom, FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone, CategoryTheory.Limits.Cones.postcomposeEquivalence_inverse, CategoryTheory.Limits.Cones.postcomposeId_inv_app_hom, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, 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.pullbackConeEquivBinaryFan_inverse_map_hom, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv_assoc, CategoryTheory.Limits.ConeMorphism.inv_hom_id, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom
equiv 📖	CompOp	4 math math: equiv_inv_pt, equiv_hom_fst, equiv_inv_π, equiv_hom_snd
extend 📖	CompOp	15 math math: CategoryTheory.Limits.Cones.extendId_inv_hom, extend_π, CategoryTheory.Limits.Cones.extend_hom, extend_pt, CategoryTheory.Limits.IsLimit.OfNatIso.cone_fac, CategoryTheory.Limits.Cones.extendComp_inv_hom, CategoryTheory.Limits.Cones.extendIso_inv_hom, CategoryTheory.Limits.Cones.extendIso_hom_hom, CategoryTheory.Limits.Cones.extendId_hom_hom, CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_fac, CategoryTheory.Limits.Cones.instIsIsoConeExtend, CategoryTheory.Limits.IsLimit.homIso_hom, CategoryTheory.Limits.Cones.extendComp_hom_hom, CategoryTheory.Limits.limit.lift_extend, CategoryTheory.Limits.IsLimit.homEquiv_apply
extensions 📖	CompOp	2 math math: extend_π, extensions_app
op 📖	CompOp	10 math math: CategoryTheory.Limits.PullbackCone.op_ι_app, Condensed.isColimitLocallyConstantPresheaf_desc_apply, CategoryTheory.Limits.Fork.op_ι_app, 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
pt 📖	CompOp	834 math math: AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_snd, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_pt, CategoryTheory.Limits.Trident.condition_assoc, CategoryTheory.Limits.Cones.postcomposeId_hom_app_hom, 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.Limits.coconeEquivalenceOpConeOp_unitIso, 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, unop_ι, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, ofTrident_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, 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, HomologicalComplex.coneOfHasLimitEval_pt_d, 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.Cones.postcompose_obj_pt, 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.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.Limits.Cones.ext_hom_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, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, CategoryTheory.Limits.FormalCoproduct.pullbackCone_fst_φ, 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, toCostructuredArrow_obj, 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, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.FunctorToTypes.binaryProductCone_pt_obj, CategoryTheory.Limits.coconeOfConeLeftOp_pt, CategoryTheory.Limits.constCone_pt, CategoryTheory.Limits.Cones.extendId_inv_hom, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, whisker_π, CategoryTheory.Limits.Multifork.isoOfι_inv_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, 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, 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, CategoryTheory.Limits.Fork.ι_postcompose, 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.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.Functor.Initial.extendCone_obj_π_app', CategoryTheory.Limits.Fork.IsLimit.homIso_symm_apply, CategoryTheory.Limits.WidePullbackCone.IsLimit.lift_base, AddCommGrpCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Limits.Types.Small.limitCone_pt, fromStructuredArrow_pt, toStructuredArrow_comp_toUnder_comp_forget, CategoryTheory.Limits.BinaryFan.braiding_inv_snd, CategoryTheory.Limits.PullbackCone.mono_fst_of_is_pullback_of_mono, 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, CommRingCat.instIsLocalHomCarrierObjWalkingParallelPairFunctorConstPtEqualizerForkZeroParallelPairRingHomHomι, 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.Limits.Cones.functoriality_obj_π_app, 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, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, ProfiniteGrp.cone_pt, TopCat.piFan_pt, CategoryTheory.Limits.limit.isoLimitCone_hom_π, 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.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, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, equiv_hom_fst, toStructuredArrowCone_π_app, CategoryTheory.Limits.Cones.whiskeringEquivalence_unitIso, 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.IsPullback.of_isLimit, CategoryTheory.Limits.Fork.ofCone_π, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_isLimit_lift, CategoryTheory.Limits.opProductIsoCoproduct'_comp_self, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_obj, CategoryTheory.Limits.Cones.postcomposeEquivalence_unitIso, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_obj, CategoryTheory.Limits.KernelFork.IsLimit.isIso_ι, CategoryTheory.Limits.Cones.postcomposeEquivalence_counitIso, 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, 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.Cones.functoriality_obj_pt, CategoryTheory.Limits.Fork.IsLimit.lift_ι, 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.Cones.extendComp_inv_hom, 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.Cones.extendIso_inv_hom, 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.Comma.limitAuxiliaryCone_π_app, 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.