Documentation Verification Report

InducedCategory

📁 Source: Mathlib/CategoryTheory/InducedCategory.lean

Statistics

MetricCount
DefinitionsInducedCategory, hom, hasCoeToSort, homEquiv, homMk, instCategory, isoMk, fullyFaithfulInducedFunctor, inducedFunctor
9
Theoremsext, ext_iff, comp_hom, comp_hom_assoc, faithful, full, homEquiv_apply, homEquiv_symm_apply_hom, homMk_hom, hom_ext, hom_ext_iff, id_hom, isoMk_hom, isoMk_inv, inducedFunctor_map, inducedFunctor_obj
16
Total25

CategoryTheory

Definitions

NameCategoryTheorems
InducedCategory 📖CompOp
32 mathmath: InducedCategory.endEquiv_symm_apply_hom, InducedCategory.endEquiv_apply, InducedCategory.faithful, InducedCategory.isoMk_inv, InducedCategory.homLinearEquiv_apply, InducedCategory.homEquiv_apply, InducedCategory.isGroupoid, Functor.inducedFunctorLinear, InducedCategory.comp_hom_assoc, TopCat.Sheaf.extend_hom_app, InducedCategory.homEquiv_symm_apply_hom, InducedCategory.comp_hom, InducedCategory.homAddEquiv_symm_apply_hom, Equivalence.induced_inverse_map, TopCat.Opens.coverDense_inducedFunctor, InducedCategory.homAddEquiv_apply, Equivalence.induced_unitIso, Equivalence.induced_inverse_obj, InducedCategory.id_hom, InducedCategory.eqToHom_hom, inducedFunctor_map, Equivalence.induced_functor, InducedCategory.isoMk_hom, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, InducedCategory.homLinearEquiv_symm_apply_hom, Functor.inducedFunctor_additive, inducedFunctor_obj, Equivalence.inducedFunctorOfEquiv, Equivalence.essSurjInducedFunctor, Equivalence.induced_counitIso, InducedCategory.full
fullyFaithfulInducedFunctor 📖CompOp
inducedFunctor 📖CompOp
16 mathmath: InducedCategory.faithful, Functor.inducedFunctorLinear, TopCat.Sheaf.extend_hom_app, Localization.whiskeringLeftFunctor'_eq, TopCat.Opens.coverDense_inducedFunctor, Equivalence.induced_unitIso, inducedFunctor_map, Equivalence.induced_functor, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, Functor.inducedFunctor_additive, inducedFunctor_obj, Equivalence.inducedFunctorOfEquiv, Equivalence.essSurjInducedFunctor, Equivalence.induced_counitIso, InducedCategory.full

Theorems

NameKindAssumesProvesValidatesDepends On
inducedFunctor_map 📖mathematicalFunctor.map
InducedCategory
InducedCategory.instCategory
inducedFunctor
InducedCategory.Hom.hom
inducedFunctor_obj 📖mathematicalFunctor.obj
InducedCategory
InducedCategory.instCategory
inducedFunctor

