Arrow

📁 Source: Mathlib/CategoryTheory/Comma/Arrow.lean

Statistics

Metric	Count
Definitions Arrow, discreteEquiv, equivSigma, homMk, homMk', instCoeOutHom, isoMk, isoMk', isoOfNatIso, leftFunc, leftToRight, mk, rightFunc, squareToSnd, mapArrow, mapArrowEquivalence, mapArrowFunctor, Arrow, instCategoryArrow, instInhabitedArrow, Arrow	21
Theorems arrow_mk_comp_eqToHom, arrow_mk_eqToHom_comp, comp_left, comp_left_assoc, comp_right, comp_right_assoc, epi_right, equivSigma_apply_fst, equivSigma_apply_snd_fst, equivSigma_apply_snd_snd, equivSigma_symm_apply_hom, equivSigma_symm_apply_left, equivSigma_symm_apply_right, ext, functor_ext, congr_left, congr_right, homMk'_left, homMk'_right, homMk_left, homMk_right, hom_ext, hom_ext_iff, hom_inv_id_left, hom_inv_id_left_assoc, hom_inv_id_right, hom_inv_id_right_assoc, id_left, id_right, inv_hom_id_left, inv_hom_id_left_assoc, inv_hom_id_right, inv_hom_id_right_assoc, inv_left, inv_left_hom_right, inv_right, isIso_hom_iff_isIso_hom_of_isIso, isIso_hom_iff_isIso_of_isIso, isIso_iff_isIso_of_isIso, isIso_left, isIso_of_isIso, isIso_of_isIso_left_of_isIso_right, isIso_right, isoMk_hom_left, isoMk_hom_right, isoMk_inv_left, isoMk_inv_right, iso_w, iso_w', leftFunc_map, leftFunc_obj, leftToRight_app, left_hom_inv_right, mk_eq, mk_eq_mk_iff, mk_hom, mk_inj, mk_injective, mk_left, mk_right, mk_surjective, mono_left, rightFunc_map, rightFunc_obj, squareToSnd_left, squareToSnd_right, square_from_iso_invert, square_to_iso_invert, w, w_assoc, w_mk_right, w_mk_right_assoc, isEquivalence_mapArrow, mapArrowFunctor_map_app_left, mapArrowFunctor_map_app_right, mapArrowFunctor_obj, mapArrow_map_left, mapArrow_map_right, mapArrow_obj	79
Total	100

