Basic

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

Statistics

Metric	Count
Definitions equivProd, fromProd, fst, hom, inhabited, isoMk, left, leftIso, map, mapFst, mapLeft, mapLeftComp, mapLeftEq, mapLeftId, mapLeftIso, mapRight, mapRightComp, mapRightEq, mapRightId, mapRightIso, mapSnd, natTrans, opEquiv, opFunctor, opFunctorCompFst, opFunctorCompSnd, post, postIso, preLeft, preLeftIso, preRight, preRightIso, right, rightIso, snd, toIdPUnitEquiv, toPUnitIdEquiv, unopFunctor, unopFunctorCompFst, unopFunctorCompSnd, CommaMorphism, inhabited, left, right, commaCategory	45
Theorems comp_left, comp_right, eqToHom_left, eqToHom_right, equivProd_counitIso_hom_app, equivProd_counitIso_inv_app, equivProd_functor_map, equivProd_functor_obj, equivProd_inverse_map_left, equivProd_inverse_map_right, equivProd_inverse_obj_left, equivProd_inverse_obj_right, equivProd_unitIso_hom_app_left, equivProd_unitIso_hom_app_right, equivProd_unitIso_inv_app_left, equivProd_unitIso_inv_app_right, essSurj_map, faithful_map, fromProd_map_left, fromProd_map_right, fromProd_obj_hom, fromProd_obj_left, fromProd_obj_right, fst_map, fst_obj, full_map, hom_ext, hom_ext_iff, id_left, id_right, instEssSurjCompPostOfFull, instEssSurjCompPreLeft, instEssSurjCompPreRight, instFaithfulCompPost, instFaithfulCompPreLeft, instFaithfulCompPreRight, instFullCompPostOfFaithful, instFullCompPreLeft, instFullCompPreRight, instIsIsoLeft, instIsIsoRight, inv_left, inv_left_hom_right, inv_right, isEquivalenceMap, isEquivalence_post, isEquivalence_preLeft, isEquivalence_preRight, isoMk_hom_left, isoMk_hom_right, isoMk_inv_left, isoMk_inv_right, leftIso_hom, leftIso_inv, left_hom_inv_right, mapFst_hom_app, mapFst_inv_app, mapLeftComp_hom_app_left, mapLeftComp_hom_app_right, mapLeftComp_inv_app_left, mapLeftComp_inv_app_right, mapLeftEq_hom_app_left, mapLeftEq_hom_app_right, mapLeftEq_inv_app_left, mapLeftEq_inv_app_right, mapLeftId_hom_app_left, mapLeftId_hom_app_right, mapLeftId_inv_app_left, mapLeftId_inv_app_right, mapLeftIso_counitIso_hom_app_left, mapLeftIso_counitIso_hom_app_right, mapLeftIso_counitIso_inv_app_left, mapLeftIso_counitIso_inv_app_right, mapLeftIso_functor_map_left, mapLeftIso_functor_map_right, mapLeftIso_functor_obj_hom, mapLeftIso_functor_obj_left, mapLeftIso_functor_obj_right, mapLeftIso_inverse_map_left, mapLeftIso_inverse_map_right, mapLeftIso_inverse_obj_hom, mapLeftIso_inverse_obj_left, mapLeftIso_inverse_obj_right, mapLeftIso_unitIso_hom_app_left, mapLeftIso_unitIso_hom_app_right, mapLeftIso_unitIso_inv_app_left, mapLeftIso_unitIso_inv_app_right, mapLeft_map_left, mapLeft_map_right, mapLeft_obj_hom, mapLeft_obj_left, mapLeft_obj_right, mapRightComp_hom_app_left, mapRightComp_hom_app_right, mapRightComp_inv_app_left, mapRightComp_inv_app_right, mapRightEq_hom_app_left, mapRightEq_hom_app_right, mapRightEq_inv_app_left, mapRightEq_inv_app_right, mapRightId_hom_app_left, mapRightId_hom_app_right, mapRightId_inv_app_left, mapRightId_inv_app_right, mapRightIso_counitIso_hom_app_left, mapRightIso_counitIso_hom_app_right, mapRightIso_counitIso_inv_app_left, mapRightIso_counitIso_inv_app_right, mapRightIso_functor_map_left, mapRightIso_functor_map_right, mapRightIso_functor_obj_hom, mapRightIso_functor_obj_left, mapRightIso_functor_obj_right, mapRightIso_inverse_map_left, mapRightIso_inverse_map_right, mapRightIso_inverse_obj_hom, mapRightIso_inverse_obj_left, mapRightIso_inverse_obj_right, mapRightIso_unitIso_hom_app_left, mapRightIso_unitIso_hom_app_right, mapRightIso_unitIso_inv_app_left, mapRightIso_unitIso_inv_app_right, mapRight_map_left, mapRight_map_right, mapRight_obj_hom, mapRight_obj_left, mapRight_obj_right, mapSnd_hom_app, mapSnd_inv_app, map_fst, map_map_left, map_map_right, map_obj_hom, map_obj_left, map_obj_right, map_snd, natTrans_app, opEquiv_counitIso, opEquiv_functor, opEquiv_inverse, opEquiv_unitIso, opFunctorCompFst_hom_app, opFunctorCompFst_inv_app, opFunctorCompSnd_hom_app, opFunctorCompSnd_inv_app, opFunctor_map, opFunctor_obj, post_map_left, post_map_right, post_obj_hom, post_obj_left, post_obj_right, preLeft_map_left, preLeft_map_right, preLeft_obj_hom, preLeft_obj_left, preLeft_obj_right, preRight_map_left, preRight_map_right, preRight_obj_hom, preRight_obj_left, preRight_obj_right, rightIso_hom, rightIso_inv, snd_map, snd_obj, toIdPUnitEquiv_counitIso_hom_app, toIdPUnitEquiv_counitIso_inv_app, toIdPUnitEquiv_functor_iso, toIdPUnitEquiv_functor_map, toIdPUnitEquiv_functor_obj, toIdPUnitEquiv_inverse_map_right, toIdPUnitEquiv_inverse_obj_left_as, toIdPUnitEquiv_inverse_obj_right, toIdPUnitEquiv_unitIso_hom_app_right, toIdPUnitEquiv_unitIso_inv_app_right, toPUnitIdEquiv_counitIso_hom_app, toPUnitIdEquiv_counitIso_inv_app, toPUnitIdEquiv_functor_iso, toPUnitIdEquiv_functor_map, toPUnitIdEquiv_functor_obj, toPUnitIdEquiv_inverse_map_left, toPUnitIdEquiv_inverse_obj_left, toPUnitIdEquiv_inverse_obj_right_as, toPUnitIdEquiv_unitIso_hom_app_left, toPUnitIdEquiv_unitIso_inv_app_left, unopFunctorCompFst_hom_app, unopFunctorCompFst_inv_app, unopFunctorCompSnd_hom_app, unopFunctorCompSnd_inv_app, unopFunctor_map, unopFunctor_obj, ext, ext_iff, w, w_assoc	196
Total	241

CategoryTheory

Definitions

Name	Category	Theorems
CommaMorphism 📖	CompData	—
commaCategory 📖	CompOp	434 math math: TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_hom, StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, WithInitial.equivComma_functor_obj_right_obj, StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, Comma.snd_obj, Comma.mapLeftEq_inv_app_right, Comma.mapLeftIso_inverse_map_right, Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, Comma.opFunctor_obj, WithTerminal.equivComma_functor_obj_left_obj, StructuredArrow.mapIso_functor_obj_left, WithTerminal.equivComma_counitIso_hom_app_left_app, Comma.toPUnitIdEquiv_functor_map, NonemptyParallelPairPresentationAux.hf, StructuredArrow.commaMapEquivalenceInverse_map, Comma.map_obj_hom, WithTerminal.equivComma_counitIso_inv_app_left_app, StructuredArrow.ofCommaSndEquivalence_functor, Comma.toIdPUnitEquiv_inverse_map_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, Comma.map_final, Comma.mapLeft_map_left, StructuredArrow.mapIso_inverse_obj_hom, CostructuredArrow.grothendieckPrecompFunctorToComma_map_left, Comma.fromProd_obj_hom, CostructuredArrow.mapNatIso_inverse_obj_left, CostructuredArrow.mapIso_functor_obj_hom, StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, Comma.fst_obj, Comma.mapLeftIso_functor_map_left, Comma.mapLeftIso_unitIso_inv_app_left, Functor.leftExtensionEquivalenceOfIso₁_functor_obj_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_left, Comma.mapRightIso_counitIso_inv_app_left, TwoSquare.EquivalenceJ.inverse_map, StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, Comma.mapRightEq_hom_app_right, Comma.initial_fst, Comma.mapRightIso_counitIso_inv_app_right, Comma.opEquiv_counitIso, Comma.mapLeftEq_hom_app_left, Comma.isConnected_comma_of_initial, Comma.hasColimitsOfSize, Comma.coneOfPreserves_π_app_right, Comma.eqToHom_left, Comma.limitAuxiliaryCone_pt, WithTerminal.equivComma_inverse_obj_obj, Comma.hasColimitsOfShape, Comma.mapRightIso_functor_map_left, Comma.mapLeftIso_counitIso_inv_app_right, WithTerminal.equivComma_counitIso_hom_app_right, Comma.map_map_right, Comma.instEssSurjCompPostOfFull, CostructuredArrow.mapNatIso_inverse_map_right, StructuredArrow.mapNatIso_functor_obj_right, Comma.mapRight_obj_hom, Comma.mapRightIso_inverse_map_right, WithTerminal.equivComma_functor_obj_left_map, CostructuredArrow.mapNatIso_unitIso_inv_app_left, Comma.inv_left, CostructuredArrow.mapIso_unitIso_hom_app_left, WithTerminal.equivComma_functor_obj_right, Comma.mapRightIso_unitIso_inv_app_right, Comma.toPUnitIdEquiv_counitIso_hom_app, Comma.mapSnd_inv_app, Comma.fromProd_obj_right, CostructuredArrow.grothendieckPrecompFunctorEquivalence_functor, Comma.mapRightIso_functor_obj_right, Comma.opFunctor_map, CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_fiber, Comma.preRight_obj_left, WithTerminal.commaFromOver_map_left, WithInitial.equivComma_functor_obj_right_map, WithInitial.equivComma_counitIso_hom_app_right_app, Comma.rightIso_hom, CostructuredArrow.ιCompGrothendieckProj_inv_app, Comma.mapLeftIso_inverse_obj_left, CostructuredArrow.mapIso_inverse_obj_right, Comma.mapRight_obj_left, Comma.equivProd_unitIso_hom_app_left, Comma.comp_right, WithTerminal.commaFromOver_obj_right, StructuredArrow.ofCommaSndEquivalence_unitIso, TwoSquare.costructuredArrowRightwards_map, StructuredArrow.ofCommaSndEquivalence_counitIso, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CostructuredArrow.mapIso_functor_map_left, Comma.mapLeftIso_inverse_obj_right, Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, Comma.equivProd_counitIso_hom_app, Comma.mapRightId_inv_app_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_obj, Comma.instFaithfulCompPreLeft, Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_left, Comma.mapLeftId_hom_app_right, Comma.post_obj_right, Comma.preRight_map_left, MorphismProperty.Comma.instFullTopCommaForget, MorphismProperty.Comma.isoFromComma_hom, StructuredArrow.mapNatIso_functor_obj_hom, CostructuredArrow.mapIso_unitIso_inv_app_left, CostructuredArrow.grothendieckPrecompFunctorToComma_obj_right, Comma.preLeft_obj_right, StructuredArrow.mapIso_inverse_obj_right, CostructuredArrow.commaToGrothendieckPrecompFunctor_map_base, Comma.mapRightComp_inv_app_right, StructuredArrow.mapNatIso_inverse_map_right, Comma.instFaithfulCompPost, StructuredArrow.mapNatIso_functor_map_right, CostructuredArrow.ofCommaFstEquivalence_inverse, StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, CostructuredArrow.mapIso_functor_obj_left, WithInitial.equivComma_counitIso_inv_app_right_app, Comma.hasColimit, CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_hom, StructuredArrow.mapNatIso_inverse_obj_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_left, WithTerminal.equivComma_functor_map_right, Comma.faithful_map, Comma.comp_left, Comma.toPUnitIdEquiv_functor_obj, WithInitial.commaFromUnder_map_left, Comma.fromProd_obj_left, StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, Comma.mapLeftComp_inv_app_left, Comma.mapLeftIso_functor_obj_left, StructuredArrow.mapNatIso_unitIso_hom_app_right, Comma.natTrans_app, Comma.map_obj_right, Comma.coneOfPreserves_pt_right, Comma.equivProd_inverse_map_left, CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, Comma.instFullCompPreLeft, Comma.equivProd_unitIso_hom_app_right, CostructuredArrow.ofCommaFstEquivalenceInverse_obj_right_as, Comma.preRight_map_right, CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_left, CostructuredArrow.mapNatIso_functor_obj_hom, Comma.map_map_left, Comma.mapRightIso_functor_obj_hom, Comma.toIdPUnitEquiv_unitIso_inv_app_right, Comma.post_map_left, CostructuredArrow.grothendieckPrecompFunctorToComma_obj_left, Comma.toPUnitIdEquiv_unitIso_inv_app_left, Comma.colimitAuxiliaryCocone_pt, StructuredArrow.ofCommaSndEquivalenceFunctor_obj_right, Comma.coconeOfPreserves_pt_right, Comma.isCofiltered_of_initial, Comma.preservesColimitsOfShape_snd, Comma.snd_map, Comma.preRight_obj_right, Comma.mapLeftIso_unitIso_inv_app_right, CostructuredArrow.mapNatIso_counitIso_inv_app_left, Comma.isEquivalence_post, Comma.mapLeftIso_unitIso_hom_app_left, CostructuredArrow.mapIso_counitIso_hom_app_left, WithInitial.equivComma_functor_map_left, CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, Comma.mapRightEq_inv_app_left, Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, Comma.isEquivalenceMap, Comma.eqToHom_right, CostructuredArrow.mapIso_functor_map_right, WithTerminal.equivComma_functor_obj_hom_app, WithInitial.equivComma_inverse_map_app, Comma.unopFunctor_obj, CostructuredArrow.mapNatIso_inverse_map_left, Comma.mapLeftComp_inv_app_right, Comma.equivProd_counitIso_inv_app, Comma.isEquivalence_preLeft, Comma.coconeOfPreserves_ι_app_right, Comma.toIdPUnitEquiv_unitIso_hom_app_right, WithInitial.equivComma_counitIso_hom_app_left, Comma.mapRightIso_inverse_obj_right, CostructuredArrow.grothendieckPrecompFunctorEquivalence_unitIso, Comma.coconeOfPreserves_pt_hom, Comma.mapLeftIso_counitIso_hom_app_left, Comma.mapRightIso_functor_map_right, Comma.limitAuxiliaryCone_π_app, WithInitial.equivComma_functor_map_right_app, Comma.toIdPUnitEquiv_functor_map, Comma.toIdPUnitEquiv_inverse_obj_left_as, Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_right, StructuredArrow.commaMapEquivalenceInverse_obj, Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, Comma.inv_right, WithInitial.equivComma_functor_obj_hom_app, Comma.toIdPUnitEquiv_functor_obj, StructuredArrow.mapNatIso_inverse_obj_hom, WithInitial.commaFromUnder_obj_hom_app, StructuredArrow.commaMapEquivalenceFunctor_obj_left, CostructuredArrow.mapNatIso_inverse_obj_hom, WithInitial.commaFromUnder_obj_right, WithInitial.equivComma_inverse_obj_map, Comma.toIdPUnitEquiv_counitIso_hom_app, Comma.mapRightComp_hom_app_left, StructuredArrow.commaMapEquivalenceFunctor_map_left, CostructuredArrow.ofCommaFstEquivalence_functor, Comma.toPUnitIdEquiv_inverse_map_left, Comma.mapRightIso_functor_obj_left, CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, MorphismProperty.Comma.forget_obj, Comma.unopFunctorCompSnd_inv_app, Comma.coconeOfPreserves_ι_app_left, Comma.equivProd_inverse_map_right, CostructuredArrow.mapNatIso_unitIso_hom_app_left, Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, Comma.isoMk_inv_left, CostructuredArrow.grothendieckPrecompFunctorEquivalence_inverse, Comma.toPUnitIdEquiv_functor_iso, CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, StructuredArrow.mapIso_functor_obj_right, Comma.mapLeftEq_hom_app_right, StructuredArrow.mapIso_unitIso_inv_app_right, Comma.mapLeft_obj_right, Comma.hasLimitsOfSize, Comma.preservesColimitsOfShape_fst, Comma.opFunctorCompSnd_hom_app, StructuredArrow.mapIso_functor_map_left, Functor.leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, Comma.mapLeftIso_inverse_obj_hom, StructuredArrow.commaMapEquivalenceFunctor_map_right, Comma.mapLeftId_hom_app_left, Comma.hasLimitsOfShape, Comma.post_obj_left, Comma.mapLeftId_inv_app_left, Comma.mapRightIso_counitIso_hom_app_right, Comma.fromProd_map_right, MorphismProperty.Comma.forget_map, Comma.equivProd_inverse_obj_right, Comma.isFiltered_of_final, WithTerminal.commaFromOver_obj_hom_app, Comma.opFunctorCompFst_hom_app, Comma.toPUnitIdEquiv_unitIso_hom_app_left, Comma.mapRightIso_unitIso_hom_app_left, WithInitial.equivComma_unitIso_inv_app_app, Comma.fromProd_map_left, Comma.full_map, WithInitial.commaFromUnder_map_right, WithInitial.equivComma_functor_obj_left, StructuredArrow.ofCommaSndEquivalenceInverse_obj_hom, Comma.opFunctorCompFst_inv_app, Comma.preRight_obj_hom, Comma.unopFunctor_map, Comma.