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, 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.Cones.eta_inv_hom, CategoryTheory.Limits.Cones.whiskeringEquivalence_counitIso, 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.Cones.extendIso_hom_hom, CategoryTheory.Limits.WidePullbackCone.condition_assoc, PresheafOfModules.isSheaf_of_isLimit, 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.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_π, Condensed.instFinalOppositeDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceCostructuredArrowFintypeCatProfiniteOpToProfiniteOpPtAsLimitConeFunctorOp, CategoryTheory.Limits.isLimitConeOfAdj_lift, CategoryTheory.Limits.Types.Limit.lift_π_apply, CategoryTheory.Limits.BinaryFan.braiding_inv_fst_assoc, 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.Cones.eta_hom_hom, 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.Functor.mapCone₂_pt, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_pt, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, CategoryTheory.Limits.BinaryFan.braiding_hom_fst, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.Limits.Fan.mk_pt, CategoryTheory.Limits.Cones.postcompose_obj_π, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.Limits.WidePullbackCone.IsLimit.lift_π, CategoryTheory.Functor.mapCone₂_π_app, CategoryTheory.Limits.Cones.functoriality_map_hom, CategoryTheory.Limits.Cones.extendId_hom_hom, 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.Cones.postcomposeComp_inv_app_hom, 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, 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.Limits.Cones.forget_obj, AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'_f, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_pt, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_inverse, 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, 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, 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.Cones.functorialityEquivalence_counitIso, 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.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, toStructuredArrow_obj, 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, CategoryTheory.Limits.Cones.ext_inv_hom, 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, 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.Limits.coconeRightOpOfCone_ι, CategoryTheory.Limits.PullbackCone.combine_pt_map, CategoryTheory.Limits.Fork.IsLimit.lift_ι_assoc, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, CategoryTheory.Limits.PullbackCone.unop_pt, CategoryTheory.Limits.limit.lift_π_assoc, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, CategoryTheory.Limits.Fork.IsLimit.lift_ι', 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, 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, CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer', CategoryTheory.Presieve.piComparison_fac, CategoryTheory.Limits.BinaryBicone.ofLimitCone_fst, toUnder_π_app, CategoryTheory.Limits.IsLimit.assoc_lift, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, 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.KernelFork.map_condition, AlgebraicGeometry.Scheme.compactSpace_of_isLimit, CategoryTheory.Limits.coconeOfConeUnop_ι, CategoryTheory.Limits.IsLimit.lift_self, CategoryTheory.Mon.limitCone_pt, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CommRingCat.piFan_pt, CategoryTheory.Limits.Fork.op_ι_app_zero, 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.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, CategoryTheory.Limits.opProductIsoCoproduct'_inv_comp_lift, ModuleCat.HasLimit.productLimitCone_cone_pt_isAddCommGroup, CategoryTheory.Limits.BinaryFan.leftUnitor_inv, 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.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, 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, AlgebraicGeometry.isAffineHom_π_app, LightProfinite.Extend.functor_obj, 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, CategoryTheory.Functor.IsEventuallyConstantTo.isIso_π_of_isLimit', LightProfinite.instEpiAppOppositeNatπAsLimitCone, CategoryTheory.FunctorToTypes.binaryProductCone_pt_map, CategoryTheory.Limits.PullbackCone.IsLimit.lift_snd_assoc, CategoryTheory.Limits.IsLimit.isZero_pt, CategoryTheory.Limits.BinaryFan.assocInv_snd, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_tensorProductIsBinaryProduct_lift_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_map_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, 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, 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.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.