CategoryTheory

Definitions

Name	Category	Theorems
Arrow 📖	CompOp	363 math math: SmallObject.functorMap_id, Limits.coker.π_app, Functor.leibnizPullback_obj_map, SmallObject.SuccStruct.prop.arrowIso_hom_left, Arrow.equivSigma_symm_apply_left, RetractArrow.right_r, Limits.instPreservesWellOrderContinuousOfShapeArrowRightFuncOfHasIterationOfShape, SmallObject.SuccStruct.prop.arrowIso_inv_left, instFiniteArrowDiscrete, Functor.mapArrow_obj, Square.arrowArrowEquivalence_functor, Sheaf.instIsLocallySurjectiveAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, MorphismProperty.FunctorialFactorizationData.hi, Arrow.hom_inv_id_right_assoc, RetractArrow.retract_left_assoc, RetractArrow.left_r, Functor.PushoutObjObj.mapArrowRight_id, Functor.PullbackObjObj.mapArrowLeft_id, SmallObject.πObj_ιIteration_app_right, Limits.IsImage.ofArrowIso_lift, Abelian.PreservesCoimageImageComparison.iso_inv_left, Limits.image.map_id, ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, SimplicialObject.Augmented.toArrow_map_right, Square.fromArrowArrowFunctor_map_τ₃, ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, Arrow.hasLimit, MorphismProperty.FunctorialFactorizationData.fac, Square.toArrowArrowFunctor_obj_hom_right, Arrow.comp_left, Arrow.isIso_of_isIso_left_of_isIso_right, RetractArrow.r_w_assoc, LocalizerMorphism.hasRightResolutions_arrow_of_functorial_resolutions, hasCardinalLT_arrow_discrete_iff, Functor.PullbackObjObj.π_iso_of_iso_left_inv, Limits.image.map_comp, Arrow.leftFunc_obj, groupCohomology.dArrowIso₀₁_inv_right, Functor.LeibnizAdjunction.adj_unit_app_left, SimplicialObject.Augmented.toArrow_map_left, MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, Limits.coker_map, Square.toArrowArrowFunctor'_obj_left_hom, Square.fromArrowArrowFunctor_obj_f₃₄, SmallObject.functorialFactorizationData_i_app, SimplicialObject.Augmented.toArrow_obj_left, Abelian.coim_map, TransfiniteCompositionOfShape.ofArrowIso_isoBot, RetractArrow.map_r_right, Functor.PullbackObjObj.mapArrowLeft_comp, ParametrizedAdjunction.arrowHomEquiv_apply_left, LocalizerMorphism.arrow_functor, RetractArrow.i_w, hasCardinalLT_arrow_shrinkHoms_iff, Functor.LeibnizAdjunction.adj_counit_app_left, groupHomology.d₁₀ArrowIso_hom_left, Functor.leibnizAdjunction_adj, OrthogonalReflection.D₁.ι_comp_t_assoc, Square.fromArrowArrowFunctor'_obj_X₂, ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, Limits.kernelSubobjectMap_comp, Limits.coker.condition_assoc, Square.fromArrowArrowFunctor'_obj_X₃, HomotopicalAlgebra.AttachCells.ofArrowIso_g₂, MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, HomologicalComplex.Hom.sqFrom_comp, HomotopicalAlgebra.FibrantObject.instHasRightResolutionsArrowArrowWeakEquivalencesArrowLocalizerMorphism, groupCohomology.dArrowIso₀₁_hom_right, Abelian.PreservesCoimageImageComparison.iso_hom_left, Functor.PullbackObjObj.π_iso_of_iso_right_hom, Functor.PushoutObjObj.mapArrowRight_comp_assoc, Abelian.im_map, Functor.PullbackObjObj.mapArrowRight_comp_assoc, Arrow.equivSigma_apply_snd_snd, HomotopicalAlgebra.CofibrantObject.instHasLeftResolutionsArrowArrowWeakEquivalencesArrowLocalizerMorphism, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, SimplicialObject.Augmented.toArrow_obj_right, Square.toArrowArrowFunctor_obj_left_left, ShortComplex.gFunctor_map, ObjectProperty.instIsClosedUnderColimitsOfShapeColimitsCardinalClosureCategoryFamily, Arrow.hasLimits, Limits.instPreservesWellOrderContinuousOfShapeArrowLeftFuncOfHasIterationOfShape, Square.fromArrowArrowFunctor_obj_X₃, RetractArrow.op_r_right, Abelian.PreservesCoimageImageComparison.iso_hom_right, Arrow.mk_injective, SmallObject.SuccStruct.prop.arrowIso_inv_right, Square.fromArrowArrowFunctor'_map_τ₃, Limits.ker.ι_app, SmallObject.functor_map, Square.fromArrowArrowFunctor_obj_X₂, Arrow.leftToRight_app, Functor.mapArrowFunctor_obj, groupCohomology.dArrowIso₀₁_inv_left, SmallObject.objMap_comp_assoc, Limits.ker_obj, SmallObject.functorialFactorizationData_Z_obj, Arrow.equivSigma_apply_fst, Limits.instHasIterationOfShapeArrow, Square.toArrowArrowFunctor'_obj_right_right, Square.toArrowArrowFunctor_map_right_right, Sheaf.instMonoAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, Limits.CokernelCofork.mapIsoOfIsColimit_inv, ShortComplex.fFunctor_obj, Functor.leibnizPushout_obj_map, Limits.ker.condition, Functor.PushoutObjObj.mapArrowLeft_id, Arrow.isoMk_inv_left, CosimplicialObject.cechConerveEquiv_symm_apply, SmallObject.ε_app, SmallObject.succStruct_prop_le_propArrow, MorphismProperty.arrow_mk_mem_toSet_iff, hasCardinalLT_arrow_walkingParallelFamily, Ind.exists_nonempty_arrow_mk_iso_ind_lim, SmallCategoryCardinalLT.hasCardinalLT, AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff, SmallObject.iterationObjRightIso_hom, SmallObject.objMap_id, SmallObject.SuccStruct.prop.arrowIso_hom_right, Limits.coker_obj, Square.toArrowArrowFunctor'_map_right_left, ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, groupCohomology.dArrowIso₀₁_hom_left, RetractArrow.r_w, Limits.KernelFork.mapIsoOfIsLimit_inv, Arrow.inv_left, Functor.LeibnizAdjunction.adj_counit_app_right, Arrow.comp_right_assoc, CosimplicialObject.augmentedCechConerve_obj, Limits.CokernelCofork.mapIsoOfIsColimit_hom, RetractArrow.right_i, Arrow.inv_hom_id_right, Arrow.hasLimitsOfShape, Arrow.isoMk_inv_right, Square.toArrowArrowFunctor_obj_right_right, ComposableArrows.arrowEquiv_symm_apply, Arrow.hasColimit, Square.fromArrowArrowFunctor_obj_f₁₃, CosimplicialObject.Augmented.toArrow_map_right, Limits.coker.condition, groupHomology.d₁₀ArrowIso_inv_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, Functor.mapArrow_map_left, SmallObject.ιFunctorObj_eq, RetractArrow.retract_left, Limits.im_map, Square.arrowArrowEquivalence_inverse, RetractArrow.retract_right_assoc, CosimplicialObject.Augmented.toArrow_map_left, Square.fromArrowArrowFunctor_obj_X₁, SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, Arrow.preservesColimitsOfShape_leftFunc, Functor.PushoutObjObj.ι_iso_of_iso_right_hom, RetractArrow.op_i_right, Abelian.coim_obj, Functor.mapArrow_map_right, RetractArrow.retract_right, Square.toArrowArrowFunctor_obj_hom_left, ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, SmallObject.πObj_ιIteration_app_right_assoc, MorphismProperty.ofHoms_homFamily, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, Functor.PullbackObjObj.mapArrowRight_comp, RetractArrow.map_r_left, Limits.im_obj, Functor.PullbackObjObj.