CategoryTheory.InducedCategory

Definitions

NameCategoryTheorems
hasCoeToSort 📖CompOp
homEquiv 📖CompOp
2 mathmath: homEquiv_apply, homEquiv_symm_apply_hom
homMk 📖CompOp
30 mathmath: homMk_hom, isoMk_inv, CategoryTheory.Preadditive.toCommGrp_map, AlgebraicGeometry.LocallyRingedSpace.Hom.toShHom_mk, AlgebraicGeometry.Scheme.forgetToTop_map, AlgebraicGeometry.SheafedSpace.isoMk_hom, lightProfiniteToLightDiagram_map, Sequential.isoOfHomeo_inv, TwoP.swap_map, Sequential.isoOfHomeo_hom, TannakaDuality.FiniteGroup.equivApp_inv, TannakaDuality.FiniteGroup.equivApp_hom, fintypeToFinBoolAlgOp_map, AlgebraicGeometry.SheafedSpace.restrictTopIso_inv, CategoryTheory.Equivalence.induced_inverse_map, CategoryTheory.Equivalence.induced_unitIso, FinBoolAlg.Iso.mk_inv, AlgebraicGeometry.LocallyRingedSpace.forgetToTop_map, CategoryTheory.Functor.FullyFaithful.mapCommGrp_preimage, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpaceHom_val, lightDiagramToLightProfinite_map, FinBoolAlg.hasForgetToFinPartOrd_forget₂_map, AlgebraicGeometry.LocallyRingedSpace.forgetToSheafedSpace_map, FinBoolAlg.Iso.mk_hom, isoMk_hom, TannakaDuality.FiniteGroup.ofRightFDRep_hom, FinBoolAlg.dual_map, AlgebraicGeometry.SheafedSpace.restrictTopIso_hom, CategoryTheory.Equivalence.induced_counitIso, AlgebraicGeometry.SheafedSpace.isoMk_inv
instCategory 📖CompOp
41 mathmath: CategoryTheory.CountableCategory.instObjAsType, endEquiv_symm_apply_hom, endEquiv_apply, faithful, isoMk_inv, homLinearEquiv_apply, homEquiv_apply, isGroupoid, CategoryTheory.Functor.inducedFunctorLinear, CategoryTheory.FinCategory.categoryAsType_comp, CategoryTheory.FinCategory.asTypeToObjAsType_map, CategoryTheory.FinCategory.categoryAsType_id, comp_hom_assoc, TopCat.Sheaf.extend_hom_app, homEquiv_symm_apply_hom, CategoryTheory.FinCategory.asTypeToObjAsType_obj, CategoryTheory.CountableCategory.instLocallySmallObjAsType, CategoryTheory.FinCategory.objAsTypeToAsType_map, comp_hom, homAddEquiv_symm_apply_hom, CategoryTheory.Equivalence.induced_inverse_map, TopCat.Opens.coverDense_inducedFunctor, homAddEquiv_apply, CategoryTheory.Equivalence.induced_unitIso, CategoryTheory.Equivalence.induced_inverse_obj, id_hom, CategoryTheory.CountableCategory.instCountableHomObjAsType, CategoryTheory.FinCategory.objAsTypeToAsType_obj, eqToHom_hom, CategoryTheory.inducedFunctor_map, CategoryTheory.Equivalence.induced_functor, isoMk_hom, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, homLinearEquiv_symm_apply_hom, CategoryTheory.Functor.inducedFunctor_additive, CategoryTheory.inducedFunctor_obj, CategoryTheory.Equivalence.inducedFunctorOfEquiv, CategoryTheory.Equivalence.essSurjInducedFunctor, CategoryTheory.Equivalence.induced_counitIso, full
isoMk 📖CompOp
3 mathmath: isoMk_inv, CategoryTheory.skeletonEquivalence_unitIso, isoMk_hom

Theorems

NameKindAssumesProvesValidatesDepends On
comp_hom 📖mathematicalHom.hom
CategoryTheory.CategoryStruct.comp
CategoryTheory.InducedCategory
CategoryTheory.Category.toCategoryStruct
instCategory
comp_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Hom.hom
CategoryTheory.InducedCategory
instCategory
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_hom
faithful 📖mathematicalCategoryTheory.Functor.Faithful
CategoryTheory.InducedCategory
instCategory
CategoryTheory.inducedFunctor
CategoryTheory.Functor.FullyFaithful.faithful
full 📖mathematicalCategoryTheory.Functor.Full
CategoryTheory.InducedCategory
instCategory
CategoryTheory.inducedFunctor
CategoryTheory.Functor.FullyFaithful.full
homEquiv_apply 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.InducedCategory
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
instCategory
EquivLike.toFunLike
Equiv.instEquivLike
homEquiv
Hom.hom
homEquiv_symm_apply_hom 📖mathematicalHom.hom
DFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.InducedCategory
instCategory
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
homEquiv
homMk_hom 📖mathematicalHom.hom
homMk
hom_ext 📖Hom.homHom.ext
hom_ext_iff 📖mathematicalHom.homhom_ext
id_hom 📖mathematicalHom.hom
CategoryTheory.CategoryStruct.id
CategoryTheory.InducedCategory
CategoryTheory.Category.toCategoryStruct
instCategory
isoMk_hom 📖mathematicalCategoryTheory.Iso.hom
CategoryTheory.InducedCategory
instCategory
isoMk
homMk
isoMk_inv 📖mathematicalCategoryTheory.Iso.inv
CategoryTheory.InducedCategory
instCategory
isoMk
homMk