instFullCompPreRight, CostructuredArrow.mapNatIso_functor_obj_left, Comma.instFullCompPostOfFaithful, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, Comma.opEquiv_functor, MorphismProperty.Comma.id_hom, Comma.initial_snd, MorphismProperty.Comma.isoFromComma_inv, Comma.instFaithfulCompPreRight, Comma.mapLeftIso_unitIso_hom_app_right, CostructuredArrow.ofCommaFstEquivalence_counitIso, Comma.opEquiv_unitIso, StructuredArrow.mapNatIso_counitIso_hom_app_right, Comma.mapRightId_hom_app_right, CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_left, Comma.mapLeftIso_counitIso_inv_app_left, Comma.toPUnitIdEquiv_inverse_obj_right_as, MorphismProperty.Comma.instIsIsoCommaHom, Comma.mapRightIso_counitIso_hom_app_left, WithInitial.equivComma_unitIso_hom_app_app, CostructuredArrow.mapNatIso_functor_obj_right, StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, Comma.mapRightId_hom_app_left, CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, Comma.final_fst, Comma.mapLeftEq_inv_app_left, WithTerminal.commaFromOver_map_right, Comma.mapLeftIso_counitIso_hom_app_right, WithInitial.equivComma_inverse_obj_obj, Comma.instEssSurjCompPreLeft, StructuredArrow.ofCommaSndEquivalenceInverse_map_right_right, CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_right, Comma.mapFst_hom_app, Comma.mapLeft_map_right, Comma.mapLeft_obj_left, Comma.coneOfPreserves_pt_hom, Comma.unopFunctorCompFst_inv_app, Comma.leftIso_hom, Comma.equivProd_unitIso_inv_app_right, WithInitial.commaFromUnder_obj_left, CostructuredArrow.grothendieckPrecompFunctorEquivalence_counitIso, TwoSquare.EquivalenceJ.functor_obj, Comma.toPUnitIdEquiv_inverse_obj_left, StructuredArrow.mapIso_unitIso_hom_app_right, MorphismProperty.Comma.instFaithfulCommaForget, Comma.mapLeftIso_functor_obj_hom, Comma.isEquivalence_preRight, StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CostructuredArrow.mapNatIso_counitIso_hom_app_left, Comma.final_snd, Comma.leftIso_inv, StructuredArrow.mapIso_functor_obj_hom, StructuredArrow.mapNatIso_unitIso_inv_app_right, WithInitial.equivComma_counitIso_inv_app_left, Comma.isConnected_comma_of_final, Comma.mapRight_map_left, Comma.mapRightId_inv_app_right, Comma.mapRightComp_hom_app_right, Comma.opFunctorCompSnd_inv_app, Comma.isoMk_hom_right, Comma.mapRightIso_inverse_obj_hom, CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_right, StructuredArrow.mapIso_inverse_map_right, Comma.id_left, TwoSquare.structuredArrowDownwards_map, CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, WithTerminal.equivComma_functor_map_left_app, Comma.preLeft_map_left, StructuredArrow.ofCommaSndEquivalenceFunctor_obj_left, Comma.opEquiv_inverse, TwoSquare.structuredArrowDownwards_obj, CostructuredArrow.mapNatIso_inverse_obj_right, MorphismProperty.Comma.inv_hom, Comma.id_right, MorphismProperty.Comma.instReflectsIsomorphismsCommaForgetOfRespectsIso, CostructuredArrow.mapNatIso_functor_map_left, Comma.mapRightIso_unitIso_inv_app_left, WithInitial.liftFromUnder_map_app, CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, Comma.essSurj_map, Comma.equivProd_inverse_obj_left, Functor.leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, Comma.hasLimit, Comma.mapSnd_hom_app, StructuredArrow.mapNatIso_functor_obj_left, StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, Comma.toPUnitIdEquiv_counitIso_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, CostructuredArrow.ofCommaFstEquivalence_unitIso, TwoSquare.EquivalenceJ.functor_map, StructuredArrow.mapIso_inverse_obj_left, Comma.instEssSurjCompPreRight, Comma.locallySmall, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_map, Comma.mapRightEq_hom_app_left, StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, Comma.mapRightEq_inv_app_right, StructuredArrow.mapIso_functor_map_right, Comma.coneOfPreserves_pt_left, StructuredArrow.ofCommaSndEquivalence_inverse, Comma.post_map_right, WithTerminal.equivComma_inverse_map_app, CostructuredArrow.mapIso_functor_obj_right, WithTerminal.equivComma_inverse_obj_map, Comma.toIdPUnitEquiv_counitIso_inv_app, Comma.coconeOfPreserves_pt_left, MorphismProperty.Comma.comp_hom, WithTerminal.liftFromOver_map_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_right_app, CostructuredArrow.grothendieckPrecompFunctorToComma_map_right, MorphismProperty.instIsClosedUnderIsomorphismsCommaCommaObjOfRespectsIso, Comma.equivProd_functor_map, TwoSquare.EquivalenceJ.inverse_obj, Comma.mapLeftIso_inverse_map_left, Comma.preLeft_obj_left, Comma.mapRight_obj_right, Comma.mapLeftComp_hom_app_left, Comma.mapLeftIso_functor_obj_right, StructuredArrow.mapIso_inverse_map_left, Comma.mapLeft_obj_hom, CostructuredArrow.ιCompGrothendieckProj_hom_app, StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_hom, CostructuredArrow.mapNatIso_functor_map_right, CostructuredArrow.mapIso_inverse_obj_hom, WithTerminal.commaFromOver_obj_left, Comma.equivProd_unitIso_inv_app_left, Comma.unopFunctorCompSnd_hom_app, Comma.preLeft_map_right, Comma.toIdPUnitEquiv_functor_iso, CostructuredArrow.mapIso_inverse_map_right, StructuredArrow.ofCommaSndEquivalenceInverse_obj_left_as, Comma.post_obj_hom, Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, WithTerminal.equivComma_counitIso_inv_app_right, Comma.unopFunctorCompFst_hom_app, CostructuredArrow.mapIso_inverse_map_left, Comma.isoMk_inv_right, StructuredArrow.mapNatIso_inverse_map_left, Comma.map_fst, CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_base, WithTerminal.equivComma_unitIso_hom_app_app, TwoSquare.costructuredArrowRightwards_obj, Comma.toIdPUnitEquiv_inverse_obj_right, Comma.colimitAuxiliaryCocone_ι_app, NonemptyParallelPairPresentationAux.hg, Comma.mapRightIso_inverse_obj_left, CostructuredArrow.ofCommaFstEquivalenceInverse_obj_hom, Comma.fst_map, StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, Comma.mapRightIso_inverse_map_left, Comma.mapLeftId_inv_app_right, StructuredArrow.mapNatIso_functor_map_left, Comma.map_snd, StructuredArrow.mapNatIso_counitIso_inv_app_right, StructuredArrow.commaMapEquivalenceFunctor_obj_right, Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_hom_app, Comma.rightIso_inv, WithTerminal.equivComma_unitIso_inv_app_app, CostructuredArrow.grothendieckPrecompFunctorToComma_obj_hom, Comma.mapLeftComp_hom_app_right, StructuredArrow.ofCommaSndEquivalenceFunctor_obj_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_obj, Comma.mapRight_map_right, Comma.isoMk_hom_left, Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, Comma.mapFst_inv_app, CostructuredArrow.mapIso_counitIso_inv_app_left, Comma.mapLeftIso_functor_map_right, StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, StructuredArrow.mapIso_counitIso_hom_app_right, Comma.equivProd_functor_obj, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, Comma.map_obj_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, Comma.mapRightComp_inv_app_left, StructuredArrow.mapNatIso_inverse_obj_right, StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_right, StructuredArrow.mapIso_counitIso_inv_app_right, Comma.mapRightIso_unitIso_hom_app_right, StructuredArrow.commaMapEquivalenceFunctor_obj_hom, Comma.preLeft_obj_hom, Functor.leftExtensionEquivalenceOfIso₁_functor_obj_right, CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_right, CostructuredArrow.mapIso_inverse_obj_left, Comma.coneOfPreserves_π_app_left

CategoryTheory.Comma

Definitions

Name	Category	Theorems
equivProd 📖	CompOp	22 math math: toIdPUnitEquiv_inverse_map_right, toPUnitIdEquiv_counitIso_hom_app, equivProd_unitIso_hom_app_left, equivProd_counitIso_hom_app, equivProd_inverse_map_left, equivProd_unitIso_hom_app_right, toIdPUnitEquiv_unitIso_inv_app_right, toPUnitIdEquiv_unitIso_inv_app_left, equivProd_counitIso_inv_app, toIdPUnitEquiv_unitIso_hom_app_right, toIdPUnitEquiv_counitIso_hom_app, toPUnitIdEquiv_inverse_map_left, equivProd_inverse_map_right, equivProd_inverse_obj_right, toPUnitIdEquiv_unitIso_hom_app_left, equivProd_unitIso_inv_app_right, equivProd_inverse_obj_left, toPUnitIdEquiv_counitIso_inv_app, toIdPUnitEquiv_counitIso_inv_app, equivProd_functor_map, equivProd_unitIso_inv_app_left, equivProd_functor_obj
fromProd 📖	CompOp	7 math math: fromProd_obj_hom, fromProd_obj_right, equivProd_counitIso_hom_app, fromProd_obj_left, equivProd_counitIso_inv_app, fromProd_map_right, fromProd_map_left
fst 📖	CompOp	69 math math: CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_hom, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_left, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_functor, fst_obj, initial_fst, coneOfPreserves_π_app_right, limitAuxiliaryCone_pt, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_unitIso, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_counitIso, equivProd_counitIso_hom_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_inverse, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_hom, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, natTrans_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_right_as, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_left, colimitAuxiliaryCocone_pt, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_right, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, equivProd_counitIso_inv_app, coconeOfPreserves_ι_app_right, coconeOfPreserves_pt_hom, limitAuxiliaryCone_π_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_functor, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, unopFunctorCompSnd_inv_app, coconeOfPreserves_ι_app_left, toPUnitIdEquiv_functor_iso, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, preservesColimitsOfShape_fst, opFunctorCompSnd_hom_app, opFunctorCompFst_hom_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_hom, opFunctorCompFst_inv_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_counitIso, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_left, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, final_fst, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_right, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_right, mapFst_hom_app, unopFunctorCompFst_inv_app, opFunctorCompSnd_inv_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_right, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_left, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_unitIso, coneOfPreserves_pt_left, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_inverse, coconeOfPreserves_pt_left, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_hom, unopFunctorCompSnd_hom_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_left_as, unopFunctorCompFst_hom_app, map_fst, colimitAuxiliaryCocone_ι_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_hom, fst_map, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_hom, mapFst_inv_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_right, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_right, coneOfPreserves_π_app_left
hom 📖	CompOp	877 math math: TopCat.Presheaf.generateEquivalenceOpensLe_functor'_obj_obj, CategoryTheory.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.Limits.coker.π_app, CategoryTheory.CostructuredArrow.homMk'_id, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.Over.prodLeftIsoPullback_hom_snd_assoc, CategoryTheory.Limits.HasImage.of_arrow_iso, CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_hom, CategoryTheory.StructuredArrow.map_map_right, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.Functor.leibnizPullback_obj_map, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, mapLeftIso_inverse_map_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.CostructuredArrow.mk_hom_eq_self, CategoryTheory.Functor.LeftExtension.precomp₂_obj_hom_app, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_e, opFunctor_obj, CategoryTheory.Limits.multicospanIndexEnd_fst, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_map, CategoryTheory.OverPresheafAux.unitAux_hom, CategoryTheory.Over.iteratedSliceBackward_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_map_left_left, CategoryTheory.Over.associator_inv_left_snd, CategoryTheory.Functor.mapArrow_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, CategoryTheory.Over.pullback_obj_left, map_obj_hom, TopCat.Presheaf.generateEquivalenceOpensLe_unitIso, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_hom, CategoryTheory.StructuredArrow.homMk'_comp, CategoryTheory.CostructuredArrow.w_assoc, CategoryTheory.MonoOver.isIso_left_iff_subobjectMk_eq, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, CategoryTheory.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_id, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_id, mapLeft_map_left, CategoryTheory.SmallObject.