π_iso_of_iso_right_inv, MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, CosimplicialObject.Augmented.toArrow_obj_left, Square.toArrowArrowFunctor'_map_left_right, Arrow.id_left, Abelian.coimageImageComparisonFunctor_obj, Square.fromArrowArrowFunctor'_obj_f₁₃, OrthogonalReflection.D₂.multispanIndex_left, Arrow.equivSigma_symm_apply_hom, MorphismProperty.homFamily_arrow_mk, RetractArrow.unop_r_right, Arrow.id_right, SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, SimplicialObject.equivalenceRightToLeft_right, Functor.PullbackObjObj.mapArrowLeft_comp_assoc, Functor.isEquivalence_mapArrow, Functor.PushoutObjObj.ι_iso_of_iso_left_inv, NatTrans.retractArrowApp_r, CosimplicialObject.Augmented.toArrow_obj_right, SimplicialObject.cechNerve_obj, SmallObject.functorialFactorizationData_Z_map, CosimplicialObject.Augmented.toArrow_obj_hom, Square.arrowArrowEquivalence'_inverse, Functor.leibnizPushout_obj_obj, Limits.multicospanShapeEnd_R, Arrow.inv_hom_id_left_assoc, Square.fromArrowArrowFunctor_obj_X₄, Square.fromArrowArrowFunctor'_obj_X₄, SimplicialObject.cechNerve_map, MorphismProperty.mem_toSet_iff, SimplicialObject.cechNerveEquiv_symm_apply, TransfiniteCompositionOfShape.ofArrowIso_incl, Arrow.rightFunc_obj, DerivedCategory.instEssSurjArrowHomotopyCategoryIntUpMapArrowQh, Abelian.PreservesCoimageImageComparison.iso_inv_right, Abelian.im_obj, CosimplicialObject.cechConerve_map, RetractArrow.instIsSplitEpiRightRArrow, SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, CosimplicialObject.augmentedCechConerve_map, Sheaf.instIsLocallyInjectiveAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, instSmallArrowOfLocallySmall, Arrow.iso_w, Arrow.comp_left_assoc, SmallObject.πFunctorObj_eq, SmallObject.objMap_comp, Square.fromArrowArrowFunctor_obj_f₁₂, Square.toArrowArrowFunctor_map_left_left, ShortComplex.gFunctor_obj, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, Abelian.coimageImageComparisonFunctor_map, RetractArrow.map_i_left, Square.fromArrowArrowFunctor'_obj_X₁, Arrow.isoMk_hom_left, SimplicialObject.equivalenceRightToLeft_left, Square.toArrowArrowFunctor_obj_right_hom, Square.toArrowArrowFunctor_obj_right_left, RetractArrow.op_r_left, Square.fromArrowArrowFunctor'_map_τ₄, MorphismProperty.FunctorialFactorizationData.fac_app, hasCardinalLT_arrow_op_iff, Functor.PushoutObjObj.ι_iso_of_iso_right_inv, ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, Square.toArrowArrowFunctor_obj_left_right, CosimplicialObject.equivalenceRightToLeft_right_app, Square.toArrowArrowFunctor'_map_left_left, MorphismProperty.FunctorialFactorizationData.mapZ_comp, Functor.PullbackObjObj.mapArrowRight_id, Arrow.hom_inv_id_left, Square.fromArrowArrowFunctor_obj_f₂₄, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, Arrow.hasColimits, Arrow.inv_hom_id_left, Square.fromArrowArrowFunctor'_map_τ₂, ComposableArrows.arrowEquiv_apply, Square.fromArrowArrowFunctor_map_τ₁, RetractArrow.op_i_left, OrthogonalReflection.D₁.ι_comp_t, CosimplicialObject.equivalenceLeftToRight_left, Functor.mapArrowFunctor_map_app_right, SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, PreGaloisCategory.autEmbedding_range, SmallObject.transfiniteCompositionOfShapeSuccStructPropιIteration_F, Square.arrowArrowEquivalence'_unitIso, SimplicialObject.Augmented.toArrow_obj_hom, Square.arrowArrowEquivalence'_functor, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, Limits.KernelFork.mapIsoOfIsLimit_hom, MorphismProperty.IsSmall.small_toSet, OrthogonalReflection.D₂.multispanIndex_fst, RetractArrow.map_i_right, Functor.PushoutObjObj.mapArrowLeft_comp_assoc, ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, TransfiniteCompositionOfShape.ofArrowIso_isColimit, Localization.essSurj_mapArrow_of_hasRightCalculusOfFractions, Localization.essSurj_mapArrow, RetractArrow.instIsSplitMonoRightIArrow, SimplicialObject.cechNerveEquiv_apply, Functor.LeibnizAdjunction.adj_unit_app_right, Arrow.finite_iff, Limits.ker.condition_assoc, Square.fromArrowArrowFunctor'_map_τ₁, Arrow.preservesColimitsOfShape_rightFunc, Square.toArrowArrowFunctor'_map_right_right, MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, RetractArrow.unop_i_left, SmallObject.functor_obj, CosimplicialObject.equivalenceRightToLeft_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, Arrow.leftFunc_map, Functor.mapArrowFunctor_map_app_left, Pretriangulated.exists_iso_of_arrow_iso, Square.fromArrowArrowFunctor_map_τ₂, RetractArrow.unop_i_right, Square.toArrowArrowFunctor'_obj_hom_right, Arrow.inv_right, Square.toArrowArrowFunctor_map_left_right, groupHomology.d₁₀ArrowIso_hom_right, SmallObject.prop_iterationFunctor_map_succ, Square.toArrowArrowFunctor_map_right_left, Arrow.hom_inv_id_right, Square.toArrowArrowFunctor'_obj_left_left, Functor.PushoutObjObj.mapArrowRight_comp, Limits.multispanShapeCoend_L, RetractArrow.left_i, Arrow.inv_hom_id_right_assoc, RetractArrow.instIsSplitEpiLeftRArrow, CosimplicialObject.cechConerve_obj, Square.arrowArrowEquivalence'_counitIso, SmallObject.functorialFactorizationData_p_app, MorphismProperty.toSet_max, SimplicialObject.augmentedCechNerve_obj_right, SimplicialObject.augmentedCechNerve_map_left_app, SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, SimplicialObject.augmentedCechNerve_obj_left_map, Arrow.finite, Square.toArrowArrowFunctor'_obj_hom_left, Limits.HasImageMap.comp, Square.arrowArrowEquivalence_unitIso, SimplicialObject.augmentedCechNerve_obj_left_obj, MorphismProperty.FunctorialFactorizationData.fac_assoc, CosimplicialObject.equivalenceLeftToRight_right, SmallObject.preservesColimit, hasCardinalLT_arrow_shrink_iff, Functor.leibnizPullback_map_app, MorphismProperty.FunctorialFactorizationData.hp, MorphismProperty.FunctorialFactorizationData.mapZ_comp_assoc, RetractArrow.i_w_assoc, RetractArrow.unop_r_left, Functor.PushoutObjObj.mapArrowLeft_comp, SmallObject.hasColimitsOfShape_discrete, SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, Functor.PullbackObjObj.π_iso_of_iso_left_hom, groupHomology.d₁₀ArrowIso_inv_left, Arrow.equivSigma_apply_snd_fst, HomotopicalAlgebra.AttachCells.ofArrowIso_g₁, Functor.PushoutObjObj.ι_iso_of_iso_left_hom, CosimplicialObject.cechConerveEquiv_apply, Arrow.hasColimitsOfShape, SmallObject.instIsIsoRightAppArrowιIteration, Arrow.comp_right, Square.toArrowArrowFunctor'_obj_right_left, RetractArrow.instIsSplitMonoLeftIArrow, Square.fromArrowArrowFunctor'_obj_f₂₄, Functor.leibnizPullback_obj_obj, MorphismProperty.FunctorialFactorizationData.fac_app_assoc, Arrow.hom_inv_id_left_assoc, Square.toArrowArrowFunctor'_obj_right_hom, MorphismProperty.homFamily_apply, ShortComplex.fFunctor_map, NatTrans.retractArrowApp_i, Functor.leibnizPushout_map_app, Square.toArrowArrowFunctor'_obj_left_right, SimplicialObject.equivalenceLeftToRight_left_app, Square.toArrowArrowFunctor_obj_left_hom, Abelian.coimIsoIm_hom_app, Square.fromArrowArrowFunctor'_obj_f₁₂, SimplicialObject.augmentedCechNerve_obj_hom_app, OrthogonalReflection.D₂.multispanIndex_snd, SimplicialObject.augmentedCechNerve_map_right, Square.arrowArrowEquivalence_counitIso, Arrow.isoMk_hom_right, Arrow.iso_w', SimplicialObject.equivalenceLeftToRight_right, Limits.ker_map, Sheaf.instEpiAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, Square.fromArrowArrowFunctor'_obj_f₃₄, Abelian.coimIsoIm_inv_app, Arrow.equivSigma_symm_apply_right, MorphismProperty.toSet_iSup, Square.fromArrowArrowFunctor_map_τ₄, ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, MorphismProperty.FunctorialFactorizationData.mapZ_id, Arrow.rightFunc_map, Limits.kernelSubobjectMap_id, HomologicalComplex.Hom.sqFrom_id