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.Cones.extendComp_hom_hom, 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.RanIsSheafOfIsCocontinuous.liftAux_map, Profinite.exists_locallyConstant_fin_two, PresheafOfModules.limitCone_pt, toStructuredArrowCone_pt, CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, ProfiniteGrp.instIsTopologicalGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂ContinuousMonoidHomToProfiniteContinuousMap, 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, CategoryTheory.Limits.Trident.IsLimit.homIso_natural, 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.Cones.postcomposeComp_hom_app_hom, CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map_aux, CategoryTheory.Limits.FormalCoproduct.pullbackCone_snd_f, CategoryTheory.Limits.Cones.postcompose_map_hom, 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.Cones.postcomposeId_inv_app_hom, CategoryTheory.Limits.Fork.unop_π, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, 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, CategoryTheory.Limits.FormalCoproduct.pullbackCone_snd_φ, CategoryTheory.Limits.WidePullbackCone.condition, CategoryTheory.Adjunction.functorialityCounit'_app_hom, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_right_as, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right, Profinite.exists_hom, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.liftAux_fac, 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.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	6 math math: CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, unop_ι, unop_pt, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_obj, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_map_hom
whisker 📖	CompOp	16 math math: whisker_π, CategoryTheory.Functor.Initial.limitConeComp_isLimit, CategoryTheory.Limits.Cones.whiskering_map_hom, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_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, whisker_pt, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, CategoryTheory.Functor.mapConeWhisker_inv_hom, CategoryTheory.Limits.Cones.whiskering_obj
π 📖	CompOp	321 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, 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, 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, CategoryTheory.Limits.Cones.functoriality_obj_π_app, 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, toStructuredArrowCone_π_app, 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.Cones.eta_inv_hom, 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.Limits.isLimitConeOfAdj_lift, CategoryTheory.Limits.Types.Limit.lift_π_apply, equiv_hom_snd, 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.Cones.eta_hom_hom, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, AddCommGrpCat.HasLimit.productLimitCone_cone_π, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.Limits.Cones.postcompose_obj_π, CategoryTheory.Functor.mapCone₂_π_app, CategoryTheory.Limits.Cones.functoriality_map_hom, 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, 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, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty, CategoryTheory.Limits.Fork.op_ι_app_zero, 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, 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.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, 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.Cones.postcompose_map_hom, 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	—	—
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	—	—
extend_pt 📖	mathematical	—	pt extend	—	—
extend_π 📖	mathematical	—	π extend 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 Opposite.op	—	—
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	—	—
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	—	—
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 CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt CategoryTheory.NatTrans.app π CategoryTheory.Functor.map	—	CategoryTheory.NatTrans.naturality CategoryTheory.Category.id_comp
w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const pt CategoryTheory.NatTrans.app 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	—	—

CategoryTheory.Limits.ConeMorphism

Definitions

Name	Category	Theorems
hom 📖	CompOp	132 math math: CategoryTheory.Limits.Cones.postcomposeId_hom_app_hom, 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.coconeEquivalenceOpConeOp_unitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, inv_hom_id_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, CategoryTheory.Limits.Cones.ext_hom_hom, CategoryTheory.Limits.Multifork.ext_hom_hom, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, CategoryTheory.Limits.Fork.isoForkOfι_hom_hom, CategoryTheory.Limits.Cone.fromCostructuredArrow_map_hom, CategoryTheory.Functor.mapConePostcompose_inv_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.Limits.Cones.extendId_inv_hom, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, CategoryTheory.Limits.Cones.forget_map, CategoryTheory.Limits.IsLimit.liftConeMorphism_hom, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, w, CategoryTheory.Limits.Cones.extend_hom, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, CategoryTheory.Limits.Cones.whiskering_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.MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, map_w, CategoryTheory.Limits.Cone.category_id_hom, 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.