πObj_ιIteration_app_right, CategoryTheory.OverPresheafAux.restrictedYoneda_map, CategoryTheory.toOver_obj_hom, CategoryTheory.Sieve.ofArrows_category', CategoryTheory.Limits.IsImage.ofArrowIso_lift, CategoryTheory.StructuredArrow.mapIso_inverse_obj_hom, CategoryTheory.CostructuredArrow.pre_obj_hom, CategoryTheory.Over.whiskerLeft_left, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_left, CategoryTheory.Limits.image.map_id, CategoryTheory.OverPresheafAux.restrictedYoneda_obj, CategoryTheory.Presheaf.isSheaf_iff_isLimit_coverage, CategoryTheory.MonoOver.isIso_iff_subobjectMk_eq, CategoryTheory.Functor.LeftExtension.postcomp₁_map_right_app, CategoryTheory.CostructuredArrow.IsUniversal.existsUnique, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, fromProd_obj_hom, CategoryTheory.CostructuredArrow.w_prod_fst, CategoryTheory.SimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₃, CategoryTheory.CostructuredArrow.mapIso_functor_obj_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, Profinite.Extend.cone_π_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, mapLeftIso_functor_map_left, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_hom, CategoryTheory.Square.toArrowArrowFunctor_obj_hom_right, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd_assoc, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.isIso_hom_app, CategoryTheory.TwoSquare.EquivalenceJ.inverse_map, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.CostructuredArrow.eq_mk, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isPullback, CategoryTheory.MorphismProperty.Under.mk_hom, CategoryTheory.StructuredArrow.map₂_map_right, CategoryTheory.Limits.Cone.fromCostructuredArrow_map_hom, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_inv, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_hom, CategoryTheory.Limits.image.map_comp, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, CategoryTheory.Functor.LeftExtension.precomp_map_right, CategoryTheory.Over.toUnit_left, CategoryTheory.SimplicialObject.Augmented.w₀, CategoryTheory.Functor.RightExtension.coneAt_π_app, mapRightIso_functor_map_left, map_map_right, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, CategoryTheory.Over.braiding_inv_left, CategoryTheory.CostructuredArrow.post_obj, CategoryTheory.Functor.RightExtension.postcomp₁_map_right, CategoryTheory.Over.prodLeftIsoPullback_inv_snd, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, CategoryTheory.SimplicialObject.Augmented.toArrow_map_left, mapRight_obj_hom, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, mapRightIso_inverse_map_right, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, CategoryTheory.Limits.coker_map, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_hom, CategoryTheory.StructuredArrow.eta_hom_right, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₃₄, CategoryTheory.SmallObject.functorialFactorizationData_i_app, CategoryTheory.CostructuredArrow.prodFunctor_map, CategoryTheory.Abelian.coim_map, CategoryTheory.StructuredArrow.prodInverse_map, CategoryTheory.StructuredArrow.eta_inv_right, CategoryTheory.Over.leftUnitor_hom_left, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp, CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback_app, CategoryTheory.Over.tensorObj_ext_iff, CategoryTheory.CosimplicialObject.augment_hom_app, CategoryTheory.CostructuredArrow.toOver_map_right, CategoryTheory.CostructuredArrow.map_obj_hom, LightProfinite.Extend.cocone_ι_app, CategoryTheory.Under.mk_hom, CategoryTheory.Functor.LeftExtension.precomp_obj_hom_app, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, CategoryTheory.StructuredArrow.eq_mk, CategoryTheory.MorphismProperty.Over.mk_hom, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_right_as, CategoryTheory.MorphismProperty.Over.pullback_obj_left, CategoryTheory.NatTrans.instIsClosedUnderLimitsOfShapeOverFunctorEquifiberedHomDiscretePUnitOfHasCoproductsOfShapeHom, opFunctor_map, CategoryTheory.CostructuredArrow.toOver_obj_hom, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext_iff, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t_assoc, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_fiber, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_hom, CategoryTheory.Over.rightUnitor_inv_left_fst, CategoryTheory.CostructuredArrow.homMk'_mk_id, CategoryTheory.Limits.Cocone.fromCostructuredArrow_ι_app, CategoryTheory.Limits.Cone.fromStructuredArrow_π_app, CategoryTheory.WithTerminal.commaFromOver_map_left, CategoryTheory.Functor.RightExtension.precomp_map_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.isLeftKanExtension, CategoryTheory.Limits.Cone.fromCostructuredArrow_obj_π, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eq, CategoryTheory.Under.pushout_map, CategoryTheory.Sieve.ofArrows_category, CategoryTheory.Limits.image.map_ι, CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, CategoryTheory.CostructuredArrow.homMk'_right, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv_assoc, CategoryTheory.Over.mk_hom, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.OverPresheafAux.counitForward_naturality₁, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_hom, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_hom_app, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_left, CategoryTheory.Over.whiskerRight_left_fst, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst_assoc, CategoryTheory.Arrow.square_from_iso_invert, CategoryTheory.MonoOver.pullback_obj_arrow, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_right_hom, CategoryTheory.Over.prodLeftIsoPullback_inv_fst, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp_assoc, CategoryTheory.Abelian.im_map, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.TwoSquare.costructuredArrowRightwards_map, CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_star, CategoryTheory.Under.postAdjunctionRight_unit_app_right, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_hom, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp_assoc, CategoryTheory.Over.opEquivOpUnder_inverse_obj, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.StructuredArrow.prodFunctor_map, CategoryTheory.Arrow.equivSigma_apply_snd_snd, CategoryTheory.Over.prodLeftIsoPullback_inv_snd_assoc, CategoryTheory.Functor.RightExtension.mk_hom, CategoryTheory.Over.rightUnitor_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, CategoryTheory.Over.post_map, CategoryTheory.regularTopology.equalizerConditionMap_iff_nonempty_isLimit, CategoryTheory.Pseudofunctor.presheafHom_obj, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.Over.iteratedSliceBackward_forget, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, preRight_map_left, CategoryTheory.SimplicialObject.Augmented.const_obj_hom, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.CostructuredArrow.post_map, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_left, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_base, CategoryTheory.Under.post_obj, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_hom, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst, CategoryTheory.Over.prodLeftIsoPullback_hom_snd, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_hom, CategoryTheory.StructuredArrow.IsUniversal.existsUnique, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, CategoryTheory.Over.whiskerRight_left_snd_assoc, CategoryTheory.Arrow.w_mk_right, CategoryTheory.ChosenPullbacksAlong.Over.snd_eq_snd', CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, CategoryTheory.CostructuredArrow.eta_hom_left, CategoryTheory.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₃, CategoryTheory.Limits.ker.ι_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_hom, CategoryTheory.Over.associator_hom_left_fst, CategoryTheory.SmallObject.functor_map, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, CategoryTheory.CostructuredArrow.toStructuredArrow'_obj, CategoryTheory.Arrow.leftToRight_app, CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk', CategoryTheory.WithInitial.commaFromUnder_map_left, CategoryTheory.StructuredArrow.homMk'_mk_comp, CategoryTheory.NatTrans.instIsClosedUnderColimitsOfShapeUnderFunctorCoequifiberedHomDiscretePUnitOfHasProductsOfShapeHom, CategoryTheory.CostructuredArrow.prodInverse_obj, CategoryTheory.ChosenPullbacksAlong.Over.tensorUnit_hom, CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc, CategoryTheory.SmallObject.objMap_comp_assoc, CategoryTheory.Limits.ker_obj, CategoryTheory.SmallObject.functorialFactorizationData_Z_obj, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, CategoryTheory.MonoOver.image_map, CategoryTheory.Under.mapPushoutAdj_unit_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, CategoryTheory.OverPresheafAux.counitForward_val_snd, CategoryTheory.Limits.instHasImageHomMk, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, CategoryTheory.Limits.ImageMap.factor_map_assoc, CategoryTheory.Over.tensorUnit_hom, CategoryTheory.Over.opEquivOpUnder_inverse_map, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_map_left_left, CategoryTheory.Over.leftUnitor_inv_left_fst, CategoryTheory.Under.post_map, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, CommRingCat.mkUnder_hom, AlgebraicGeometry.opensDiagram_map, natTrans_app, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, CategoryTheory.Functor.leibnizPushout_obj_map, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_id, CategoryTheory.Over.tensorHom_left_snd_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, CategoryTheory.SmallObject.ε_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂_map_right_app, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.Limits.image.map_homMk'_ι, CategoryTheory.Under.map_obj_hom, CategoryTheory.CommaMorphism.w_assoc, CategoryTheory.WithInitial.mkCommaObject_hom_app, CategoryTheory.CostructuredArrow.map_map_right, CategoryTheory.Over.leftUnitor_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst_assoc, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, AlgebraicGeometry.opensDiagramι_app, CategoryTheory.Arrow.w, CategoryTheory.StructuredArrow.homMk'_left, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd', CategoryTheory.OverClass.fromOver_over, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_zero, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, CategoryTheory.SmallObject.objMap_id, CategoryTheory.MonoOver.image_obj, preRight_map_right, CategoryTheory.Limits.coker_obj, CategoryTheory.Over.μ_pullback_left_fst_snd', CategoryTheory.Over.mapPullbackAdj_unit_app, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_hom, map_map_left, CategoryTheory.CostructuredArrow.w_prod_snd, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, mapRightIso_functor_obj_hom, CategoryTheory.Limits.imageSubobjectIso_comp_image_map, CategoryTheory.SmallObject.SuccStruct.toSuccArrow_hom, post_map_left, CategoryTheory.CommaMorphism.w, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, CategoryTheory.CostructuredArrow.CreatesConnected.natTransInCostructuredArrow_app, CategoryTheory.Limits.multispanIndexCoend_snd, CategoryTheory.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂_obj_hom_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁_assoc, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_map_right_right, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.MorphismProperty.instHasPullbackHomDiscretePUnitOfHasPullbacksAlong, CategoryTheory.ChosenPullbacksAlong.iso_pullback_obj, CategoryTheory.SimplicialObject.augment_hom_zero, CategoryTheory.SmallObject.ιObj_naturality, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, CategoryTheory.Presieve.ofArrows_category, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.OverPresheafAux.counitAuxAux_inv, CategoryTheory.Functor.LeftExtension.postcomp₁_obj_hom_app, CategoryTheory.CategoryOfElements.fromStructuredArrow_obj, CategoryTheory.Arrow.w_mk_right_assoc, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.ComposableArrows.arrowEquiv_symm_apply, CategoryTheory.OverPresheafAux.restrictedYonedaObj_map, CategoryTheory.Over.map_obj_hom, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₃, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Over.associator_hom_left_snd_fst, CategoryTheory.CostructuredArrow.toOver_map_left, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', CategoryTheory.Functor.mapArrow_map_left, CategoryTheory.CostructuredArrow.eta_inv_left, CategoryTheory.MorphismProperty.over_iso_iff, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp_obj, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_snd, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_hom, CategoryTheory.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.WithTerminal.equivComma_functor_obj_hom_app, CategoryTheory.Over.toOverSectionsAdj_counit_app, CategoryTheory.StructuredArrow.toCostructuredArrow_map, CategoryTheory.Limits.ImageMap.factor_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd, left_hom_inv_right, CategoryTheory.forgetAdjToOver_unit_app, CategoryTheory.OverPresheafAux.counitBackward_counitForward, CategoryTheory.Arrow.isIso_hom_iff_isIso_of_isIso, unopFunctor_obj, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_obj, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.StructuredArrow.toUnder_map_right, CategoryTheory.regularTopology.parallelPair_pullback_initial, CategoryTheory.overToCoalgebra_map_f, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_left, CategoryTheory.Pseudofunctor.isStackFor_iff, CategoryTheory.SimplicialObject.augment_hom_app, CategoryTheory.StructuredArrow.IsUniversal.hom_desc, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst_assoc, coconeOfPreserves_pt_hom, CategoryTheory.TwoSquare.isIso_lanBaseChange_app_iff, CategoryTheory.Over.pullback_map_left, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst, mapRightIso_functor_map_right, limitAuxiliaryCone_π_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.Pseudofunctor.presheafHom_map, CategoryTheory.MorphismProperty.costructuredArrow_iso_iff, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_hom, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.Over.sections_obj, CategoryTheory.MorphismProperty.Comma.ext_iff, AlgebraicGeometry.opensDiagram_obj, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_right_hom, CategoryTheory.CostructuredArrow.toStructuredArrow'_map, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.Abelian.coim_obj, CategoryTheory.Functor.mapArrow_map_right, CategoryTheory.MorphismProperty.overObj_iff, AlgebraicGeometry.opensCone_π_app, CategoryTheory.Over.tensorHom_left, CategoryTheory.CostructuredArrow.w, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.StructuredArrow.homMk'_id, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isIso_hom, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_hom, CategoryTheory.Presheaf.isSheaf_iff_isLimit, CategoryTheory.Under.opEquivOpOver_functor_obj, CategoryTheory.WithInitial.equivComma_functor_obj_hom_app, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Over.associator_inv_left_fst_snd, CategoryTheory.Square.toArrowArrowFunctor_obj_hom_left, CategoryTheory.WithInitial.commaFromUnder_obj_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.WithInitial.equivComma_inverse_obj_map, CategoryTheory.MorphismProperty.Over.w_assoc, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, CategoryTheory.Over.star_obj_hom, CategoryTheory.Functor.RightExtension.postcomp₁_map_left_app, CategoryTheory.Arrow.mk_hom, CategoryTheory.SmallObject.πObj_ιIteration_app_right_assoc, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.StructuredArrow.post_map, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π_assoc, CategoryTheory.Limits.im_obj, CategoryTheory.SmallObject.πObj_naturality_assoc, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_right_inv, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, TopCat.Presheaf.generateEquivalenceOpensLe_functor, CategoryTheory.Bicategory.LeftExtension.ofCompId_hom, CategoryTheory.Over.