instCategoryArrow 📖	CompOp	324 math math: SmallObject.functorMap_id, Limits.coker.π_app, Functor.leibnizPullback_obj_map, SmallObject.SuccStruct.prop.arrowIso_hom_left, RetractArrow.right_r, Limits.instPreservesWellOrderContinuousOfShapeArrowRightFuncOfHasIterationOfShape, SmallObject.SuccStruct.prop.arrowIso_inv_left, Functor.mapArrow_obj, Square.arrowArrowEquivalence_functor, Sheaf.instIsLocallySurjectiveAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, MorphismProperty.FunctorialFactorizationData.hi, Arrow.hom_inv_id_right_assoc, RetractArrow.retract_left_assoc, RetractArrow.left_r, Functor.PushoutObjObj.mapArrowRight_id, Functor.PullbackObjObj.mapArrowLeft_id, SmallObject.πObj_ιIteration_app_right, Limits.IsImage.ofArrowIso_lift, Abelian.PreservesCoimageImageComparison.iso_inv_left, Limits.image.map_id, ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, SimplicialObject.Augmented.toArrow_map_right, Square.fromArrowArrowFunctor_map_τ₃, ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, Arrow.hasLimit, MorphismProperty.FunctorialFactorizationData.fac, Square.toArrowArrowFunctor_obj_hom_right, Arrow.comp_left, Arrow.isIso_of_isIso_left_of_isIso_right, RetractArrow.r_w_assoc, LocalizerMorphism.hasRightResolutions_arrow_of_functorial_resolutions, Functor.PullbackObjObj.π_iso_of_iso_left_inv, Limits.image.map_comp, Arrow.leftFunc_obj, groupCohomology.dArrowIso₀₁_inv_right, Functor.LeibnizAdjunction.adj_unit_app_left, SimplicialObject.Augmented.toArrow_map_left, MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, Limits.coker_map, Square.toArrowArrowFunctor'_obj_left_hom, Square.fromArrowArrowFunctor_obj_f₃₄, SmallObject.functorialFactorizationData_i_app, SimplicialObject.Augmented.toArrow_obj_left, Abelian.coim_map, TransfiniteCompositionOfShape.ofArrowIso_isoBot, RetractArrow.map_r_right, Functor.PullbackObjObj.mapArrowLeft_comp, ParametrizedAdjunction.arrowHomEquiv_apply_left, LocalizerMorphism.arrow_functor, RetractArrow.i_w, Functor.LeibnizAdjunction.adj_counit_app_left, groupHomology.d₁₀ArrowIso_hom_left, Functor.leibnizAdjunction_adj, Square.fromArrowArrowFunctor'_obj_X₂, ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, Limits.kernelSubobjectMap_comp, Limits.coker.condition_assoc, Square.fromArrowArrowFunctor'_obj_X₃, HomotopicalAlgebra.AttachCells.ofArrowIso_g₂, MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, HomologicalComplex.Hom.sqFrom_comp, HomotopicalAlgebra.FibrantObject.instHasRightResolutionsArrowArrowWeakEquivalencesArrowLocalizerMorphism, groupCohomology.dArrowIso₀₁_hom_right, Abelian.PreservesCoimageImageComparison.iso_hom_left, Functor.PullbackObjObj.π_iso_of_iso_right_hom, Functor.PushoutObjObj.mapArrowRight_comp_assoc, Abelian.im_map, Functor.PullbackObjObj.mapArrowRight_comp_assoc, HomotopicalAlgebra.CofibrantObject.instHasLeftResolutionsArrowArrowWeakEquivalencesArrowLocalizerMorphism, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, SimplicialObject.Augmented.toArrow_obj_right, Square.toArrowArrowFunctor_obj_left_left, ShortComplex.gFunctor_map, Arrow.hasLimits, Limits.instPreservesWellOrderContinuousOfShapeArrowLeftFuncOfHasIterationOfShape, Square.fromArrowArrowFunctor_obj_X₃, RetractArrow.op_r_right, Abelian.PreservesCoimageImageComparison.iso_hom_right, SmallObject.SuccStruct.prop.arrowIso_inv_right, Square.fromArrowArrowFunctor'_map_τ₃, Limits.ker.ι_app, SmallObject.functor_map, Square.fromArrowArrowFunctor_obj_X₂, Arrow.leftToRight_app, Functor.mapArrowFunctor_obj, groupCohomology.dArrowIso₀₁_inv_left, SmallObject.objMap_comp_assoc, Limits.ker_obj, SmallObject.functorialFactorizationData_Z_obj, Limits.instHasIterationOfShapeArrow, Square.toArrowArrowFunctor'_obj_right_right, Square.toArrowArrowFunctor_map_right_right, Sheaf.instMonoAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, Limits.CokernelCofork.mapIsoOfIsColimit_inv, ShortComplex.fFunctor_obj, Functor.leibnizPushout_obj_map, Limits.ker.condition, Functor.PushoutObjObj.mapArrowLeft_id, Arrow.isoMk_inv_left, CosimplicialObject.cechConerveEquiv_symm_apply, SmallObject.ε_app, SmallObject.succStruct_prop_le_propArrow, Ind.exists_nonempty_arrow_mk_iso_ind_lim, AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff, SmallObject.iterationObjRightIso_hom, SmallObject.objMap_id, SmallObject.SuccStruct.prop.arrowIso_hom_right, Limits.coker_obj, Square.toArrowArrowFunctor'_map_right_left, ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, groupCohomology.dArrowIso₀₁_hom_left, RetractArrow.r_w, Limits.KernelFork.mapIsoOfIsLimit_inv, Arrow.inv_left, Functor.LeibnizAdjunction.adj_counit_app_right, Arrow.comp_right_assoc, CosimplicialObject.augmentedCechConerve_obj, Limits.CokernelCofork.mapIsoOfIsColimit_hom, RetractArrow.right_i, Arrow.inv_hom_id_right, Arrow.hasLimitsOfShape, Arrow.isoMk_inv_right, Square.toArrowArrowFunctor_obj_right_right, Arrow.hasColimit, Square.fromArrowArrowFunctor_obj_f₁₃, CosimplicialObject.Augmented.toArrow_map_right, Limits.coker.condition, groupHomology.d₁₀ArrowIso_inv_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, Functor.mapArrow_map_left, SmallObject.ιFunctorObj_eq, RetractArrow.retract_left, Limits.im_map, Square.arrowArrowEquivalence_inverse, RetractArrow.retract_right_assoc, CosimplicialObject.Augmented.toArrow_map_left, Square.fromArrowArrowFunctor_obj_X₁, SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, Arrow.preservesColimitsOfShape_leftFunc, Functor.PushoutObjObj.ι_iso_of_iso_right_hom, RetractArrow.op_i_right, Abelian.coim_obj, Functor.mapArrow_map_right, RetractArrow.retract_right, Square.toArrowArrowFunctor_obj_hom_left, ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, SmallObject.πObj_ιIteration_app_right_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, Functor.PullbackObjObj.mapArrowRight_comp, RetractArrow.map_r_left, Limits.im_obj, Functor.PullbackObjObj.