CategoryTheory.InducedCategory.Hom

Definitions

NameCategoryTheorems
hom 📖CompOp
465 mathmath: CategoryTheory.Grp.mkIso_inv_hom, CategoryTheory.InducedCategory.homMk_hom, CategoryTheory.Grp.Hom.hom_div, CategoryTheory.Grp.comp', CategoryTheory.LeftExactFunctor.ofExact_map, CategoryTheory.InducedCategory.hom_ext_iff, CategoryTheory.Grp.mkIso_hom_hom, CategoryTheory.Grp.instIsIsoHomHomMon, CategoryTheory.Grp.homMk'_hom, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, CategoryTheory.CommMon.comp_hom, LinearMap.id_fgModuleCat_comp, CategoryTheory.Grp.Hom.hom_hom_zpow, CategoryTheory.ExactFunctor.forget_map, DeltaGenerated.topToDeltaGenerated_map_hom_hom_apply, CategoryTheory.Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.LeftExactFunctor.forget_map, CategoryTheory.Functor.mapCommMonNatIso_inv_app_hom_hom, FGModuleCat.hom_hom_id, HomotopicalAlgebra.weakEquivalence_iff_of_objectProperty, CategoryTheory.ObjectProperty.FullSubcategory.comp_hom_assoc, CategoryTheory.InducedCategory.endEquiv_symm_apply_hom, CategoryTheory.Grp.id', CategoryTheory.InducedCategory.endEquiv_apply, AlgebraicGeometry.SheafedSpace.colimit_exists_rep, CategoryTheory.MonoOver.isIso_left_iff_subobjectMk_eq, CategoryTheory.CommMon.forget_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Functor.FullyFaithful.mapGrp_preimage, CategoryTheory.InducedCategory.homLinearEquiv_apply, TwoP.hom_ext_iff, CategoryTheory.CommGrp.mkIso_inv_hom, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_rightUnitor_hom_hom, AlgebraicGeometry.LocallyRingedSpace.homMk_toHom, CategoryTheory.Grp.whiskerLeft_hom_hom, CategoryTheory.LaxBraidedFunctor.isoOfComponents_inv_hom_hom_app, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_leftUnitor_inv_hom, CategoryTheory.Functor.mapGrpIdIso_hom_app_hom_hom, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm_assoc, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.Grp.leftUnitor_hom_hom, AlgebraicGeometry.localRingHom_comp_stalkIso_apply, CategoryTheory.Functor.mapCommMonNatTrans_app_hom_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSheafedSpaceHom_hom_c, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp, CategoryTheory.CommComon.comp_hom, LinearMap.comp_id_fgModuleCat, CategoryTheory.CommGrp.id', CategoryTheory.InducedCategory.homEquiv_apply, CategoryTheory.ObjectProperty.eqToHom_hom, CategoryTheory.CommGrp.comp', CategoryTheory.CartesianMonoidalCategory.fullSubcategory_snd_hom, CategoryTheory.ObjectProperty.tensorHom_def, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.CommMon.mkIso'_inv_hom_hom, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac', CategoryTheory.LaxBraidedFunctor.comp_hom, CategoryTheory.Grp.rightUnitor_hom_hom_hom, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_eq, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_isTerminalTensorUnit_lift_hom, CategoryTheory.Grp.lift_hom, CategoryTheory.ObjectProperty.isoHom_inv_id_hom, lightDiagramToProfinite_map, CategoryTheory.CommGrp.comp_hom, CategoryTheory.Grp.hom_mul, CategoryTheory.LaxBraidedFunctor.isoOfComponents_hom_hom_app, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_fst_hom, CategoryTheory.RightExactFunctor.whiskeringLeft_map_app, CategoryTheory.MonoOver.mkArrowIso_hom_hom_left, TwoP.swapEquiv_functor_map_hom_toFun, AlgebraicGeometry.SheafedSpace.comp_hom_c_app, CategoryTheory.LaxBraidedFunctor.forget_map, lightProfiniteToLightDiagram_map, Profinite.exists_locallyConstant_finite_aux, CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eq, CategoryTheory.Grp.Hom.hom_zpow, CategoryTheory.RightExactFunctor.whiskeringRight_map_app, CategoryTheory.Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, HomotopicalAlgebra.FibrantObject.homRel_iff_leftHomotopyRel, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, CategoryTheory.AdditiveFunctor.ofLeftExact_map, CategoryTheory.RightExactFunctor.ofExact_map_hom, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.LeftExactFunctor.whiskeringRight_map_app, FGModuleCat.hom_comp, CategoryTheory.MorphismProperty.FunctorsInverting.id_hom, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_associator_inv_hom, SimplexCategory.Truncated.Hom.tr_comp', CategoryTheory.Grp.associator_inv_hom_hom, CategoryTheory.ObjectProperty.ι_map, CompHausLike.homeoOfIso_symm_apply, CategoryTheory.LeftExactFunctor.whiskeringRight_obj_map, CategoryTheory.Functor.mapCommMonNatIso_hom_app_hom_hom, CategoryTheory.AdditiveFunctor.ofRightExact_map, CategoryTheory.Grp.Hom.hom_hom_div, CategoryTheory.AdditiveFunctor.ofExact_map, CategoryTheory.Grp.leftUnitor_hom_hom_hom, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, FintypeCat.toProfinite_map_hom_hom_apply, CategoryTheory.CommGrp.instIsIsoMonHomGrp, CategoryTheory.Grp.forget_map, FGModuleCat.FGModuleCatEvaluation_apply, CategoryTheory.Grp.mkIso_hom_hom_hom, CategoryTheory.LeftExactFunctor.whiskeringLeft_map_app, FintypeCat.comp_hom, CategoryTheory.CommMon.instIsIsoHomHomMon, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_open, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.sheafedSpace_toSheafedSpace, CategoryTheory.RightExactFunctor.forget_map, CategoryTheory.CommGrp.forget₂CommMon_map_hom, UniformSpaceCat.extension_comp_coe, CategoryTheory.CommComon.forget₂Comon_map, FintypeCat.incl_map, CategoryTheory.InducedCategory.comp_hom_assoc, NonemptyFinLinOrd.hom_hom_ofHom, CategoryTheory.Grp.rightUnitor_inv_hom_hom, CategoryTheory.Grp.forget₂Mon_map_hom, AlgebraicGeometry.SheafedSpace.comp_base, AlgebraicGeometry.SheafedSpace.comp_c_app, FinPartOrd.hom_ofHom, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, AlgebraicGeometry.SheafedSpace.id_hom_c_app, FinPartOrd.hom_hom_comp, CategoryTheory.InducedCategory.homEquiv_symm_apply_hom, NonemptyFinLinOrd.hom_comp, CategoryTheory.Grp.whiskerRight_hom_hom, FGModuleCat.hom_id, AlgebraicGeometry.morphismRestrict_appLE, CategoryTheory.Functor.partialRightAdjointHomEquiv_map, CategoryTheory.Grp.Hom.hom_hom_inv, CategoryTheory.ObjectProperty.FullSubcategory.comp_def, CategoryTheory.LaxBraidedFunctor.isoOfComponents_hom_hom_hom_app, FinPartOrd.ofHom_hom_hom, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, CompactlyGenerated.compactlyGeneratedToTop_map, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map, CategoryTheory.Functor.essImage.liftFunctorCompIso_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Grp.snd_hom, CategoryTheory.Functor.toEssImage_map_hom, CategoryTheory.Functor.mapCommMonFunctor_map_app, CategoryTheory.Functor.mapContAction_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, FDRep.hom_hom_action_ρ, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac, CategoryTheory.ExactFunctor.whiskeringLeft_map_app, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_map_app, SSet.Truncated.spine_map_vertex, TwoP.swapEquiv_unitIso_hom_app_hom_toFun, CategoryTheory.Grp.whiskerLeft_hom, Condensed.isColimitLocallyConstantPresheaf_desc_apply, CategoryTheory.Pseudofunctor.ObjectProperty.map_map_hom, CompHausLike.LocallyConstant.functorToPresheaves_map_app