μ_pullback_left_fst_fst', CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, Types.monoOverEquivalenceSet_functor_map, CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Over.whiskerRight_left, CategoryTheory.CostructuredArrow.homMk'_left, CategoryTheory.StructuredArrow.homMk'_right, CategoryTheory.Abelian.coimageImageComparisonFunctor_obj, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₃, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_hom, CategoryTheory.StructuredArrow.pre_map_left, inv_left_hom_right, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.CostructuredArrow.prodFunctor_obj, CategoryTheory.OverPresheafAux.counitAux_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isIso_hom_app, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_F, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, CategoryTheory.Arrow.equivSigma_symm_apply_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, CategoryTheory.StructuredArrow.map_map_left, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.Over.w, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_map, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_map, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp_assoc, TopCat.Presheaf.generateEquivalenceOpensLe_counitIso, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_m, CategoryTheory.StructuredArrow.prodFunctor_obj, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left_inv, CategoryTheory.Sieve.yonedaFamily_fromCocone_compatible, CategoryTheory.CosimplicialObject.augment_hom_zero, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.isIso_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.Arrow.mk_eq, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_obj, Types.monoOverEquivalenceSet_functor_obj, CategoryTheory.MorphismProperty.Under.w, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_hom, CategoryTheory.StructuredArrow.mapIso_functor_map_left, AlgebraicGeometry.Scheme.kerFunctor_map, CategoryTheory.MorphismProperty.Comma.prop, CategoryTheory.Pseudofunctor.IsStack.essSurj_of_sieve, CategoryTheory.CostructuredArrow.homMk'_mk_comp, CategoryTheory.Over.associator_inv_left_fst_fst, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_map_right_right, mapLeftIso_inverse_obj_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.Over.snd_left, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_map_left_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.Limits.ImageMap.map_ι, CategoryTheory.CostructuredArrow.prodInverse_map, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst_assoc, CategoryTheory.Functor.leibnizPushout_obj_obj, CategoryTheory.Arrow.isIso_hom_iff_isIso_hom_of_isIso, CategoryTheory.Over.tensorHom_left_fst, CategoryTheory.Over.whiskerRight_left_snd, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, CategoryTheory.MorphismProperty.structuredArrowObj_iff, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, CategoryTheory.WithTerminal.commaFromOver_obj_hom_app, CategoryTheory.MorphismProperty.mem_toSet_iff, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isRightKanExtension, CategoryTheory.underToAlgebra_obj_a, CategoryTheory.CommSq.of_arrow, CategoryTheory.WithInitial.commaFromUnder_map_right, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_hom, CategoryTheory.CostructuredArrow.toStructuredArrow_obj, preRight_obj_hom, unopFunctor_map, CategoryTheory.Arrow.isIso_of_isIso, CategoryTheory.Over.tensorHom_left_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd_assoc, CategoryTheory.OverPresheafAux.restrictedYonedaObj_obj, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_hom, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.Over.prodLeftIsoPullback_inv_fst_assoc, CategoryTheory.Abelian.im_obj, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_hom_left, CategoryTheory.OverClass.asOver_hom, SSet.Augmented.stdSimplex_obj_hom_app, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_hom_left, CategoryTheory.OverPresheafAux.restrictedYonedaObjMap₁_app, CategoryTheory.Arrow.iso_w, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_obj, CategoryTheory.Limits.Cocone.fromStructuredArrow_map_hom, CategoryTheory.Over.whiskerLeft_left_fst, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_counit_app, CategoryTheory.SmallObject.πFunctorObj_eq, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp_map, CategoryTheory.SmallObject.objMap_comp, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_left, CategoryTheory.Functor.LeftExtension.postcompose₂_map_left, CategoryTheory.CosimplicialObject.Augmented.const_obj_hom, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Over.post_obj, CategoryTheory.Arrow.inv_left_hom_right, CategoryTheory.Limits.Cone.equivCostructuredArrow_counitIso, CategoryTheory.WithTerminal.mkCommaObject_hom_app, CategoryTheory.StructuredArrow.toUnder_obj_hom, CategoryTheory.Functor.RightExtension.postcompose₂_obj_hom_app, CategoryTheory.Functor.RightExtension.precomp_obj_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, CategoryTheory.Pseudofunctor.isPrestackFor_iff, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, CategoryTheory.Functor.RightExtension.precomp_map_right, CategoryTheory.ChosenPullbacksAlong.Over.lift_left, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₂, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, CategoryTheory.Abelian.coimageImageComparisonFunctor_map, CategoryTheory.Bicategory.LeftLift.ofIdComp_hom, CategoryTheory.WithTerminal.commaFromOver_map_right, CategoryTheory.CostructuredArrow.map_map_left, CategoryTheory.CostructuredArrow.map₂_map_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε_assoc, CategoryTheory.Over.isPullback_of_binaryFan_isLimit, CategoryTheory.MorphismProperty.commaObj_iff, CategoryTheory.Pseudofunctor.IsStackFor.isEquivalence, CategoryTheory.Over.whiskerLeft_left_fst_assoc, CategoryTheory.Under.pushout_obj, CategoryTheory.MorphismProperty.Over.w, CategoryTheory.Square.toArrowArrowFunctor_obj_right_hom, CategoryTheory.Functor.RightExtension.postcompose₂_map_left_app, CategoryTheory.Over.coprodObj_obj, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_obj, CategoryTheory.StructuredArrow.preEquivalenceInverse_map_right_right, mapLeft_map_right, coneOfPreserves_pt_hom, CategoryTheory.CostructuredArrow.IsUniversal.fac, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₄, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_right_inv, CategoryTheory.MonoOver.subobjectMk_le_mk_of_hom, CategoryTheory.Over.whiskerLeft_left_snd_assoc, CategoryTheory.TwoSquare.EquivalenceJ.functor_obj, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, CategoryTheory.StructuredArrow.w, CategoryTheory.Functor.RightExtension.postcompose₂_map_right, CategoryTheory.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left, CategoryTheory.Sieve.forallYonedaIsSheaf_iff_colimit, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_id, CategoryTheory.WithTerminal.liftFromOver_obj_map, CategoryTheory.Functor.LeftExtension.precomp_map_left, mapLeftIso_functor_obj_hom, CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_I, CategoryTheory.MorphismProperty.comma_iso_iff, CategoryTheory.StructuredArrow.pre_map_right, CategoryTheory.StructuredArrow.w_prod_fst_assoc, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₂₄, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.StructuredArrow.mapIso_functor_obj_hom, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_left, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π, CategoryTheory.underToAlgebra_map_f, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, Profinite.Extend.cocone_ι_app, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_isImage, CategoryTheory.Pseudofunctor.IsStackFor.essSurj, CategoryTheory.Over.associator_inv_left_fst_snd_assoc, mapRight_map_left, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_counit_app, CategoryTheory.Functor.LeftExtension.postcomp₁_map_left, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₂, CategoryTheory.CechNerveTerminalFrom.hasWidePullback, CategoryTheory.MonoOver.forget_obj_hom, CategoryTheory.Over.rightUnitor_hom_left, CategoryTheory.MorphismProperty.Over.pullback_map_left, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₁, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, CategoryTheory.Limits.HasImageMaps.has_image_map, CategoryTheory.Over.sections_map, mapRightIso_inverse_obj_hom, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.Over.μ_pullback_left_snd, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_right, CategoryTheory.Under.mapPushoutAdj_counit_app, CategoryTheory.Over.iteratedSliceBackward_obj, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.CostructuredArrow.homMk'_comp, CategoryTheory.TwoSquare.structuredArrowDownwards_map, CategoryTheory.ChosenPullbacksAlong.Over.toUnit_left, CategoryTheory.Localization.structuredArrowEquiv_symm_apply, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_hom, preLeft_map_left, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_left, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_hom, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp_assoc, CategoryTheory.TwoSquare.structuredArrowDownwards_obj, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Over.braiding_hom_left, CategoryTheory.MonoOver.instMonoHomDiscretePUnitObjOverForget, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_hom, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CategoryTheory.MorphismProperty.Over.pullback_obj_hom, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, CategoryTheory.StructuredArrow.projectSubobject_factors, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, CategoryTheory.overToCoalgebra_obj_a, CategoryTheory.FunctorToTypes.mem_fromOverSubfunctor_iff, CategoryTheory.Over.μ_pullback_left_fst_fst, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.Over.iteratedSliceForward_map, CategoryTheory.MorphismProperty.underObj_iff, CategoryTheory.Presheaf.tautologicalCocone_ι_app, CategoryTheory.CostructuredArrow.pre_map_right, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, CategoryTheory.StructuredArrow.mk_hom_eq_self, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₁, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.MorphismProperty.Under.w_assoc, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.Presheaf.tautologicalCocone'_ι_app, CategoryTheory.StructuredArrow.preEquivalenceFunctor_map_right, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_hom_right, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_left, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.Limits.image_map_comp_imageSubobjectIso_inv, CategoryTheory.Under.opEquivOpOver_inverse_obj, Types.monoOverEquivalenceSet_unitIso, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π, CategoryTheory.TwoSquare.EquivalenceJ.functor_map, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_obj, CategoryTheory.Over.coe_hom, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_left, CategoryTheory.MorphismProperty.instHasPullbackSndHomDiscretePUnitOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, AlgebraicGeometry.Scheme.kerFunctor_obj, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, CategoryTheory.Over.forgetCocone_ι_app, CategoryTheory.SmallObject.functor_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.Over.whiskerRight_left_fst_assoc, post_map_right, CategoryTheory.StructuredArrow.pre_obj_hom, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.Over.tensorHom_left_snd, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.StructuredArrow.toUnder_map_left, CategoryTheory.StructuredArrow.w_prod_snd_assoc, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_hom_left, CategoryTheory.StructuredArrow.prodInverse_obj, CategoryTheory.CostructuredArrow.preEquivalence.functor_map_left, CategoryTheory.Functor.RightExtension.postcomp₁_obj_hom_app, CategoryTheory.SmallObject.ιObj_naturality_assoc, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₂, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.Limits.ImageMap.map_ι_assoc, CategoryTheory.Square.toArrowArrowFunctor'_obj_hom_right, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, CategoryTheory.Arrow.left_hom_inv_right, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp, CategoryTheory.Under.mkIdInitial_to_right, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_right, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.Under.costar_obj_hom, CategoryTheory.Functor.LeftExtension.coconeAt_ι_app, CategoryTheory.Presheaf.isLimit_iff_isSheafFor, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.Over.lift_left, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.TwoSquare.EquivalenceJ.inverse_obj, mapLeftIso_inverse_map_left, CategoryTheory.Arrow.w_assoc, CategoryTheory.StructuredArrow.map_obj_hom, CategoryTheory.CostructuredArrow.preEquivalence.inverse_map_left_left, CategoryTheory.SmallObject.functorialFactorizationData_p_app, CategoryTheory.Over.opEquivOpUnder_functor_map, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_right, CategoryTheory.OverPresheafAux.counitForward_counitBackward, SSet.Truncated.rightExtensionInclusion_hom_app, CategoryTheory.Limits.multispanIndexCoend_fst, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, mapLeft_obj_hom, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, TopCat.Presheaf.generateEquivalenceOpensLe_functor'_map, CategoryTheory.CostructuredArrow.pre_map_left, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_hom, CategoryTheory.Over.mkIdTerminal_from_left, CategoryTheory.ChosenPullbacksAlong.Over.fst_eq_fst', CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.Under.opEquivOpOver_functor_map, CategoryTheory.Square.toArrowArrowFunctor'_obj_hom_left, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_hom, CategoryTheory.CostructuredArrow.projectQuotient_factors, CategoryTheory.Over.fst_left, CategoryTheory.Over.prodLeftIsoPullback_hom_fst, CategoryTheory.Over.associator_hom_left_fst_assoc, CategoryTheory.TwoSquare.lanBaseChange_app, CategoryTheory.Over.isMonHom_pullbackFst_id_right, CategoryTheory.Over.pullback_obj_hom, CategoryTheory.Over.forgetAdjStar_unit_app_left, preLeft_map_right, CategoryTheory.Functor.leibnizPullback_map_app, CategoryTheory.StructuredArrow.toCostructuredArrow'_map, CategoryTheory.Over.tensorObj_left, Types.monoOverEquivalenceSet_counitIso, CategoryTheory.StructuredArrow.post_obj, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst, CategoryTheory.StructuredArrow.toCostructuredArrow'_obj, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp, CategoryTheory.Abelian.app_hom, post_obj_hom, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd', CategoryTheory.SmallObject.