π_iso_of_iso_right_inv, MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, CosimplicialObject.Augmented.toArrow_obj_left, Square.toArrowArrowFunctor'_map_left_right, Arrow.id_left, Abelian.coimageImageComparisonFunctor_obj, Square.fromArrowArrowFunctor'_obj_f₁₃, RetractArrow.unop_r_right, Arrow.id_right, SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, SimplicialObject.equivalenceRightToLeft_right, Functor.PullbackObjObj.mapArrowLeft_comp_assoc, Functor.isEquivalence_mapArrow, Functor.PushoutObjObj.ι_iso_of_iso_left_inv, NatTrans.retractArrowApp_r, CosimplicialObject.Augmented.toArrow_obj_right, SimplicialObject.cechNerve_obj, SmallObject.functorialFactorizationData_Z_map, CosimplicialObject.Augmented.toArrow_obj_hom, Square.arrowArrowEquivalence'_inverse, Functor.leibnizPushout_obj_obj, Arrow.inv_hom_id_left_assoc, Square.fromArrowArrowFunctor_obj_X₄, Square.fromArrowArrowFunctor'_obj_X₄, SimplicialObject.cechNerve_map, SimplicialObject.cechNerveEquiv_symm_apply, TransfiniteCompositionOfShape.ofArrowIso_incl, Arrow.rightFunc_obj, DerivedCategory.instEssSurjArrowHomotopyCategoryIntUpMapArrowQh, Abelian.PreservesCoimageImageComparison.iso_inv_right, Abelian.im_obj, CosimplicialObject.cechConerve_map, RetractArrow.instIsSplitEpiRightRArrow, SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, CosimplicialObject.augmentedCechConerve_map, Sheaf.instIsLocallyInjectiveAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, Arrow.iso_w, Arrow.comp_left_assoc, SmallObject.πFunctorObj_eq, SmallObject.objMap_comp, Square.fromArrowArrowFunctor_obj_f₁₂, Square.toArrowArrowFunctor_map_left_left, ShortComplex.gFunctor_obj, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, Abelian.coimageImageComparisonFunctor_map, RetractArrow.map_i_left, Square.fromArrowArrowFunctor'_obj_X₁, Arrow.isoMk_hom_left, SimplicialObject.equivalenceRightToLeft_left, Square.toArrowArrowFunctor_obj_right_hom, Square.toArrowArrowFunctor_obj_right_left, RetractArrow.op_r_left, Square.fromArrowArrowFunctor'_map_τ₄, MorphismProperty.FunctorialFactorizationData.fac_app, Functor.PushoutObjObj.ι_iso_of_iso_right_inv, ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, Square.toArrowArrowFunctor_obj_left_right, CosimplicialObject.equivalenceRightToLeft_right_app, Square.toArrowArrowFunctor'_map_left_left, MorphismProperty.FunctorialFactorizationData.mapZ_comp, Functor.PullbackObjObj.mapArrowRight_id, Arrow.hom_inv_id_left, Square.fromArrowArrowFunctor_obj_f₂₄, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, Arrow.hasColimits, Arrow.inv_hom_id_left, Square.fromArrowArrowFunctor'_map_τ₂, Square.fromArrowArrowFunctor_map_τ₁, RetractArrow.op_i_left, CosimplicialObject.equivalenceLeftToRight_left, Functor.mapArrowFunctor_map_app_right, SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, SmallObject.transfiniteCompositionOfShapeSuccStructPropιIteration_F, Square.arrowArrowEquivalence'_unitIso, SimplicialObject.Augmented.toArrow_obj_hom, Square.arrowArrowEquivalence'_functor, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, Limits.KernelFork.mapIsoOfIsLimit_hom, RetractArrow.map_i_right, Functor.PushoutObjObj.mapArrowLeft_comp_assoc, ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, TransfiniteCompositionOfShape.ofArrowIso_isColimit, Localization.essSurj_mapArrow_of_hasRightCalculusOfFractions, Localization.essSurj_mapArrow, RetractArrow.instIsSplitMonoRightIArrow, SimplicialObject.cechNerveEquiv_apply, Functor.LeibnizAdjunction.adj_unit_app_right, Limits.ker.condition_assoc, Square.fromArrowArrowFunctor'_map_τ₁, Arrow.preservesColimitsOfShape_rightFunc, Square.toArrowArrowFunctor'_map_right_right, RetractArrow.unop_i_left, SmallObject.functor_obj, CosimplicialObject.equivalenceRightToLeft_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, Arrow.leftFunc_map, Functor.mapArrowFunctor_map_app_left, Pretriangulated.exists_iso_of_arrow_iso, Square.fromArrowArrowFunctor_map_τ₂, RetractArrow.unop_i_right, Square.toArrowArrowFunctor'_obj_hom_right, Arrow.inv_right, Square.toArrowArrowFunctor_map_left_right, groupHomology.d₁₀ArrowIso_hom_right, SmallObject.prop_iterationFunctor_map_succ, Square.toArrowArrowFunctor_map_right_left, Arrow.hom_inv_id_right, Square.toArrowArrowFunctor'_obj_left_left, Functor.PushoutObjObj.mapArrowRight_comp, RetractArrow.left_i, Arrow.inv_hom_id_right_assoc, RetractArrow.instIsSplitEpiLeftRArrow, CosimplicialObject.cechConerve_obj, Square.arrowArrowEquivalence'_counitIso, SmallObject.functorialFactorizationData_p_app, SimplicialObject.augmentedCechNerve_obj_right, SimplicialObject.augmentedCechNerve_map_left_app, SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, SimplicialObject.augmentedCechNerve_obj_left_map, Square.toArrowArrowFunctor'_obj_hom_left, Limits.HasImageMap.comp, Square.arrowArrowEquivalence_unitIso, SimplicialObject.augmentedCechNerve_obj_left_obj, MorphismProperty.FunctorialFactorizationData.fac_assoc, CosimplicialObject.equivalenceLeftToRight_right, Functor.leibnizPullback_map_app, MorphismProperty.FunctorialFactorizationData.hp, MorphismProperty.FunctorialFactorizationData.mapZ_comp_assoc, RetractArrow.i_w_assoc, RetractArrow.unop_r_left, Functor.PushoutObjObj.mapArrowLeft_comp, SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, Functor.PullbackObjObj.π_iso_of_iso_left_hom, groupHomology.d₁₀ArrowIso_inv_left, HomotopicalAlgebra.AttachCells.ofArrowIso_g₁, Functor.PushoutObjObj.ι_iso_of_iso_left_hom, CosimplicialObject.cechConerveEquiv_apply, Arrow.hasColimitsOfShape, SmallObject.instIsIsoRightAppArrowιIteration, Arrow.comp_right, Square.toArrowArrowFunctor'_obj_right_left, RetractArrow.instIsSplitMonoLeftIArrow, Square.fromArrowArrowFunctor'_obj_f₂₄, Functor.leibnizPullback_obj_obj, MorphismProperty.FunctorialFactorizationData.fac_app_assoc, Arrow.hom_inv_id_left_assoc, Square.toArrowArrowFunctor'_obj_right_hom, ShortComplex.fFunctor_map, NatTrans.retractArrowApp_i, Functor.leibnizPushout_map_app, Square.toArrowArrowFunctor'_obj_left_right, SimplicialObject.equivalenceLeftToRight_left_app, Square.toArrowArrowFunctor_obj_left_hom, Abelian.coimIsoIm_hom_app, Square.fromArrowArrowFunctor'_obj_f₁₂, SimplicialObject.augmentedCechNerve_obj_hom_app, SimplicialObject.augmentedCechNerve_map_right, Square.arrowArrowEquivalence_counitIso, Arrow.isoMk_hom_right, Arrow.iso_w', SimplicialObject.equivalenceLeftToRight_right, Limits.ker_map, Sheaf.instEpiAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, Square.fromArrowArrowFunctor'_obj_f₃₄, Abelian.coimIsoIm_inv_app, Square.fromArrowArrowFunctor_map_τ₄, ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, MorphismProperty.FunctorialFactorizationData.mapZ_id, Arrow.rightFunc_map, Limits.kernelSubobjectMap_id, HomologicalComplex.Hom.sqFrom_id
instInhabitedArrow 📖	CompOp	—