, FGModuleCat.FGModuleCatCoevaluation_apply_one, TwoP.swap_map, CategoryTheory.LeftExactFunctor.ofExact_map_hom, CategoryTheory.LaxBraidedFunctor.comp_hom_assoc, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_app, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, CategoryTheory.Functor.mapGrpNatIso_hom_app_hom_hom, pointedToTwoPFst_map_hom_toFun, CategoryTheory.Functor.mapGrpFunctor_map_app, CategoryTheory.Functor.mapCommMonCompIso_inv_app_hom_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSheafedSpaceHom_base, Sequential.sequentialToTop_map, CategoryTheory.Functor.mapCommMonIdIso_hom_app_hom_hom, CategoryTheory.Grp.leftUnitor_inv_hom_hom, CategoryTheory.InducedCategory.comp_hom, AlgebraicGeometry.SheafedSpace.id_hom_base, DeltaGenerated.deltaGeneratedToTop_map, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_map_hom_app, CategoryTheory.ExactFunctor.whiskeringLeft_obj_map, CategoryTheory.Functor.mapCommGrpNatIso_inv_app_hom_hom_hom, FintypeCat.toLightProfinite_map_hom_hom_apply, AlgebraicGeometry.Spec.toPresheafedSpace_map_op, CategoryTheory.subterminalsEquivMonoOverTerminal_inverse_map, CategoryTheory.Grp.rightUnitor_inv_hom, TwoP.swapEquiv_counitIso_inv_app_hom_toFun, AlgebraicGeometry.stalkMap_toStalk, CategoryTheory.InducedCategory.homAddEquiv_symm_apply_hom, CategoryTheory.MonoOver.w, CategoryTheory.MorphismProperty.FunctorsInverting.comp_hom_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_map_hom_hom, CategoryTheory.CommGrp.hom_ext_iff, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, CategoryTheory.Grp.Hom.hom_pow, CategoryTheory.Grp.associator_hom_hom_hom, NonemptyFinLinOrd.hom_ext_iff, AlgebraicGeometry.SheafedSpace.Γ_map, CategoryTheory.CommMon.mkIso_inv_hom_hom, CategoryTheory.Grp.braiding_inv_hom, CategoryTheory.Grp.mkIso'_hom_hom_hom, CategoryTheory.CommComon.hom_ext_iff, FinPartOrd.dual_map, CategoryTheory.Grp.id_hom, CategoryTheory.Functor.mapGrpCompIso_hom_app_hom_hom, AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_app, CategoryTheory.Grp.fst_hom, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, CategoryTheory.CommGrp.mkIso_inv_hom_hom_hom, CategoryTheory.CommGrp.mkIso'_inv_hom_hom_hom, AlgebraicGeometry.SheafedSpace.fullyFaithfulForgetToPresheafedSpace_preimage_hom, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_stalk_isLocalHom, AlgebraicGeometry.AffineScheme.forgetToScheme_map, CategoryTheory.LaxBraidedFunctor.homMk_hom_hom, NonemptyFinLinOrd.ofHom_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSheafedSpaceHom_hom_base, CategoryTheory.InducedCategory.homAddEquiv_apply, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map_comp, AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, CategoryTheory.AdditiveFunctor.forget_map, AlgebraicGeometry.Spec.locallyRingedSpaceMap_toHom, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_app_isLocalHom, CpltSepUniformSpace.hom_comp, FGModuleCat.Iso.conj_eq_conj, CategoryTheory.ObjectProperty.FullSubcategory.id_def, CategoryTheory.ObjectProperty.ihom_map, SimplexCategory.Truncated.Hom.ext_iff, NonemptyFinLinOrd.hom_hom_id, CategoryTheory.fromSkeleton_map, CategoryTheory.RightExactFunctor.ofExact_map, CategoryTheory.Functor.mapCommMon_map_hom_hom, CategoryTheory.ObjectProperty.isoHom_inv_id_hom_assoc, CategoryTheory.Functor.FullyFaithful.mapCommMon_preimage, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, NonemptyFinLinOrd.dual_map, FGModuleCat.hom_hom_comp, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, CategoryTheory.Functor.mapGrp_map_hom_hom, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac_assoc, CategoryTheory.MonoOver.isIso_iff_isIso_hom_left, CategoryTheory.CommGrp.forget₂Grp_map_hom, HomotopicalAlgebra.BifibrantObject.homRel_iff_leftHomotopyRel, CategoryTheory.Grp.comp_hom_hom, CategoryTheory.ObjectProperty.whiskerLeft_def, AlgebraicGeometry.SheafedSpace.comp_hom_c_app', FGModuleCat.hom_ext_iff, CategoryTheory.Grp.braiding_inv_hom_hom, CategoryTheory.Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.LaxBraidedFunctor.isoOfComponents_inv_hom_app, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app, FintypeCat.comp_hom_assoc, CategoryTheory.CommGrp.mkIso_hom_hom, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π_assoc, AlgebraicGeometry.SheafedSpace.comp_hom_base, Profinite.exists_locallyConstant, CategoryTheory.ObjectProperty.whiskerRight_def, AlgebraicGeometry.stalkMap_toStalk_apply, CategoryTheory.ExactFunctor.whiskeringRight_map_app, CategoryTheory.Grp.Hom.hom_mul, AlgebraicGeometry.LocallyRingedSpace.homOfSheafedSpaceHomOfIsIso_toHom, CategoryTheory.subterminalsEquivMonoOverTerminal_functor_map, FintypeCat.hom_apply, CategoryTheory.Grp.rightUnitor_hom_hom, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.Grp.hom_ext_iff, CategoryTheory.InducedCategory.id_hom, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.Grp.homMk''_hom_hom, CategoryTheory.MonoOver.mkArrowIso_inv_hom_left, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_leftUnitor_hom_hom, CategoryTheory.CommMon.id_hom, CompHausLike.homeoOfIso_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Functor.essImage.liftFunctorCompIso_inv_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.stalk_iso, CategoryTheory.MonoOver.w_assoc, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app, ext_iff, CategoryTheory.Functor.FullyFaithful.mapCommGrp_preimage, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_map, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, CategoryTheory.CommGrp.instIsIsoGrpHom, AlgebraicGeometry.SheafedSpace.forgetToPresheafedSpace_map, CategoryTheory.Skeleton.comp_hom, CategoryTheory.Functor.mapGrpIdIso_inv_app_hom_hom, AlgebraicGeometry.SheafedSpace.id_hom, CategoryTheory.MonoOver.lift_map_hom, LightDiagram.id_hom_hom_hom_apply, CategoryTheory.toSkeletonFunctor_map_hom, CategoryTheory.CommGrp.mkIso_hom_hom_hom_hom, CategoryTheory.CommMon.homMk_hom, TwoP.swapEquiv_inverse_map_hom_toFun, CategoryTheory.Grp.leftUnitor_inv_hom, CompHausLike.compHausLikeToTop_map, CategoryTheory.CommGrp.id_hom, CategoryTheory.CommMon.mkIso_hom_hom_hom, AlgebraicGeometry.SheafedSpace.id_hom_c, AlgebraicGeometry.SheafedSpace.id_c_app, CompHausLike.toCompHausLike_map, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, FinPartOrd.hom_id, CategoryTheory.MorphismProperty.FunctorsInverting.comp_hom, CategoryTheory.ObjectProperty.ιOfLE_map, CategoryTheory.subterminalsEquivMonoOverTerminal_unitIso, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_associator_hom_hom, CategoryTheory.CommComon.id_hom, CategoryTheory.CommMon.hom_ext_iff, CategoryTheory.Functor.mapCommGrpFunctor_map, CategoryTheory.Grp.mkIso_inv_hom_hom, CategoryTheory.Grp.snd_hom_hom, CategoryTheory.Functor.mapGrpNatTrans_app_hom_hom, CategoryTheory.Grp.hom_one, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, TopCat.toSheafCompHausLike_val_map, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_comp, NonemptyFinLinOrd.hom_hom_comp, CategoryTheory.Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, CategoryTheory.yonedaCommGrpGrp_map_app, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp_assoc, CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, CategoryTheory.Grp.associator_inv_hom, CategoryTheory.subterminalsEquivMonoOverTerminal_counitIso, AlgebraicGeometry.Spec.sheafedSpaceMap_hom_base, CategoryTheory.Grp.homMk_hom_hom, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π, lightDiagramToLightProfinite_map, CategoryTheory.InducedCategory.eqToHom_hom, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_base, CategoryTheory.ObjectProperty.FullSubcategory.comp_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSheafedSpaceHom_c, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc, CategoryTheory.Functor.mapGrpNatIso_inv_app_hom_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, CompHausLike.isoOfHomeo_inv_hom_hom_apply, LightCondensed.isColimitLocallyConstantPresheaf_desc_apply, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_whiskerRight_hom, CategoryTheory.Functor.mapGrpCompIso_inv_app_hom_hom, CategoryTheory.Grp.Hom.hom_inv, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenEmbedding, CategoryTheory.Functor.mapCommGrpNatIso_hom_app_hom_hom_hom, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_preimage, FGModuleCat.FGModuleCatEvaluation_apply', AlgebraicGeometry.SheafedSpace.id_c, LightDiagram.comp_hom_hom_hom_apply, AlgebraicGeometry.Spec.toPresheafedSpace_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, FinBoolAlg.hasForgetToFinPartOrd_forget₂_map, pointedToTwoPSnd_map_hom_toFun, TwoP.swapEquiv_counitIso_hom_app_hom_toFun, CategoryTheory.inducedFunctor_map, CategoryTheory.Grp.braiding_hom_hom, CategoryTheory.Functor.mapCommGrp_map_hom_hom_hom, AlgebraicGeometry.Scheme.Opens.ι_appLE, AlgebraicGeometry.SheafedSpace.isOpenImmersion_iff_hom, AlgebraicGeometry.SheafedSpace.id_base, CompHausLike.LocallyConstant.incl_comap, CategoryTheory.ObjectProperty.hom_ext_iff, AlgebraicGeometry.SheafedSpace.congr_hom_app, CategoryTheory.Grp.associator_hom_hom, CategoryTheory.Preadditive.commGrpEquivalence_inverse_map, CategoryTheory.Functor.mapCommGrpNatTrans_app_hom_hom_hom, SimplexCategory.skeletalFunctor.coe_map, CategoryTheory.Functor.mapCommMonIdIso_inv_app_hom_hom, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_tensorProductIsBinaryProduct_lift_hom, CategoryTheory.RightExactFunctor.whiskeringLeft_obj_map, AlgebraicGeometry.SheafedSpace.is_presheafedSpace_iso, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.LaxBraidedFunctor.id_hom, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_val_app_hom_hom, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, CategoryTheory.AdditiveFunctor.ofExact_map_hom, TopCat.Presheaf.generateEquivalenceOpensLe_functor'_map, CategoryTheory.LaxBraidedFunctor.hom_ext_iff, CompHausLike.isoOfHomeo_hom_hom_hom_apply, CategoryTheory.yonedaGrp_map_app, AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec, CategoryTheory.subterminalInclusion_map, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, CategoryTheory.CommGrp.mkIso'_hom_hom_hom_hom, FinPartOrd.hom_comp, CategoryTheory.Grp.whiskerRight_hom, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_whiskerLeft_hom, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, AlgebraicGeometry.SheafedSpace.congr_app, HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject_map_toHoCat_map, CategoryTheory.Grp.tensorHom_hom, FintypeCat.id_hom, HomotopicalAlgebra.BifibrantObject.homRel_iff_rightHomotopyRel, AlgebraicGeometry.SheafedSpace.instEpiTopCatBaseHomPresheafedSpaceπ, AlgebraicGeometry.LocallyRingedSpace.isLocalHom_stalkMap_congr, Profinite.exists_locallyConstant_finite_nonempty, CategoryTheory.CommMon.mkIso'_hom_hom_hom, CategoryTheory.Grp.Hom.hom_one, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm, CategoryTheory.ExactFunctor.whiskeringRight_obj_map, CategoryTheory.Functor.essImage.liftFunctor_map, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.ObjectProperty.isoInv_hom_id_hom_assoc, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHomFullSubcategoryCofibrantObjectsIBifibrantResolutionObj, CategoryTheory.Grp.fst_hom_hom, CategoryTheory.LeftExactFunctor.whiskeringLeft_obj_map, FinBoolAlg.dual_map, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, SimplexCategory.Truncated.Hom.tr_comp'_assoc, CategoryTheory.Functor.EssImageSubcategory.lift_def, FGModuleCat.Iso.conj_hom_eq_conj, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.Grp.mkIso'_inv_hom_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, UniformSpaceCat.extension_comp_hom, CategoryTheory.InducedCategory.homLinearEquiv_symm_apply_hom, Profinite.exists_locallyConstant_fin_two, CategoryTheory.AdditiveFunctor.ofLeftExact_map_hom, CategoryTheory.ObjectProperty.homMk_hom, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_map, AlgebraicGeometry.localRingHom_comp_stalkIso, CategoryTheory.Preadditive.commGrpEquivalence_functor_map_hom_hom_hom, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'_app, ContAction.res_map, CategoryTheory.Grp.braiding_hom_hom_hom, FDRep.hom_action_ρ, FinPartOrd.ofHom_hom, FinPartOrd.hom_hom_id, CategoryTheory.CommMon.forget₂Mon_map_hom, CategoryTheory.Skeleton.comp_hom_assoc, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_tensorHom_hom, HomotopicalAlgebra.CofibrantObject.instCofibrationHomFullSubcategoryCofibrantObjectsIBifibrantResolutionObj, CategoryTheory.ObjectProperty.ihom_map_hom, CategoryTheory.Pseudofunctor.ObjectProperty.map₂_app_hom, CategoryTheory.ObjectProperty.isoInv_hom_id_hom, CategoryTheory.Functor.partialRightAdjointHomEquiv_map_comp, CategoryTheory.ObjectProperty.FullSubcategory.id_hom, HomotopicalAlgebra.instWeakEquivalenceHomFullSubcategory, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_map_app_hom_hom, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, CategoryTheory.Grp.comp_hom, FinPartOrd.hom_hom_ofHom, CategoryTheory.Grp.id_hom_hom, CategoryTheory.AdditiveFunctor.ofRightExact_map_hom, HomotopicalAlgebra.CofibrantObject.homRel_iff_rightHomotopyRel, AlgebraicGeometry.SheafedSpace.Γ_map_op, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, NonemptyFinLinOrd.hom_id, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac'_assoc, NonemptyFinLinOrd.hom_ofHom, TwoP.swapEquiv_unitIso_inv_app_hom_toFun, CategoryTheory.RightExactFunctor.whiskeringRight_obj_map, AlgebraicGeometry.SheafedSpace.comp_c_app', AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, CategoryTheory.MonoOver.isIso_iff_isIso_left, CategoryTheory.CommGrp.forget_map, FinPartOrd.hom_ext_iff, HomotopicalAlgebra.BifibrantObject.HoCat.ιFibrantObject_map_toHoCat_map, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_rightUnitor_inv_hom, CategoryTheory.MonoOver.instIsIsoLeftDiscretePUnitHomFullSubcategoryOverIsMono, CategoryTheory.Functor.mapCommMonCompIso_hom_app_hom_hom, CategoryTheory.MorphismProperty.FunctorsInverting.hom_ext_iff

Theorems

NameKindAssumesProvesValidatesDepends On
ext 📖hom
ext_iff 📖mathematicalhomext

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