πObj_naturality, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_hom, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom_assoc, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, CategoryTheory.StructuredArrow.IsUniversal.fac_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.Limits.Cocone.fromStructuredArrow_obj_ι, CategoryTheory.CostructuredArrow.map₂_obj_hom, CategoryTheory.Limits.Cocone.equivStructuredArrow_counitIso, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_map, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, CategoryTheory.TwoSquare.costructuredArrowRightwards_obj, colimitAuxiliaryCocone_ι_app, CategoryTheory.StructuredArrow.IsUniversal.fac, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₂₄, AlgebraicGeometry.Scheme.restrictFunctor_obj_hom, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.relativeGluingData_natTrans_app, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, CategoryTheory.OverPresheafAux.counitAuxAux_hom, ext_iff, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_hom, CategoryTheory.Over.associator_hom_left_snd_snd, CategoryTheory.Over.associator_inv_left_snd_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.Over.coprodObj_map, CategoryTheory.MorphismProperty.arrow_iso_iff, CategoryTheory.Functor.leibnizPullback_obj_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, mapRightIso_inverse_map_left, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.Under.w_assoc, CategoryTheory.Limits.image.factor_map, CategoryTheory.StructuredArrow.w_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_hom, CategoryTheory.StructuredArrow.map₂_obj_hom, CategoryTheory.MorphismProperty.homFamily_apply, CategoryTheory.Under.opEquivOpOver_inverse_map, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_hom_app, CategoryTheory.Under.forgetCone_π_app, CategoryTheory.Over.iteratedSliceForward_obj, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_hom, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_obj_hom, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.Over.whiskerLeft_left_snd, CategoryTheory.Functor.leibnizPushout_map_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_hom, CategoryTheory.Over.w_assoc, CategoryTheory.OverPresheafAux.counitForward_val_fst, mapRight_map_right, CategoryTheory.StructuredArrow.homMk'_mk_id, CategoryTheory.CostructuredArrow.IsUniversal.fac_assoc, CategoryTheory.Pseudofunctor.IsPrestackFor.nonempty_fullyFaithful, CategoryTheory.Square.toArrowArrowFunctor_obj_left_hom, CategoryTheory.Abelian.coimIsoIm_hom_app, CategoryTheory.Limits.diagonal_pullback_fst, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.Under.w, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst_assoc, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₂, CategoryTheory.MonoOver.mono_obj_hom, CategoryTheory.Sieve.overEquiv_iff, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd, mapLeftIso_functor_map_right, CategoryTheory.Over.opEquivOpUnder_functor_obj, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.Functor.costructuredArrowMapCocone_ι_app, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, CategoryTheory.MorphismProperty.CostructuredArrow.mk_hom, CategoryTheory.Over.tensorObj_hom, CategoryTheory.StructuredArrow.toCostructuredArrow_obj, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, CategoryTheory.toOverUnit_obj_hom, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_hom, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_hom, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_hom, TopCat.Presheaf.generateEquivalenceOpensLe_inverse, CategoryTheory.Limits.ker_map, CategoryTheory.Functor.LeftExtension.mk_hom, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₃₄, CategoryTheory.MorphismProperty.costructuredArrowObj_iff, CategoryTheory.MorphismProperty.Over.map_obj_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, CategoryTheory.CostructuredArrow.IsUniversal.hom_desc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Abelian.coimIsoIm_inv_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, preLeft_obj_hom, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₄, CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology, CategoryTheory.Functor.structuredArrowMapCone_π_app, CategoryTheory.OverPresheafAux.counitForward_naturality₂, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Localization.structuredArrowEquiv_apply
inhabited 📖	CompOp	—
isoMk 📖	CompOp	4 math math: isoMk_inv_left, isoMk_hom_right, isoMk_inv_right, isoMk_hom_left
left 📖	CompOp	1218 math math: TopCat.Presheaf.generateEquivalenceOpensLe_functor'_obj_obj, CategoryTheory.IsGrothendieckAbelian.subobjectMk_of_isColimit_eq_iSup, CategoryTheory.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.Limits.coker.π_app, CategoryTheory.CostructuredArrow.homMk'_id, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst, CategoryTheory.SimplicialObject.id_left_app, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.Over.prodLeftIsoPullback_hom_snd_assoc, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_left, CategoryTheory.Limits.HasImage.of_arrow_iso, CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, CategoryTheory.Bicategory.RightExtension.w_assoc, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_hom, CategoryTheory.StructuredArrow.map_map_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.Functor.leibnizPullback_obj_map, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, CategoryTheory.Arrow.equivSigma_symm_apply_left, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver_X, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_pt, mapLeftIso_inverse_map_right, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_hom_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.Functor.LeftExtension.precomp₂_obj_hom_app, CategoryTheory.CostructuredArrow.toOver_obj_left, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_e, CategoryTheory.MonoOver.mk_coe, opFunctor_obj, CategoryTheory.Limits.multicospanIndexEnd_fst, CategoryTheory.WithTerminal.equivComma_functor_obj_left_obj, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst, CategoryTheory.StructuredArrow.mapIso_functor_obj_left, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_map, CategoryTheory.MonoOver.congr_unitIso, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.OverPresheafAux.unitAux_hom, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ_assoc, CategoryTheory.Over.iteratedSliceBackward_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_map_left_left, CategoryTheory.Over.associator_inv_left_snd, CategoryTheory.Functor.mapArrow_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, CategoryTheory.Over.pullback_obj_left, CategoryTheory.Over.inv_left_hom_left_assoc, map_obj_hom, TopCat.Presheaf.generateEquivalenceOpensLe_unitIso, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_hom, CategoryTheory.StructuredArrow.homMk'_comp, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.RetractArrow.retract_left_assoc, CategoryTheory.CostructuredArrow.w_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.MonoOver.isIso_left_iff_subobjectMk_eq, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, CategoryTheory.Sieve.overEquiv_pullback, CategoryTheory.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_id, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_id, mapLeft_map_left, CategoryTheory.OverPresheafAux.restrictedYoneda_map, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_left_as, CategoryTheory.Bicategory.RightLift.w_assoc, CategoryTheory.Sieve.ofArrows_category', CategoryTheory.Over.comp_left_assoc, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_right_as, CategoryTheory.Limits.IsImage.ofArrowIso_lift, CategoryTheory.Over.hom_left_inv_left, CategoryTheory.StructuredArrow.toUnder_obj_left, CategoryTheory.Functor.RightExtension.postcompose₂_obj_left_map, CategoryTheory.MorphismProperty.Comma.eqToHom_left, CategoryTheory.Over.whiskerLeft_left, CategoryTheory.CosimplicialObject.Augmented.leftOp_right, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_left, CategoryTheory.Over.forgetMapTerminal_hom_app, CategoryTheory.Limits.image.map_id, CategoryTheory.OverPresheafAux.restrictedYoneda_obj, CategoryTheory.Over.mk_left, CategoryTheory.Presheaf.isSheaf_iff_isLimit_coverage, CategoryTheory.MonoOver.isIso_iff_subobjectMk_eq, CategoryTheory.Functor.LeftExtension.postcomp₁_map_right_app, CategoryTheory.CostructuredArrow.IsUniversal.existsUnique, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.CostructuredArrow.w_prod_fst, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_left, CategoryTheory.SimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₃, CategoryTheory.Over.epi_iff_epi_left, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, CategoryTheory.CostructuredArrow.mapIso_functor_obj_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, fst_obj, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver'_X, mapLeftIso_functor_map_left, CategoryTheory.SimplicialObject.augment_left, CategoryTheory.MorphismProperty.Over.map_obj_left, mapLeftIso_unitIso_inv_app_left, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_obj_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_left, CategoryTheory.Arrow.comp_left, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd_assoc, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.isIso_hom_app, mapRightIso_counitIso_inv_app_left, CategoryTheory.TwoSquare.EquivalenceJ.inverse_map, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_left, CategoryTheory.Functor.RightExtension.coneAt_pt, CategoryTheory.CostructuredArrow.eq_mk, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isPullback, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀_assoc, CategoryTheory.Functor.LeftExtension.postcomp₁_obj_left, CategoryTheory.RetractArrow.r_w_assoc, CategoryTheory.StructuredArrow.map₂_map_right, mapLeftEq_hom_app_left, CategoryTheory.Limits.Cone.fromCostructuredArrow_map_hom, AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_inv, CategoryTheory.toOver_obj_left, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_hom, CategoryTheory.Limits.image.map_comp, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, eqToHom_left, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, CategoryTheory.WithInitial.ofCommaObject_obj, CategoryTheory.Functor.LeftExtension.precomp_map_right, CategoryTheory.WithTerminal.equivComma_inverse_obj_obj, CategoryTheory.Functor.LeftExtension.precomp₂_obj_left, CategoryTheory.SimplicialObject.Augmented.w₀, CategoryTheory.Functor.RightExtension.coneAt_π_app, mapRightIso_functor_map_left, map_map_right, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CategoryTheory.Arrow.leftFunc_obj, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.Over.braiding_inv_left, CategoryTheory.Functor.RightExtension.postcomp₁_obj_left_map, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, CategoryTheory.CostructuredArrow.post_obj, CategoryTheory.Functor.RightExtension.postcomp₁_map_right, CategoryTheory.Over.prodLeftIsoPullback_inv_snd, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, CategoryTheory.SimplicialObject.Augmented.toArrow_map_left, mapRight_obj_hom, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, mapRightIso_inverse_map_right, CategoryTheory.WithTerminal.equivComma_functor_obj_left_map, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, CategoryTheory.Limits.coker_map, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.instIsContinuousOverLeftDiscretePUnitIteratedSliceForwardOver, inv_left, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_hom, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₃₄, CategoryTheory.SmallObject.functorialFactorizationData_i_app, CategoryTheory.CostructuredArrow.prodFunctor_map, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_right, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_left, CategoryTheory.Abelian.coim_map, CategoryTheory.Over.leftUnitor_hom_left, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp, CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback_app, CategoryTheory.Over.tensorObj_ext_iff, CategoryTheory.RetractArrow.i_w, CategoryTheory.CostructuredArrow.toOver_map_right, CategoryTheory.CostructuredArrow.map_obj_hom, CategoryTheory.Functor.LeftExtension.precomp_obj_hom_app, CategoryTheory.WithTerminal.ofCommaObject_obj, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, CategoryTheory.Over.iteratedSliceForward_forget, CategoryTheory.StructuredArrow.eq_mk, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_right_as, CategoryTheory.MorphismProperty.Over.pullback_obj_left, CategoryTheory.Over.postAdjunctionRight_counit_app, CategoryTheory.Over.conePost_obj_π_app, CategoryTheory.Limits.multicospanIndexEnd_right, CategoryTheory.MonoOver.mkArrowIso_hom_hom_left, CategoryTheory.NatTrans.instIsClosedUnderLimitsOfShapeOverFunctorEquifiberedHomDiscretePUnitOfHasCoproductsOfShapeHom, opFunctor_map, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_left_as, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, CategoryTheory.Sieve.overEquiv_le_overEquiv_iff, CategoryTheory.MonoOver.map_obj_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext_iff, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t_assoc, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_fiber, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₂, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_hom, CategoryTheory.Over.rightUnitor_inv_left_fst, CategoryTheory.CostructuredArrow.homMk'_mk_id, preRight_obj_left, CategoryTheory.Functor.RightExtension.precomp_map_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd_assoc, CategoryTheory.Bicategory.LeftExtension.ofCompId_left_as, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.isLeftKanExtension, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eq, CategoryTheory.Under.pushout_map, CategoryTheory.Over.mapCongr_inv_app_left, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_left_as, CategoryTheory.StructuredArrow.map₂_obj_left, CategoryTheory.Sieve.ofArrows_category, CategoryTheory.MorphismProperty.Comma.comp_left_assoc, CategoryTheory.Limits.image.map_ι, CategoryTheory.Over.mapCongr_hom_app_left, CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, CategoryTheory.equivToOverUnit_unitIso, CategoryTheory.CostructuredArrow.homMk'_right, CategoryTheory.Over.postCongr_inv_app_left, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₃, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv_assoc, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_left, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.OverPresheafAux.counitForward_naturality₁, CategoryTheory.Over.mapComp_hom_app_left, mapLeftIso_inverse_obj_left, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_hom, mapRight_obj_left, equivProd_unitIso_hom_app_left, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_left, CategoryTheory.Over.whiskerRight_left_fst, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst_assoc, CategoryTheory.Arrow.square_from_iso_invert, CategoryTheory.MonoOver.pullback_obj_arrow, CategoryTheory.Over.preservesTerminalIso_pullback, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_right_hom, CategoryTheory.Over.prodLeftIsoPullback_inv_fst, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp_assoc, CategoryTheory.Abelian.im_map, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.TwoSquare.costructuredArrowRightwards_map, CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_hom, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp_assoc, CategoryTheory.Over.opEquivOpUnder_inverse_obj, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