CategoryTheory.Arrow

Definitions

Name	Category	Theorems
discreteEquiv 📖	CompOp	—
equivSigma 📖	CompOp	6 math math: equivSigma_symm_apply_left, equivSigma_apply_snd_snd, equivSigma_apply_fst, equivSigma_symm_apply_hom, equivSigma_apply_snd_fst, equivSigma_symm_apply_right
homMk 📖	CompOp	17 math math: CategoryTheory.ShortComplex.gFunctor_map, CategoryTheory.SmallObject.functor_map, CategoryTheory.Square.toArrowArrowFunctor_map_right_right, CategoryTheory.SmallObject.ε_app, CategoryTheory.Square.toArrowArrowFunctor'_map_right_left, CategoryTheory.Square.toArrowArrowFunctor'_map_left_right, CategoryTheory.NatTrans.retractArrowApp_r, homMk_right, CategoryTheory.Square.toArrowArrowFunctor_map_left_left, CategoryTheory.Abelian.coimageImageComparisonFunctor_map, CategoryTheory.Square.toArrowArrowFunctor'_map_left_left, CategoryTheory.Square.toArrowArrowFunctor'_map_right_right, CategoryTheory.Square.toArrowArrowFunctor_map_left_right, CategoryTheory.Square.toArrowArrowFunctor_map_right_left, homMk_left, CategoryTheory.ShortComplex.fFunctor_map, CategoryTheory.NatTrans.retractArrowApp_i
homMk' 📖	CompOp	3 math math: CategoryTheory.Limits.image.map_homMk'_ι, homMk'_right, homMk'_left
instCoeOutHom 📖	CompOp	—
isoMk 📖	CompOp	4 math math: isoMk_inv_left, isoMk_inv_right, isoMk_hom_left, isoMk_hom_right
isoMk' 📖	CompOp	—
isoOfNatIso 📖	CompOp	—
leftFunc 📖	CompOp	20 math math: CategoryTheory.Sheaf.instIsLocallySurjectiveAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.MorphismProperty.FunctorialFactorizationData.hi, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac, leftFunc_obj, CategoryTheory.SmallObject.functorialFactorizationData_i_app, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isoBot, CategoryTheory.Limits.coker.condition_assoc, CategoryTheory.Limits.instPreservesWellOrderContinuousOfShapeArrowLeftFuncOfHasIterationOfShape, CategoryTheory.Limits.ker.ι_app, leftToRight_app, CategoryTheory.Limits.ker.condition, CategoryTheory.Limits.coker.condition, preservesColimitsOfShape_leftFunc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app, CategoryTheory.Limits.ker.condition_assoc, leftFunc_map, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_assoc, HomotopicalAlgebra.AttachCells.ofArrowIso_g₁, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assoc, CategoryTheory.Sheaf.instEpiAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization
leftToRight 📖	CompOp	7 math math: CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac, CategoryTheory.Limits.coker.condition_assoc, leftToRight_app, CategoryTheory.Limits.ker.condition, CategoryTheory.Limits.coker.condition, CategoryTheory.Limits.ker.condition_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_assoc
mk 📖	CompOp	—
rightFunc 📖	CompOp	20 math math: CategoryTheory.Limits.coker.π_app, CategoryTheory.Limits.instPreservesWellOrderContinuousOfShapeArrowRightFuncOfHasIterationOfShape, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac, CategoryTheory.Limits.coker.condition_assoc, HomotopicalAlgebra.AttachCells.ofArrowIso_g₂, leftToRight_app, CategoryTheory.Sheaf.instMonoAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.Limits.ker.condition, CategoryTheory.Limits.coker.condition, rightFunc_obj, CategoryTheory.Sheaf.instIsLocallyInjectiveAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, CategoryTheory.Limits.ker.condition_assoc, preservesColimitsOfShape_rightFunc, CategoryTheory.SmallObject.functorialFactorizationData_p_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.hp, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assoc, rightFunc_map
squareToSnd 📖	CompOp	2 math math: squareToSnd_left, squareToSnd_right