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.Cones.extendComp_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.Limits.Cones.extendIso_inv_hom, CategoryTheory.Limits.Fan.ext_inv_hom, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, 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.Cones.eta_inv_hom, CategoryTheory.Limits.Cones.extendIso_hom_hom, CategoryTheory.Limits.instIsIsoHomInvCone, w_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, CategoryTheory.Limits.Cones.eta_hom_hom, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.Limits.Cones.functoriality_map_hom, CategoryTheory.Limits.Cones.extendId_hom_hom, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Limits.Cones.postcomposeComp_inv_app_hom, 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, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Limits.IsLimit.mkConeMorphism_lift, CategoryTheory.Functor.mapConeWhisker_hom_hom, CategoryTheory.Limits.Wedge.ext_inv_hom, CategoryTheory.Limits.Cones.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.limit.coneMorphism_hom, 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.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.Limits.Cone.mapConeToUnder_hom_hom, CategoryTheory.Limits.Multifork.hom_comp_ι, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, 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.coconeEquivalenceOpConeOp_inverse_map_hom, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, CategoryTheory.Limits.Fork.isoForkOfι_inv_hom, CategoryTheory.Functor.mapConeWhisker_inv_hom, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.Limits.Cones.extendComp_hom_hom, CategoryTheory.Limits.Multifork.hom_comp_ι_assoc, CategoryTheory.Limits.Cones.postcomposeComp_hom_app_hom, CategoryTheory.Limits.Cones.postcompose_map_hom, CategoryTheory.Limits.Cones.postcomposeId_inv_app_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.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	6 math math: equivalenceOfReindexing_inverse, equivalenceOfReindexing_counitIso, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_inv, equivalenceOfReindexing_unitIso, equivalenceOfReindexing_functor
eta 📖	CompOp	3 math math: eta_inv_hom, eta_hom_hom, CategoryTheory.Limits.Cone.equivCostructuredArrow_unitIso
ext 📖	CompOp	14 math math: ext_hom_hom, CategoryTheory.Functor.Initial.conesEquiv_counitIso, equivalenceOfReindexing_counitIso, whiskeringEquivalence_unitIso, postcomposeEquivalence_unitIso, postcomposeEquivalence_counitIso, functorialityEquivalence_unitIso, CategoryTheory.Functor.Initial.conesEquiv_unitIso, whiskeringEquivalence_counitIso, functorialityEquivalence_counitIso, ext_inv_hom, equivalenceOfReindexing_unitIso, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso
extend 📖	CompOp	2 math math: extend_hom, instIsIsoConeExtend
extendComp 📖	CompOp	2 math math: extendComp_inv_hom, extendComp_hom_hom
extendId 📖	CompOp	2 math math: extendId_inv_hom, extendId_hom_hom
extendIso 📖	CompOp	2 math math: extendIso_inv_hom, extendIso_hom_hom
forget 📖	CompOp	2 math math: forget_map, forget_obj
functoriality 📖	CompOp	18 math math: functorialityEquivalence_functor, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, CategoryTheory.Over.conePostIso_hom_app_hom, functoriality_obj_π_app, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, functorialityEquivalence_unitIso, functoriality_obj_pt, functoriality_faithful, functoriality_full, CategoryTheory.Adjunction.functorialityUnit'_app_hom, functoriality_map_hom, functorialityEquivalence_inverse, CategoryTheory.Over.conePostIso_inv_app_hom, functorialityEquivalence_counitIso, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, reflects_cone_isomorphism, CategoryTheory.Adjunction.functorialityCounit'_app_hom
functorialityCompFunctoriality 📖	CompOp	—
functorialityEquivalence 📖	CompOp	4 math math: functorialityEquivalence_functor, functorialityEquivalence_unitIso, functorialityEquivalence_inverse, functorialityEquivalence_counitIso
postcompose 📖	CompOp	38 math math: postcomposeId_hom_app_hom, CategoryTheory.Limits.DiagramOfCones.id, equivalenceOfReindexing_inverse, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, postcompose_obj_pt, CategoryTheory.Functor.mapConePostcompose_inv_hom, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, CategoryTheory.Limits.Fork.ι_postcompose, whiskeringEquivalence_inverse, equivalenceOfReindexing_counitIso, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_map_hom, whiskeringEquivalence_unitIso, postcomposeEquivalence_unitIso, postcomposeEquivalence_counitIso, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.Limits.DiagramOfCones.conePoints_map, postcomposeEquivalence_functor, whiskeringEquivalence_counitIso, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, postcompose_obj_π, postcomposeComp_inv_app_hom, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Limits.limit.lift_map, CategoryTheory.Functor.mapConePostcompose_hom_hom, CategoryTheory.Limits.DiagramOfCones.comp, equivalenceOfReindexing_unitIso, equivalenceOfReindexing_functor, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv, CategoryTheory.Limits.limit.lift_map_assoc, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, postcomposeComp_hom_app_hom, postcompose_map_hom, postcomposeEquivalence_inverse, postcomposeId_inv_app_hom, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv_assoc