CategoryTheory.Arrow.mono_left, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.StructuredArrow.prodFunctor_map, CategoryTheory.Arrow.equivSigma_apply_snd_snd, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ, CategoryTheory.Over.prodLeftIsoPullback_inv_snd_assoc, CategoryTheory.Over.rightUnitor_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, AlgebraicGeometry.instIsClosedImmersionLeftSchemeDiscretePUnitOneOverSpecOf, CategoryTheory.Over.post_map, CategoryTheory.Square.toArrowArrowFunctor_obj_left_left, CategoryTheory.regularTopology.equalizerConditionMap_iff_nonempty_isLimit, mapRightId_inv_app_left, CategoryTheory.Pseudofunctor.presheafHom_obj, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_obj, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.CostructuredArrow.pre_obj_left, CategoryTheory.Over.iteratedSliceBackward_forget, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_left, CategoryTheory.Over.postCongr_hom_app_left, preRight_map_left, CategoryTheory.toOverUnit_obj_left, CategoryTheory.CostructuredArrow.post_map, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_left, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_base, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.Over.iteratedSliceBackward_forget_forget, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₃, CategoryTheory.CostructuredArrow.proj_obj, CategoryTheory.RetractArrow.op_r_right, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst, CategoryTheory.Over.prodLeftIsoPullback_hom_snd, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_hom, CategoryTheory.StructuredArrow.IsUniversal.existsUnique, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, CategoryTheory.IsGrothendieckAbelian.exists_isIso_of_functor_from_monoOver, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, CategoryTheory.CostructuredArrow.mapIso_functor_obj_left, CategoryTheory.Over.whiskerRight_left_snd_assoc, CategoryTheory.Arrow.w_mk_right, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_left, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.ChosenPullbacksAlong.Over.snd_eq_snd', CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctor_lift_left, CategoryTheory.CostructuredArrow.map_obj_left, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, CategoryTheory.CostructuredArrow.eta_hom_left, CategoryTheory.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Sieve.overEquiv_symm_iff, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₃, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_left, CategoryTheory.Sieve.functorPushforward_over_map, CategoryTheory.Limits.ker.ι_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_hom, CategoryTheory.Over.associator_hom_left_fst, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_left, CategoryTheory.SmallObject.functor_map, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_left_as, CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_map, comp_left, toPUnitIdEquiv_functor_obj, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₂, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, CategoryTheory.CostructuredArrow.toStructuredArrow'_obj, CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk', CategoryTheory.NatTrans.instIsClosedUnderColimitsOfShapeUnderFunctorCoequifiberedHomDiscretePUnitOfHasProductsOfShapeHom, CategoryTheory.CostructuredArrow.prodInverse_obj, CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc, SSet.Augmented.stdSimplex_obj_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc, CategoryTheory.MorphismProperty.Over.mapId_inv_app_left, CategoryTheory.Under.costar_obj_left, CategoryTheory.SmallObject.objMap_comp_assoc, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_left, CategoryTheory.Limits.ker_obj, CategoryTheory.SmallObject.functorialFactorizationData_Z_obj, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, fromProd_obj_left, CategoryTheory.MonoOver.image_map, CategoryTheory.Arrow.equivSigma_apply_fst, CategoryTheory.Under.under_left, CategoryTheory.Under.mapPushoutAdj_unit_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, CategoryTheory.GrothendieckTopology.mem_over_iff, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_obj, CategoryTheory.OverPresheafAux.counitForward_val_snd, mapLeftComp_inv_app_left, CategoryTheory.Limits.instHasImageHomMk, CategoryTheory.Limits.ImageMap.factor_map_assoc, CategoryTheory.Over.opEquivOpUnder_inverse_map, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_map_left_left, CategoryTheory.StructuredArrow.mkPostcomp_left, CategoryTheory.StructuredArrow.left_eq_id, CategoryTheory.Over.leftUnitor_inv_left_fst, mapLeftIso_functor_obj_left, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Over.inv_left_hom_left, AlgebraicGeometry.opensDiagram_map, CategoryTheory.CostructuredArrow.id_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left, HomotopicalAlgebra.cofibrations_over_iff, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.Over.forgetMapTerminal_inv_app, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, CategoryTheory.Subobject.inf_eq_map_pullback', CategoryTheory.CosimplicialObject.Augmented.leftOp_left_map, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, CategoryTheory.Over.eqToHom_left, CategoryTheory.Sieve.overEquiv_top, CategoryTheory.Functor.leibnizPushout_obj_map, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_id, CategoryTheory.Over.tensorHom_left_snd_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, CategoryTheory.SmallObject.ε_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂_map_right_app, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.Limits.image.map_homMk'_ι, CategoryTheory.CommaMorphism.w_assoc, CategoryTheory.CostructuredArrow.map_map_right, CategoryTheory.Over.leftUnitor_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst_assoc, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, AlgebraicGeometry.opensDiagramι_app, CategoryTheory.Arrow.w, CategoryTheory.StructuredArrow.homMk'_left, HomotopicalAlgebra.instCofibrationLeftDiscretePUnitOfOver, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd', CategoryTheory.OverClass.fromOver_over, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_zero, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, CategoryTheory.SmallObject.objMap_id, CategoryTheory.MonoOver.image_obj, preRight_map_right, TopologicalSpace.Opens.coe_overEquivalence_functor_obj, CategoryTheory.OverClass.asOver_left, CategoryTheory.Limits.coker_obj, CategoryTheory.Over.μ_pullback_left_fst_snd', CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_left, CategoryTheory.Over.comp_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorUnit_left, CategoryTheory.Over.mapPullbackAdj_unit_app, CategoryTheory.Functor.RightExtension.postcomp₁_obj_left_obj, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.Over.mapId_inv_app_left, map_map_left, CategoryTheory.Limits.multicospanShapeEnd_fst, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.CostructuredArrow.w_prod_snd, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, mapRightIso_functor_obj_hom, CategoryTheory.Limits.imageSubobjectIso_comp_image_map, post_map_left, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_obj_left, CategoryTheory.CommaMorphism.w, toPUnitIdEquiv_unitIso_inv_app_left, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, CategoryTheory.Sieve.overEquiv_symm_pullback, CategoryTheory.Limits.multispanIndexCoend_snd, CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_obj, CategoryTheory.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.MorphismProperty.Comma.Hom.prop_hom_left, CategoryTheory.RetractArrow.r_w, CategoryTheory.Functor.LeftExtension.postcompose₂_obj_hom_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁_assoc, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_counitIso, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.MorphismProperty.instHasPullbackHomDiscretePUnitOfHasPullbacksAlong, CategoryTheory.ChosenPullbacksAlong.iso_pullback_obj, CategoryTheory.Arrow.inv_left, CategoryTheory.SimplicialObject.augment_hom_zero, CategoryTheory.SmallObject.ιObj_naturality, CategoryTheory.SmallObject.ιFunctorObj_naturality, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_left, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, CategoryTheory.Over.conePost_map_hom, CategoryTheory.WithTerminal.mkCommaObject_left_map, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, CategoryTheory.SimplicialObject.Augmented.rightOp_right_map, CategoryTheory.MonoOver.bot_left, CategoryTheory.Presieve.ofArrows_category, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_inv_hom, CategoryTheory.WithTerminal.ofCommaMorphism_app, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, CategoryTheory.OverPresheafAux.counitAuxAux_inv, CategoryTheory.Functor.LeftExtension.postcomp₁_obj_hom_app, CategoryTheory.SmallObject.functorMapSrc_functorObjTop, CategoryTheory.StructuredArrow.mk_left, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, mapLeftIso_unitIso_hom_app_left, CategoryTheory.MonoOver.map_obj_arrow, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_left_as, CategoryTheory.Arrow.w_mk_right_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_obj, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, CategoryTheory.ComposableArrows.arrowEquiv_symm_apply, CategoryTheory.OverPresheafAux.restrictedYonedaObj_map, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_left_as, CategoryTheory.Over.map_obj_hom, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₃, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Over.associator_hom_left_snd_fst, CategoryTheory.CostructuredArrow.toOver_map_left, CategoryTheory.Over.postComp_inv_app_left, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', mapRightEq_inv_app_left, CategoryTheory.Functor.mapArrow_map_left, CategoryTheory.subterminalsEquivMonoOverTerminal_inverse_map, CategoryTheory.CostructuredArrow.eta_inv_left, CategoryTheory.MorphismProperty.over_iso_iff, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, CategoryTheory.RetractArrow.retract_left, CategoryTheory.Functor.toOver_obj_left, CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp_obj, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_snd, CategoryTheory.Arrow.squareToSnd_left, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.Over.toOverSectionsAdj_counit_app, CategoryTheory.StructuredArrow.toCostructuredArrow_map, CategoryTheory.Limits.ImageMap.factor_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd, CategoryTheory.MonoOver.w, CategoryTheory.MonoOver.bot_arrow_eq_zero, CategoryTheory.WithInitial.equivComma_inverse_map_app, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_X, left_hom_inv_right, CategoryTheory.forgetAdjToOver_unit_app, CategoryTheory.Arrow.isIso_left, CategoryTheory.OverPresheafAux.counitBackward_counitForward, CategoryTheory.Arrow.isIso_hom_iff_isIso_of_isIso, unopFunctor_obj, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_app, CategoryTheory.Over.iteratedSliceEquivOverMapIso_inv_app_left_left, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_obj, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_left, CategoryTheory.StructuredArrow.toUnder_map_right, CategoryTheory.regularTopology.parallelPair_pullback_initial, CategoryTheory.WithTerminal.liftFromOver_obj_obj, CategoryTheory.overToCoalgebra_map_f, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_left, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_left, CategoryTheory.Pseudofunctor.isStackFor_iff, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_right_as, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_app, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst_assoc, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₁, CategoryTheory.TwoSquare.isIso_lanBaseChange_app_iff, mapLeftIso_counitIso_hom_app_left, CategoryTheory.Over.pullback_map_left, CategoryTheory.instIsContinuousOverLeftDiscretePUnitIteratedSliceBackwardOver, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst, mapRightIso_functor_map_right, limitAuxiliaryCone_π_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.Pseudofunctor.presheafHom_map, CategoryTheory.MorphismProperty.costructuredArrow_iso_iff, CategoryTheory.Over.postEquiv_counitIso, CategoryTheory.Limits.multispanIndexCoend_left, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.Over.sections_obj, CategoryTheory.MorphismProperty.Comma.ext_iff, toIdPUnitEquiv_inverse_obj_left_as, AlgebraicGeometry.opensDiagram_obj, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_right_hom, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, CategoryTheory.CostructuredArrow.toStructuredArrow'_map, CategoryTheory.RetractArrow.op_i_right, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.Abelian.coim_obj, CategoryTheory.Over.star_obj_left, CategoryTheory.Functor.mapArrow_map_right, CategoryTheory.Over.iteratedSliceEquiv_functor, CategoryTheory.MorphismProperty.overObj_iff, AlgebraicGeometry.opensCone_π_app, CategoryTheory.Over.tensorHom_left, CategoryTheory.CostructuredArrow.w, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isIso_hom, CategoryTheory.MonoOver.mk'_coe', CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_right, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_hom, CategoryTheory.Presheaf.isSheaf_iff_isLimit, CategoryTheory.Under.opEquivOpOver_functor_obj, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_left_as, CategoryTheory.MonoOver.mono, CategoryTheory.Over.associator_inv_left_fst_snd, CategoryTheory.SimplicialObject.comp_left_app, CategoryTheory.MonoOver.forget_obj_left, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.WithInitial.equivComma_inverse_obj_map, CategoryTheory.Over.forget_obj, CategoryTheory.MorphismProperty.Over.w_assoc, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, CategoryTheory.SimplicialObject.Augmented.rightOp_right_obj, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, CategoryTheory.Functor.RightExtension.postcomp₁_map_left_app, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.MorphismProperty.ofHoms_homFamily, CategoryTheory.Over.associator_hom_left_snd_snd_assoc, mapRightComp_hom_app_left, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π_assoc, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, CategoryTheory.Limits.im_obj, CategoryTheory.SmallObject.πObj_naturality_assoc, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_right_inv, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, CategoryTheory.CostructuredArrow.epi_left_of_epi, TopCat.Presheaf.generateEquivalenceOpensLe_functor, CategoryTheory.Limits.multispanShapeCoend_fst, mapRightIso_functor_obj_left, CategoryTheory.Over.