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
arrow_mk_comp_eqToHom 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.eqToHom	—	ext CategoryTheory.Category.id_comp
arrow_mk_eqToHom_comp 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.eqToHom	—	ext CategoryTheory.Category.comp_id
comp_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.id CategoryTheory.CategoryStruct.comp CategoryTheory.Arrow CategoryTheory.Category.toCategoryStruct CategoryTheory.instCategoryArrow CategoryTheory.Comma.left	—	—
comp_left_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left CategoryTheory.Arrow CategoryTheory.instCategoryArrow	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' comp_left
comp_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.id CategoryTheory.CategoryStruct.comp CategoryTheory.Arrow CategoryTheory.Category.toCategoryStruct CategoryTheory.instCategoryArrow CategoryTheory.Comma.right	—	—
comp_right_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.right CategoryTheory.Functor.id CategoryTheory.CommaMorphism.right CategoryTheory.Arrow CategoryTheory.instCategoryArrow	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' comp_right
epi_right 📖	mathematical	—	CategoryTheory.Epi CategoryTheory.Comma.right CategoryTheory.Functor.id CategoryTheory.CommaMorphism.right	—	CategoryTheory.Category.comp_id CategoryTheory.cancel_epi CategoryTheory.CommaMorphism.ext CategoryTheory.Comma.comp_left w_assoc
equivSigma_apply_fst 📖	mathematical	—	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct DFunLike.coe Equiv CategoryTheory.Arrow EquivLike.toFunLike Equiv.instEquivLike equivSigma CategoryTheory.Comma.left CategoryTheory.Functor.id	—	—
equivSigma_apply_snd_fst 📖	mathematical	—	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.id CategoryTheory.Comma.left DFunLike.coe Equiv CategoryTheory.Arrow EquivLike.toFunLike Equiv.instEquivLike equivSigma CategoryTheory.Comma.right	—	—
equivSigma_apply_snd_snd 📖	mathematical	—	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.id CategoryTheory.Comma.left DFunLike.coe Equiv CategoryTheory.Arrow EquivLike.toFunLike Equiv.instEquivLike equivSigma CategoryTheory.Comma.hom	—	—
equivSigma_symm_apply_hom 📖	mathematical	—	CategoryTheory.Comma.hom CategoryTheory.Functor.id DFunLike.coe Equiv Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Arrow EquivLike.toFunLike Equiv.instEquivLike Equiv.symm equivSigma	—	—
equivSigma_symm_apply_left 📖	mathematical	—	CategoryTheory.Comma.left CategoryTheory.Functor.id DFunLike.coe Equiv Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Arrow EquivLike.toFunLike Equiv.instEquivLike Equiv.symm equivSigma	—	—
equivSigma_symm_apply_right 📖	mathematical	—	CategoryTheory.Comma.right CategoryTheory.Functor.id DFunLike.coe Equiv Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Arrow EquivLike.toFunLike Equiv.instEquivLike Equiv.symm equivSigma	—	—
ext 📖	—	CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Comma.right CategoryTheory.Comma.hom CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.eqToHom CategoryTheory.Functor.obj	—	—	mk_eq_mk_iff
functor_ext 📖	—	CategoryTheory.Functor.obj CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Functor.mapArrow	—	—	CategoryTheory.Functor.ext
homMk'_left 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.comp	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.id homMk'	—	—
homMk'_right 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.comp	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.id homMk'	—	—
homMk_left 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Functor.obj CategoryTheory.Comma.right CategoryTheory.CategoryStruct.comp CategoryTheory.Comma.hom	CategoryTheory.CommaMorphism.left homMk	—	—
homMk_right 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Functor.obj CategoryTheory.Comma.right CategoryTheory.CategoryStruct.comp CategoryTheory.Comma.hom	CategoryTheory.CommaMorphism.right homMk	—	—
hom_ext 📖	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.right	—	—	CategoryTheory.CommaMorphism.ext
hom_ext_iff 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.right	—	hom_ext
hom_inv_id_left 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left CategoryTheory.Iso.hom CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Iso.inv CategoryTheory.CategoryStruct.id	—	comp_left CategoryTheory.Iso.hom_inv_id id_left
hom_inv_id_left_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left CategoryTheory.Iso.hom CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Iso.inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' hom_inv_id_left
hom_inv_id_right 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.right CategoryTheory.Functor.id CategoryTheory.CommaMorphism.right CategoryTheory.Iso.hom CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Iso.inv CategoryTheory.CategoryStruct.id	—	comp_right CategoryTheory.Iso.hom_inv_id id_right
hom_inv_id_right_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.right CategoryTheory.Functor.id CategoryTheory.CommaMorphism.right CategoryTheory.Iso.hom CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Iso.inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' hom_inv_id_right
id_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.id CategoryTheory.CategoryStruct.id CategoryTheory.Arrow CategoryTheory.Category.toCategoryStruct CategoryTheory.instCategoryArrow CategoryTheory.Comma.left	—	—
id_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.id CategoryTheory.CategoryStruct.id CategoryTheory.Arrow CategoryTheory.Category.toCategoryStruct CategoryTheory.instCategoryArrow CategoryTheory.Comma.right	—	—
inv_hom_id_left 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left CategoryTheory.Iso.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Iso.hom CategoryTheory.CategoryStruct.id	—	comp_left CategoryTheory.Iso.inv_hom_id id_left
inv_hom_id_left_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left CategoryTheory.Iso.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Iso.hom	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' inv_hom_id_left
inv_hom_id_right 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.right CategoryTheory.Functor.id CategoryTheory.CommaMorphism.right CategoryTheory.Iso.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Iso.hom CategoryTheory.CategoryStruct.id	—	comp_right CategoryTheory.Iso.inv_hom_id id_right
inv_hom_id_right_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.right CategoryTheory.Functor.id CategoryTheory.CommaMorphism.right CategoryTheory.Iso.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Iso.hom	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' inv_hom_id_right
inv_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.id CategoryTheory.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Comma.left isIso_left	—	CategoryTheory.IsIso.eq_inv_of_hom_inv_id isIso_left CategoryTheory.Comma.comp_left CategoryTheory.IsIso.hom_inv_id id_left
inv_left_hom_right 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Comma.right CategoryTheory.inv CategoryTheory.CommaMorphism.left isIso_left CategoryTheory.Functor.obj CategoryTheory.Comma.hom CategoryTheory.CommaMorphism.right	—	isIso_left w
inv_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.id CategoryTheory.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Comma.right isIso_right	—	CategoryTheory.IsIso.eq_inv_of_hom_inv_id isIso_right CategoryTheory.Comma.comp_right CategoryTheory.IsIso.hom_inv_id id_right
isIso_hom_iff_isIso_hom_of_isIso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Functor.obj CategoryTheory.Functor.id CategoryTheory.Comma.left CategoryTheory.Comma.right CategoryTheory.Comma.hom	—	isIso_of_isIso CategoryTheory.IsIso.inv_isIso
isIso_hom_iff_isIso_of_isIso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Functor.obj CategoryTheory.Functor.id CategoryTheory.Comma.left CategoryTheory.Comma.right CategoryTheory.Comma.hom	—	isIso_hom_iff_isIso_hom_of_isIso
isIso_iff_isIso_of_isIso 📖	mathematical	—	CategoryTheory.IsIso	—	isIso_hom_iff_isIso_hom_of_isIso
isIso_left 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left	—	CategoryTheory.IsIso.hom_inv_id CategoryTheory.IsIso.inv_hom_id
isIso_of_isIso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Functor.obj CategoryTheory.Functor.id CategoryTheory.Comma.left CategoryTheory.Comma.right CategoryTheory.Comma.hom	—	iso_w' CategoryTheory.IsIso.comp_isIso isIso_left CategoryTheory.Iso.isIso_inv isIso_right CategoryTheory.Iso.isIso_hom
isIso_of_isIso_left_of_isIso_right 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Arrow CategoryTheory.instCategoryArrow	—	CategoryTheory.Category.assoc w_mk_right hom_ext CategoryTheory.IsIso.hom_inv_id CategoryTheory.IsIso.inv_hom_id
isIso_right 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.Comma.right CategoryTheory.Functor.id CategoryTheory.CommaMorphism.right	—	CategoryTheory.IsIso.hom_inv_id CategoryTheory.IsIso.inv_hom_id
isoMk_hom_left 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Functor.obj CategoryTheory.Comma.right CategoryTheory.CategoryStruct.comp CategoryTheory.Iso.hom CategoryTheory.Comma.hom	CategoryTheory.CommaMorphism.left CategoryTheory.Arrow CategoryTheory.instCategoryArrow isoMk	—	—
isoMk_hom_right 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Functor.obj CategoryTheory.Comma.right CategoryTheory.CategoryStruct.comp CategoryTheory.Iso.hom CategoryTheory.Comma.hom	CategoryTheory.CommaMorphism.right CategoryTheory.Arrow CategoryTheory.instCategoryArrow isoMk	—	—
isoMk_inv_left 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Functor.obj CategoryTheory.Comma.right CategoryTheory.CategoryStruct.comp CategoryTheory.Iso.hom CategoryTheory.Comma.hom	CategoryTheory.CommaMorphism.left CategoryTheory.Iso.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow isoMk	—	—
isoMk_inv_right 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Functor.obj CategoryTheory.Comma.right CategoryTheory.CategoryStruct.comp CategoryTheory.Iso.hom CategoryTheory.Comma.hom	CategoryTheory.CommaMorphism.right CategoryTheory.Iso.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow isoMk	—	—
iso_w 📖	mathematical	—	CategoryTheory.Comma.hom CategoryTheory.Functor.id CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Comma.right CategoryTheory.CommaMorphism.left CategoryTheory.Iso.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.Functor.obj CategoryTheory.CommaMorphism.right CategoryTheory.Iso.hom	—	hom.congr_right CategoryTheory.Iso.inv_hom_id w_assoc id_right comp_right CategoryTheory.Category.comp_id
iso_w' 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Comma.right CategoryTheory.CommaMorphism.left CategoryTheory.Iso.inv CategoryTheory.Arrow CategoryTheory.instCategoryArrow CategoryTheory.CommaMorphism.right CategoryTheory.Iso.hom	—	iso_w
leftFunc_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Arrow CategoryTheory.instCategoryArrow leftFunc CategoryTheory.CommaMorphism.left CategoryTheory.Functor.id	—	—
leftFunc_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Arrow CategoryTheory.instCategoryArrow leftFunc CategoryTheory.Comma.left CategoryTheory.Functor.id	—	—
leftToRight_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Arrow CategoryTheory.instCategoryArrow leftFunc rightFunc leftToRight CategoryTheory.Comma.hom CategoryTheory.Functor.id	—	—
left_hom_inv_right 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Comma.right CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma.hom CategoryTheory.inv CategoryTheory.CommaMorphism.right isIso_right	—	isIso_right w
mk_eq 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Functor.id CategoryTheory.Comma.left CategoryTheory.Comma.right CategoryTheory.Comma.hom	—	—
mk_eq_mk_iff 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.eqToHom	—	CategoryTheory.CommaMorphism.w CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' CategoryTheory.Comma.eqToHom_right CategoryTheory.Comma.eqToHom_left CategoryTheory.eqToHom_trans CategoryTheory.eqToHom_refl CategoryTheory.Category.comp_id CategoryTheory.Category.id_comp
mk_hom 📖	mathematical	—	CategoryTheory.Comma.hom CategoryTheory.Functor.id	—	—
mk_inj 📖	—	—	—	—	mk_injective
mk_injective 📖	mathematical	—	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Arrow	—	—
mk_left 📖	mathematical	—	CategoryTheory.Comma.left CategoryTheory.Functor.id	—	—
mk_right 📖	mathematical	—	CategoryTheory.Comma.right CategoryTheory.Functor.id	—	—
mk_surjective 📖	—	—	—	—	—
mono_left 📖	mathematical	—	CategoryTheory.Mono CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left	—	CategoryTheory.Category.id_comp CategoryTheory.cancel_mono CategoryTheory.CommaMorphism.ext CategoryTheory.Comma.comp_right CategoryTheory.Category.assoc w
rightFunc_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Arrow CategoryTheory.instCategoryArrow rightFunc CategoryTheory.CommaMorphism.right CategoryTheory.Functor.id	—	—
rightFunc_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Arrow CategoryTheory.instCategoryArrow rightFunc CategoryTheory.Comma.right CategoryTheory.Functor.id	—	—
squareToSnd_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.id squareToSnd CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left	—	—
squareToSnd_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.id squareToSnd CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	—	—
square_from_iso_invert 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.id CategoryTheory.Comma.right CategoryTheory.Iso.inv CategoryTheory.Comma.left CategoryTheory.CommaMorphism.left CategoryTheory.Iso.hom CategoryTheory.Comma.hom CategoryTheory.CommaMorphism.right	—	w CategoryTheory.Iso.inv_hom_id_assoc
square_to_iso_invert 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.id CategoryTheory.Comma.left CategoryTheory.Comma.right CategoryTheory.Comma.hom CategoryTheory.Iso.hom CategoryTheory.CommaMorphism.right CategoryTheory.Iso.inv CategoryTheory.CommaMorphism.left	—	CategoryTheory.Category.assoc CategoryTheory.Iso.comp_inv_eq w_mk_right
w 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.Functor.obj CategoryTheory.Comma.right CategoryTheory.CommaMorphism.left CategoryTheory.Comma.hom CategoryTheory.CommaMorphism.right	—	w_mk_right
w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left CategoryTheory.Comma.right CategoryTheory.Comma.hom CategoryTheory.CommaMorphism.right	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' w
w_mk_right 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma.right CategoryTheory.Comma.hom CategoryTheory.CommaMorphism.right	—	CategoryTheory.CommaMorphism.w
w_mk_right_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Comma.left CategoryTheory.Functor.id CategoryTheory.CommaMorphism.left CategoryTheory.Comma.right CategoryTheory.Comma.hom CategoryTheory.CommaMorphism.right	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' w_mk_right