postcomposeComp 📖	CompOp	2 math math: postcomposeComp_inv_app_hom, postcomposeComp_hom_app_hom
postcomposeEquivalence 📖	CompOp	9 math math: postcomposeEquivalence_unitIso, postcomposeEquivalence_counitIso, functorialityEquivalence_unitIso, postcomposeEquivalence_functor, functorialityEquivalence_inverse, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_hom_hom, functorialityEquivalence_counitIso, postcomposeEquivalence_inverse
postcomposeId 📖	CompOp	2 math math: postcomposeId_hom_app_hom, postcomposeId_inv_app_hom
whiskering 📖	CompOp	15 math math: equivalenceOfReindexing_inverse, whiskeringEquivalence_functor, CategoryTheory.Functor.Initial.conesEquiv_counitIso, whiskering_map_hom, whiskeringEquivalence_inverse, CategoryTheory.Over.conePostIso_hom_app_hom, equivalenceOfReindexing_counitIso, whiskeringEquivalence_unitIso, CategoryTheory.Functor.Initial.conesEquiv_unitIso, CategoryTheory.Functor.Initial.conesEquiv_inverse, whiskeringEquivalence_counitIso, CategoryTheory.Over.conePostIso_inv_app_hom, equivalenceOfReindexing_unitIso, equivalenceOfReindexing_functor, whiskering_obj
whiskeringEquivalence 📖	CompOp	4 math math: whiskeringEquivalence_functor, whiskeringEquivalence_inverse, whiskeringEquivalence_unitIso, whiskeringEquivalence_counitIso

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cone_iso_of_hom_iso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cone 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
equivalenceOfReindexing_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cone 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 CategoryTheory.Limits.Cone.whisker CategoryTheory.Functor.obj CategoryTheory.Iso.refl CategoryTheory.Limits.Cone.pt CategoryTheory.Functor.rightUnitor	—	CategoryTheory.Functor.isoWhiskerRight_trans CategoryTheory.Iso.trans_assoc
equivalenceOfReindexing_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone 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 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 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 CategoryTheory.Limits.Cone.whisker CategoryTheory.Iso.refl CategoryTheory.Limits.Cone.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 CategoryTheory.Limits.Cone.pt CategoryTheory.Limits.Cone.π CategoryTheory.Iso.hom CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category eta CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	—
eta_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Limits.Cone.pt CategoryTheory.Limits.Cone.π CategoryTheory.Iso.inv CategoryTheory.Limits.Cone 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 CategoryTheory.Limits.Cone.category ext CategoryTheory.Limits.Cone.pt	—	—
ext_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Iso.inv CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category ext CategoryTheory.Limits.Cone.pt	—	—
extendComp_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Limits.Cone.extend CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt CategoryTheory.Iso.hom CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category extendComp CategoryTheory.CategoryStruct.id	—	—
extendComp_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Limits.Cone.extend CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Limits.Cone.pt CategoryTheory.Iso.inv CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category extendComp CategoryTheory.CategoryStruct.id	—	—
extendId_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Limits.Cone.extend CategoryTheory.Limits.Cone.pt CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Iso.hom CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category extendId	—	—
extendId_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Limits.Cone.extend CategoryTheory.Limits.Cone.pt CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Iso.inv CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category extendId	—	—
extendIso_hom_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Limits.Cone.extend CategoryTheory.Iso.hom CategoryTheory.Limits.Cone.pt CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category extendIso	—	—
extendIso_inv_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Limits.Cone.extend CategoryTheory.Iso.hom CategoryTheory.Limits.Cone.pt CategoryTheory.Iso.inv CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category extendIso	—	—
extend_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Limits.Cone.extend extend	—	—
forget_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category forget CategoryTheory.Limits.ConeMorphism.hom	—	—