μ_pullback_left_fst_fst', CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_pullback_obj, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, Types.monoOverEquivalenceSet_functor_map, CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Over.whiskerRight_left, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_left, CategoryTheory.CostructuredArrow.homMk'_left, CategoryTheory.Square.toArrowArrowFunctor'_map_left_right, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, CategoryTheory.Arrow.id_left, CategoryTheory.Abelian.coimageImageComparisonFunctor_obj, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₃, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.StructuredArrow.pre_map_left, unopFunctorCompSnd_inv_app, inv_left_hom_right, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.CostructuredArrow.prodFunctor_obj, CategoryTheory.OverPresheafAux.counitAux_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isIso_hom_app, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_F, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, CategoryTheory.RetractArrow.unop_r_right, CategoryTheory.StructuredArrow.map_map_left, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_apply, CategoryTheory.Over.w, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_map, CategoryTheory.SimplicialObject.Augmented.drop_obj, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_map, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp_assoc, TopCat.Presheaf.generateEquivalenceOpensLe_counitIso, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_m, CategoryTheory.StructuredArrow.prodFunctor_obj, CategoryTheory.MorphismProperty.Comma.Hom.comp_left, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left_inv, CategoryTheory.Functor.LeftExtension.postcompose₂_obj_left, CategoryTheory.Sieve.yonedaFamily_fromCocone_compatible, CategoryTheory.subterminalsEquivMonoOverTerminal_inverse_obj_obj, CategoryTheory.CostructuredArrow.comp_left, CategoryTheory.CosimplicialObject.augment_hom_zero, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁, CategoryTheory.coalgebraEquivOver_counitIso, opFunctorCompSnd_hom_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.isIso_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.Functor.LeftExtension.precomp_obj_left, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.Arrow.mk_eq, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_obj, Types.monoOverEquivalenceSet_functor_obj, CategoryTheory.MorphismProperty.Under.w, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_hom, CategoryTheory.StructuredArrow.mapIso_functor_map_left, AlgebraicGeometry.Scheme.kerFunctor_map, CategoryTheory.CostructuredArrow.mk_left, CategoryTheory.MorphismProperty.Comma.prop, SSet.Truncated.rightExtensionInclusion_left, CategoryTheory.Pseudofunctor.IsStack.essSurj_of_sieve, CategoryTheory.CostructuredArrow.homMk'_mk_comp, CategoryTheory.Over.associator_inv_left_fst_fst, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, mapLeftIso_inverse_obj_hom, CategoryTheory.MonoOver.isIso_iff_isIso_hom_left, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, mapLeftId_hom_app_left, post_obj_left, CategoryTheory.Over.snd_left, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_map_left_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.Limits.ImageMap.map_ι, CategoryTheory.CostructuredArrow.prodInverse_map, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst_assoc, CategoryTheory.Functor.leibnizPushout_obj_obj, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ_assoc, mapLeftId_inv_app_left, CategoryTheory.instIsCocontinuousOverLeftDiscretePUnitIteratedSliceBackwardOver, CategoryTheory.Arrow.isIso_hom_iff_isIso_hom_of_isIso, CategoryTheory.Arrow.inv_hom_id_left_assoc, CategoryTheory.Over.tensorHom_left_fst, CategoryTheory.Sieve.overEquiv_symm_generate, CategoryTheory.MorphismProperty.Over.mk_left, CategoryTheory.Over.whiskerRight_left_snd, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, CategoryTheory.MorphismProperty.structuredArrowObj_iff, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, CategoryTheory.StructuredArrow.map_obj_left, AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iff, CategoryTheory.MorphismProperty.mem_toSet_iff, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ_assoc, CategoryTheory.MorphismProperty.CostructuredArrow.mk_left, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isRightKanExtension, HomotopicalAlgebra.instFibrationLeftDiscretePUnitOfOver, CategoryTheory.Over.iteratedSliceEquiv_unitIso, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π_assoc, toPUnitIdEquiv_unitIso_hom_app_left, CategoryTheory.CommSq.of_arrow, mapRightIso_unitIso_hom_app_left, CategoryTheory.SimplicialObject.Augmented.const_obj_left, CategoryTheory.WithInitial.equivComma_functor_obj_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_hom, CategoryTheory.CostructuredArrow.toStructuredArrow_obj, unopFunctor_map, CategoryTheory.Arrow.isIso_of_isIso, CategoryTheory.Over.tensorHom_left_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd_assoc, CategoryTheory.forgetAdjToOver.homEquiv_symm, AlgebraicGeometry.Scheme.Cover.overEquiv_generate_toPresieveOver_eq_ofArrows, CategoryTheory.OverPresheafAux.restrictedYonedaObj_obj, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_hom, CategoryTheory.Over.prodLeftIsoPullback_inv_fst_assoc, CategoryTheory.Abelian.im_obj, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_hom_left, CategoryTheory.SmallObject.SuccStruct.toSuccArrow_left, CategoryTheory.MorphismProperty.Comma.comp_left, CategoryTheory.Functor.RightExtension.mk_left, CategoryTheory.Over.postAdjunctionRight_unit_app, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_left, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, CategoryTheory.Over.id_left, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_hom_left, CategoryTheory.OverPresheafAux.restrictedYonedaObjMap₁_app, CategoryTheory.Arrow.iso_w, CategoryTheory.CosimplicialObject.augment_left, CategoryTheory.MorphismProperty.Under.mk_left, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_obj, CategoryTheory.Arrow.comp_left_assoc, CategoryTheory.Over.postComp_hom_app_left, CategoryTheory.Over.whiskerLeft_left_fst, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_counit_app, CategoryTheory.SmallObject.πFunctorObj_eq, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp_map, CategoryTheory.SmallObject.objMap_comp, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_left, CategoryTheory.Functor.LeftExtension.postcompose₂_map_left, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, mapLeftIso_counitIso_inv_app_left, CategoryTheory.Over.post_obj, CategoryTheory.MonoOver.mkArrowIso_inv_hom_left, CategoryTheory.Arrow.inv_left_hom_right, CategoryTheory.Limits.Cone.equivCostructuredArrow_counitIso, CategoryTheory.WithTerminal.mkCommaObject_left_obj, CategoryTheory.Functor.RightExtension.postcompose₂_obj_hom_app, CategoryTheory.ObjectProperty.ColimitOfShape.toCostructuredArrow_map, mapRightIso_counitIso_hom_app_left, CategoryTheory.Functor.RightExtension.precomp_obj_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, mapRightId_hom_app_left, CategoryTheory.Pseudofunctor.isPrestackFor_iff, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, CategoryTheory.Functor.RightExtension.precomp_map_right, CategoryTheory.ChosenPullbacksAlong.Over.lift_left, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₂, CategoryTheory.Over.mapId_hom_app_left, mapLeftEq_inv_app_left, CategoryTheory.Square.toArrowArrowFunctor_map_left_left, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, CategoryTheory.Abelian.coimageImageComparisonFunctor_map, CategoryTheory.MonoOver.w_assoc, CategoryTheory.CostructuredArrow.map_map_left, CategoryTheory.MorphismProperty.over_iff, CategoryTheory.CostructuredArrow.map₂_map_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε_assoc, CategoryTheory.WithInitial.equivComma_inverse_obj_obj, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₁, CategoryTheory.Over.isPullback_of_binaryFan_isLimit, CategoryTheory.MorphismProperty.commaObj_iff, CategoryTheory.Pseudofunctor.IsStackFor.isEquivalence, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp_assoc, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_X, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_right, CategoryTheory.Over.whiskerLeft_left_fst_assoc, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_inv_left_app, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_left, CategoryTheory.MonoOver.pullback_obj_left, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_left, CategoryTheory.Under.pushout_obj, CategoryTheory.MorphismProperty.Over.w, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀, CategoryTheory.Square.toArrowArrowFunctor_obj_right_left, CategoryTheory.Functor.RightExtension.postcompose₂_map_left_app, mapFst_hom_app, CategoryTheory.Over.coprodObj_obj, AlgebraicGeometry.isClosedImmersion_equalizer_ι_left, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, CategoryTheory.Functor.RightExtension.postcompose₂_obj_left_obj, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_obj, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_right_as, CategoryTheory.StructuredArrow.preEquivalenceInverse_map_right_right, mapLeft_map_right, mapLeft_obj_left, CategoryTheory.CostructuredArrow.IsUniversal.fac, CategoryTheory.Subfunctor.equivalenceMonoOver_unitIso, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₄, CategoryTheory.Over.prodComparisonIso_pullback_Spec_inv_left_fst_fst', leftIso_hom, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_right_inv, CategoryTheory.MonoOver.subobjectMk_le_mk_of_hom, CategoryTheory.Over.whiskerLeft_left_snd_assoc, CategoryTheory.WithInitial.commaFromUnder_obj_left, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.CostructuredArrow.grothendieckProj_obj, CategoryTheory.Over.equivalenceOfIsTerminal_unitIso, CategoryTheory.Square.toArrowArrowFunctor_obj_left_right, CategoryTheory.TwoSquare.EquivalenceJ.functor_obj, TopologicalSpace.Opens.coe_overEquivalence_inverse_obj_left, toPUnitIdEquiv_inverse_obj_left, CategoryTheory.Over.iteratedSliceEquiv_counitIso, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, CategoryTheory.StructuredArrow.w, CategoryTheory.Functor.RightExtension.postcompose₂_map_right, CategoryTheory.Square.toArrowArrowFunctor'_map_left_left, CategoryTheory.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.Cone.fromCostructuredArrow_obj_pt, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left, CategoryTheory.Sieve.forallYonedaIsSheaf_iff_colimit, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_id, CategoryTheory.WithTerminal.liftFromOver_obj_map, CategoryTheory.Functor.LeftExtension.precomp_map_left, mapLeftIso_functor_obj_hom, CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_I, CategoryTheory.MorphismProperty.comma_iso_iff, CategoryTheory.StructuredArrow.pre_map_right, CategoryTheory.Arrow.hom_inv_id_left, CategoryTheory.StructuredArrow.w_prod_fst_assoc, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, leftIso_inv, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_left, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_counit_app, CategoryTheory.subterminalsEquivMonoOverTerminal_unitIso, CategoryTheory.overToCoalgebra_obj_A, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, CategoryTheory.Over.postEquiv_unitIso, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_isImage, CategoryTheory.Pseudofunctor.IsStackFor.essSurj, CategoryTheory.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_obj, mapRight_map_left, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_counit_app, CategoryTheory.SimplicialObject.Augmented.rightOp_left, CategoryTheory.Arrow.inv_hom_id_left, CategoryTheory.Functor.LeftExtension.postcomp₁_map_left, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₂, CategoryTheory.Functor.RightExtension.coneAtFunctor_map_hom, CategoryTheory.CechNerveTerminalFrom.hasWidePullback, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_comp, CategoryTheory.Over.rightUnitor_hom_left, CategoryTheory.MorphismProperty.Over.pullback_map_left, opFunctorCompSnd_inv_app, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₁, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, CategoryTheory.Limits.HasImageMaps.has_image_map, CategoryTheory.Over.sections_map, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_hom_hom, mapRightIso_inverse_obj_hom, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_right, CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.Over.μ_pullback_left_snd, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_right, CategoryTheory.Over.iteratedSliceBackward_obj, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.subterminalsEquivMonoOverTerminal_counitIso, CategoryTheory.CostructuredArrow.homMk'_comp, id_left, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_map_left, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π, CategoryTheory.Over.map_obj_left, CategoryTheory.Over.epi_left_of_epi, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_hom, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, preLeft_map_left, CategoryTheory.Sieve.overEquiv_symm_top, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_left, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp_assoc, CategoryTheory.CostructuredArrow.eqToHom_left, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.instHomIsOverLeftDiscretePUnit, mapRightIso_unitIso_inv_app_left, CategoryTheory.Over.braiding_hom_left, CategoryTheory.MonoOver.instMonoHomDiscretePUnitObjOverForget, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_hom, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CategoryTheory.MorphismProperty.Over.pullback_obj_hom, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, equivProd_inverse_obj_left, CategoryTheory.StructuredArrow.projectSubobject_factors, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, CategoryTheory.overToCoalgebra_obj_a, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, CategoryTheory.FunctorToTypes.mem_fromOverSubfunctor_iff, CategoryTheory.Over.μ_pullback_left_fst_fst, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_left_as, CategoryTheory.Over.iteratedSliceForward_map, CategoryTheory.simplicialToCosimplicialAugmented_map_right, CategoryTheory.MorphismProperty.underObj_iff, CategoryTheory.MonoOver.inf_obj, CategoryTheory.CostructuredArrow.pre_map_right, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₁, CategoryTheory.WithInitial.mkCommaObject_left, CategoryTheory.SmallObject.