CategoryTheory.Arrow.hom

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
congr_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.id	—	—
congr_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.id	—	—

CategoryTheory.Functor

Definitions

Name	Category	Theorems
mapArrow 📖	CompOp	15 math math: mapArrow_obj, CategoryTheory.RetractArrow.map_r_right, CategoryTheory.LocalizerMorphism.arrow_functor, mapArrowFunctor_obj, mapArrow_map_left, mapArrow_map_right, CategoryTheory.RetractArrow.map_r_left, isEquivalence_mapArrow, DerivedCategory.instEssSurjArrowHomotopyCategoryIntUpMapArrowQh, CategoryTheory.RetractArrow.map_i_left, mapArrowFunctor_map_app_right, CategoryTheory.RetractArrow.map_i_right, CategoryTheory.Localization.essSurj_mapArrow_of_hasRightCalculusOfFractions, CategoryTheory.Localization.essSurj_mapArrow, mapArrowFunctor_map_app_left
mapArrowEquivalence 📖	CompOp	—
mapArrowFunctor 📖	CompOp	11 math math: AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, mapArrowFunctor_obj, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, mapArrowFunctor_map_app_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, mapArrowFunctor_map_app_left

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
isEquivalence_mapArrow 📖	mathematical	—	IsEquivalence CategoryTheory.Arrow CategoryTheory.instCategoryArrow mapArrow	—	CategoryTheory.Equivalence.isEquivalence_functor
mapArrowFunctor_map_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left id obj CategoryTheory.Arrow CategoryTheory.instCategoryArrow mapArrow CategoryTheory.NatTrans.app map CategoryTheory.Functor category mapArrowFunctor CategoryTheory.Comma.left	—	—
mapArrowFunctor_map_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right id obj CategoryTheory.Arrow CategoryTheory.instCategoryArrow mapArrow CategoryTheory.NatTrans.app map CategoryTheory.Functor category mapArrowFunctor CategoryTheory.Comma.right	—	—
mapArrowFunctor_obj 📖	mathematical	—	obj CategoryTheory.Functor category CategoryTheory.Arrow CategoryTheory.instCategoryArrow mapArrowFunctor mapArrow	—	—
mapArrow_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left id obj CategoryTheory.Comma.left CategoryTheory.Comma.right map CategoryTheory.Comma.hom CategoryTheory.Arrow CategoryTheory.instCategoryArrow mapArrow	—	—
mapArrow_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right id obj CategoryTheory.Comma.left CategoryTheory.Comma.right map CategoryTheory.Comma.hom CategoryTheory.Arrow CategoryTheory.instCategoryArrow mapArrow	—	—
mapArrow_obj 📖	mathematical	—	obj CategoryTheory.Arrow CategoryTheory.instCategoryArrow mapArrow id CategoryTheory.Comma.left CategoryTheory.Comma.right map CategoryTheory.Comma.hom	—	—

CategoryTheory.GrothendieckTopology.Cover

Definitions

Name	Category	Theorems
Arrow 📖	CompData	2 math math: preOneHypercover_I₀, shape_L

TypeVec

Definitions

Name	Category	Theorems
Arrow 📖	CompOp	16 math math: MvQPF.has_good_supp_iff, MvPFunctor.wDest'_wMk, MvPFunctor.wMk_eq, MvQPF.Fix.ind_aux, MvPFunctor.M.dest_eq_dest', MvPFunctor.map_eq, MvPFunctor.supp_eq, MvQPF.liftR_iff, MvPFunctor.liftP_iff', MvPFunctor.liftR_iff, MvQPF.wrepr_wMk, MvPFunctor.M.dest_corec', MvQPF.supp_eq_of_isUniform, MvPFunctor.liftP_iff, MvQPF.liftP_iff, MvQPF.recF_eq

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