forget_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category forget CategoryTheory.Limits.Cone.pt	—	—
functorialityEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone.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 CategoryTheory.Limits.Cone.pt	—	—
functorialityEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Limits.Cone.category functorialityEquivalence functoriality	—	—
functorialityEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone.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 CategoryTheory.Limits.Cone.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 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 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 CategoryTheory.Limits.Cone.pt CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Functor.map CategoryTheory.NatTrans.app CategoryTheory.Limits.Cone.π CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category functoriality	—	—
functoriality_obj_pt 📖	mathematical	—	CategoryTheory.Limits.Cone.pt CategoryTheory.Functor.comp CategoryTheory.Functor.obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category functoriality	—	—
functoriality_obj_π_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Functor.obj CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cone.pt CategoryTheory.Functor.comp CategoryTheory.Limits.Cone.π CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category functoriality CategoryTheory.Functor.map	—	—
instIsIsoConeExtend 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Limits.Cone.extend extend	—	CategoryTheory.Limits.ConeMorphism.ext CategoryTheory.IsIso.hom_inv_id CategoryTheory.IsIso.inv_hom_id
postcomposeComp_hom_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cone 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 CategoryTheory.Limits.Cone.pt	—	—
postcomposeComp_inv_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cone 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 CategoryTheory.Limits.Cone.pt	—	—
postcomposeEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cone 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 CategoryTheory.Limits.Cone.pt	—	—
postcomposeEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category postcomposeEquivalence postcompose CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category	—	—
postcomposeEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category postcomposeEquivalence postcompose CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category	—	—
postcomposeEquivalence_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Limits.Cone 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 CategoryTheory.Limits.Cone.pt	—	—
postcomposeId_hom_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cone 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 CategoryTheory.Limits.Cone.pt	—	—
postcomposeId_inv_app_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.obj CategoryTheory.Limits.Cone 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 CategoryTheory.Limits.Cone.pt	—	—
postcompose_map_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Limits.Cone.pt CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.obj CategoryTheory.Functor.const CategoryTheory.Limits.Cone.π CategoryTheory.Functor.map CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category postcompose	—	—
postcompose_obj_pt 📖	mathematical	—	CategoryTheory.Limits.Cone.pt CategoryTheory.Functor.obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category postcompose	—	—
postcompose_obj_π 📖	mathematical	—	CategoryTheory.Limits.Cone.π CategoryTheory.Functor.obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category postcompose CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.const CategoryTheory.Limits.Cone.pt	—	—
reflects_cone_isomorphism 📖	mathematical	—	CategoryTheory.Functor.ReflectsIsomorphisms CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Functor.comp functoriality	—	cone_iso_of_hom_iso CategoryTheory.Functor.ReflectsIsomorphisms.reflects CategoryTheory.Functor.map_isIso
whiskeringEquivalence_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone.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 CategoryTheory.Limits.Cone.pt	—	—
whiskeringEquivalence_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Limits.Cone.category whiskeringEquivalence whiskering	—	—
whiskeringEquivalence_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Limits.Cone CategoryTheory.Functor.comp CategoryTheory.Equivalence.functor CategoryTheory.Limits.Cone.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 CategoryTheory.Limits.Cone.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 CategoryTheory.Limits.Cone.pt	—	—
whiskering_map_hom 📖	mathematical	—	CategoryTheory.Limits.ConeMorphism.hom CategoryTheory.Functor.comp CategoryTheory.Limits.Cone.whisker CategoryTheory.Functor.map CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category whiskering	—	—
whiskering_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Limits.Cone CategoryTheory.Limits.Cone.category CategoryTheory.Functor.comp whiskering CategoryTheory.Limits.Cone.whisker	—	—

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