ιFunctorObj_naturality_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_left, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.MorphismProperty.Under.w_assoc, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.MonoOver.top_left, CategoryTheory.Over.tensorUnit_left, CategoryTheory.StructuredArrow.preEquivalenceFunctor_map_right, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Over.hom_left_inv_left_assoc, CategoryTheory.Arrow.mk_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_inv_app, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_hom_right, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_left, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.Limits.image_map_comp_imageSubobjectIso_inv, CategoryTheory.Under.opEquivOpOver_inverse_obj, Types.monoOverEquivalenceSet_unitIso, CategoryTheory.TwoSquare.EquivalenceJ.functor_map, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_obj, CategoryTheory.Over.iteratedSliceEquiv_inverse, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, CategoryTheory.StructuredArrow.mapIso_inverse_obj_left, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_left, CategoryTheory.MorphismProperty.instHasPullbackSndHomDiscretePUnitOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, CategoryTheory.cosimplicialToSimplicialAugmented_map, AlgebraicGeometry.Scheme.kerFunctor_obj, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, mapRightEq_hom_app_left, CategoryTheory.SmallObject.functor_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, CategoryTheory.StructuredArrow.mapIso_functor_map_right, coneOfPreserves_pt_left, CategoryTheory.Under.costar_map_left, CategoryTheory.Over.whiskerRight_left_fst_assoc, post_map_right, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.Over.tensorHom_left_snd, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Limits.Cone.overPost_π_app, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.StructuredArrow.toUnder_map_left, CategoryTheory.StructuredArrow.w_prod_snd_assoc, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_hom_left, CategoryTheory.Functor.mapArrowFunctor_map_app_left, CategoryTheory.CostructuredArrow.preEquivalence.functor_map_left, CategoryTheory.Functor.RightExtension.postcomp₁_obj_hom_app, CategoryTheory.SmallObject.ιObj_naturality_assoc, CategoryTheory.Subobject.representative_coe, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₂, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom, CategoryTheory.RetractArrow.unop_i_right, CategoryTheory.Limits.ImageMap.map_ι_assoc, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, coconeOfPreserves_pt_left, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_right_as, CategoryTheory.Square.toArrowArrowFunctor_map_left_right, CategoryTheory.WithTerminal.liftFromOver_map_app, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_left_as, CategoryTheory.Sieve.overEquiv_generate, CategoryTheory.Bicategory.LeftLift.ofIdComp_left_as, CategoryTheory.Arrow.left_hom_inv_right, CategoryTheory.Subobject.inf_eq_map_pullback, CategoryTheory.Over.postMap_app, instIsIsoLeft, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_left, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_right_as, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_right, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.RetractArrow.instIsSplitEpiLeftRArrow, CategoryTheory.Functor.LeftExtension.coconeAt_ι_app, equivProd_functor_map, CategoryTheory.Presheaf.isLimit_iff_isSheafFor, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_left_as, CategoryTheory.Over.lift_left, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Functor.LeftExtension.mk_left_as, CategoryTheory.TwoSquare.EquivalenceJ.inverse_obj, AlgebraicGeometry.Scheme.restrictFunctor_obj_left, mapLeftIso_inverse_map_left, CategoryTheory.MonoOver.congr_counitIso, CategoryTheory.Arrow.w_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_map_left_left, preLeft_obj_left, CategoryTheory.SmallObject.functorialFactorizationData_p_app, CategoryTheory.Over.opEquivOpUnder_functor_map, mapLeftComp_hom_app_left, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_right, CategoryTheory.Functor.LeftExtension.precomp₂_map_left, CategoryTheory.OverPresheafAux.counitForward_counitBackward, CategoryTheory.Limits.multispanIndexCoend_fst, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_pullback_map, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, mapLeft_obj_hom, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, TopCat.Presheaf.generateEquivalenceOpensLe_functor'_map, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.CostructuredArrow.pre_map_left, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, HomotopicalAlgebra.weakEquivalences_over_iff, CategoryTheory.ChosenPullbacksAlong.Over.fst_eq_fst', CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.WithTerminal.coneEquiv_functor_obj_pt, CategoryTheory.Under.opEquivOpOver_functor_map, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_hom, CategoryTheory.CostructuredArrow.projectQuotient_factors, CategoryTheory.Functor.essImage_overPost, CategoryTheory.WithTerminal.commaFromOver_obj_left, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, CategoryTheory.Over.fst_left, CategoryTheory.Over.prodLeftIsoPullback_hom_fst, CategoryTheory.Over.associator_hom_left_fst_assoc, equivProd_unitIso_inv_app_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.SmallObject.preservesColimit, CategoryTheory.Over.isMonHom_pullbackFst_id_right, CategoryTheory.Over.pullback_obj_hom, CategoryTheory.Over.forgetAdjStar_unit_app_left, unopFunctorCompSnd_hom_app, HomotopicalAlgebra.instWeakEquivalenceLeftDiscretePUnitOfOver, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor', preLeft_map_right, CategoryTheory.Functor.leibnizPullback_map_app, CategoryTheory.CostructuredArrow.epi_iff_epi_left, CategoryTheory.StructuredArrow.toCostructuredArrow'_map, CategoryTheory.Over.tensorObj_left, CategoryTheory.RetractArrow.i_w_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_right_as, Types.monoOverEquivalenceSet_counitIso, CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd, CategoryTheory.instIsCocontinuousOverLeftDiscretePUnitIteratedSliceForwardOver, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst, CategoryTheory.StructuredArrow.toCostructuredArrow'_obj, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp, CategoryTheory.Abelian.app_hom, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_left_as, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_left, CategoryTheory.SmallObject.hasColimitsOfShape_discrete, post_obj_hom, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd', CategoryTheory.SmallObject.πObj_naturality, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_hom, CategoryTheory.instIsDenseSubsiteOverLeftDiscretePUnitOverInverseIteratedSliceEquiv, CategoryTheory.Over.coprod_map_app, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_obj, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, CategoryTheory.StructuredArrow.IsUniversal.fac_assoc, CategoryTheory.Arrow.equivSigma_apply_snd_fst, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.WithInitial.ofCommaMorphism_app, CategoryTheory.CostructuredArrow.map₂_obj_hom, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.CosimplicialObject.Augmented.const_obj_left, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_map, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, CategoryTheory.CostructuredArrow.map₂_obj_left, CategoryTheory.TwoSquare.costructuredArrowRightwards_obj, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, colimitAuxiliaryCocone_ι_app, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_left, CategoryTheory.RetractArrow.instIsSplitMonoLeftIArrow, CategoryTheory.MorphismProperty.Over.mapId_hom_app_left, mapRightIso_inverse_obj_left, CategoryTheory.StructuredArrow.IsUniversal.fac, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₂₄, CategoryTheory.CosimplicialObject.comp_left, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_left_as, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, CategoryTheory.OverPresheafAux.counitAuxAux_hom, ext_iff, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_hom, CategoryTheory.Limits.kernelSubobjectMap_arrow, CategoryTheory.Over.associator_hom_left_snd_snd, CategoryTheory.Over.associator_inv_left_snd_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.Over.coprodObj_map, CategoryTheory.MorphismProperty.arrow_iso_iff, CategoryTheory.Functor.leibnizPullback_obj_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, mapRightIso_inverse_map_left, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.Under.w_assoc, CategoryTheory.Limits.image.factor_map, CategoryTheory.StructuredArrow.w_assoc, CategoryTheory.Arrow.hom_inv_id_left_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.CosimplicialObject.Augmented.point_obj, CategoryTheory.Under.opEquivOpOver_inverse_map, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, CategoryTheory.Over.iteratedSliceForward_obj, CategoryTheory.Functor.essImage.of_overPost, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_hom_left_app, CategoryTheory.CostructuredArrow.projectQuotient_mk, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_left, CategoryTheory.MorphismProperty.Comma.id_left, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.Over.whiskerLeft_left_snd, CategoryTheory.Functor.leibnizPushout_map_app, CategoryTheory.Over.w_assoc, CategoryTheory.OverPresheafAux.counitForward_val_fst, mapRight_map_right, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_right, CategoryTheory.CostructuredArrow.IsUniversal.fac_assoc, CategoryTheory.Pseudofunctor.IsPrestackFor.nonempty_fullyFaithful, mapFst_inv_app, CategoryTheory.Subfunctor.equivalenceMonoOver_counitIso, CategoryTheory.Square.toArrowArrowFunctor_obj_left_hom, CategoryTheory.Abelian.coimIsoIm_hom_app, CategoryTheory.Limits.diagonal_pullback_fst, CategoryTheory.Bicategory.RightLift.w, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_fst, CategoryTheory.StructuredArrow.pre_obj_left, CategoryTheory.Under.w, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst_assoc, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_left_as, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_obj, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₂, CategoryTheory.MonoOver.mono_obj_hom, CategoryTheory.Sieve.overEquiv_iff, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd, mapLeftIso_functor_map_right, CategoryTheory.Over.opEquivOpUnder_functor_obj, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, HomotopicalAlgebra.fibrations_over_iff, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.Functor.costructuredArrowMapCocone_ι_app, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, equivProd_functor_obj, CategoryTheory.Bicategory.RightExtension.w, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, CategoryTheory.Over.tensorObj_hom, CategoryTheory.StructuredArrow.toCostructuredArrow_obj, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, map_obj_left, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_hom, mapRightComp_inv_app_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_map_hom, CategoryTheory.Arrow.iso_w', TopCat.Presheaf.generateEquivalenceOpensLe_inverse, CategoryTheory.Over.mapComp_inv_app_left, CategoryTheory.CosimplicialObject.id_left, CategoryTheory.Limits.ker_map, CategoryTheory.Over.mono_left_of_mono, CategoryTheory.MorphismProperty.costructuredArrowObj_iff, CategoryTheory.MorphismProperty.Over.map_obj_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, CategoryTheory.CostructuredArrow.IsUniversal.hom_desc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.MonoOver.isIso_iff_isIso_left, CategoryTheory.Abelian.coimIsoIm_inv_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.MonoOver.instIsIsoLeftDiscretePUnitHomFullSubcategoryOverIsMono, CategoryTheory.Functor.RightExtension.precomp_obj_left, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₄, CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_left, CategoryTheory.OverPresheafAux.counitForward_naturality₂, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right
leftIso 📖	CompOp	2 math math: leftIso_hom, leftIso_inv
map 📖	CompOp	31 math math: CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, map_obj_hom, map_final, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, map_map_right, mapSnd_inv_app, faithful_map, map_obj_right, map_map_left, isEquivalenceMap, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, full_map, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, mapFst_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, essSurj_map, mapSnd_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, map_fst, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, map_snd, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, mapFst_inv_app, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, map_obj_left, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom
mapFst 📖	CompOp	2 math math: mapFst_hom_app, mapFst_inv_app
mapLeft 📖	CompOp	38 math math: CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, mapLeftEq_inv_app_right, mapLeft_map_left, mapLeftIso_unitIso_inv_app_left, mapLeftEq_hom_app_left, mapLeftIso_counitIso_inv_app_right, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.TwoSquare.costructuredArrowRightwards_map, mapLeftId_hom_app_right, mapLeftComp_inv_app_left, mapLeftIso_unitIso_inv_app_right, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, mapLeftIso_unitIso_hom_app_left, mapLeftComp_inv_app_right, mapLeftIso_counitIso_hom_app_left, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, mapLeftEq_hom_app_right, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, mapLeft_obj_right, mapLeftId_hom_app_left, mapLeftId_inv_app_left, mapLeftIso_unitIso_hom_app_right, mapLeftIso_counitIso_inv_app_left, mapLeftEq_inv_app_left, mapLeftIso_counitIso_hom_app_right, mapLeft_map_right, mapLeft_obj_left, CategoryTheory.TwoSquare.EquivalenceJ.functor_obj, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.TwoSquare.EquivalenceJ.functor_map, mapLeftComp_hom_app_left, mapLeft_obj_hom, CategoryTheory.TwoSquare.costructuredArrowRightwards_obj, mapLeftId_inv_app_right, mapLeftComp_hom_app_right, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right
mapLeftComp 📖	CompOp	4 math math: mapLeftComp_inv_app_left, mapLeftComp_inv_app_right, mapLeftComp_hom_app_left, mapLeftComp_hom_app_right
mapLeftEq 📖	CompOp	4 math math: mapLeftEq_inv_app_right, mapLeftEq_hom_app_left, mapLeftEq_hom_app_right, mapLeftEq_inv_app_left
mapLeftId 📖	CompOp	4 math math: mapLeftId_hom_app_right, mapLeftId_hom_app_left, mapLeftId_inv_app_left, mapLeftId_inv_app_right
mapLeftIso 📖	CompOp	18 math math: mapLeftIso_inverse_map_right, mapLeftIso_functor_map_left, mapLeftIso_unitIso_inv_app_left, mapLeftIso_counitIso_inv_app_right, mapLeftIso_inverse_obj_left, mapLeftIso_inverse_obj_right, mapLeftIso_functor_obj_left, mapLeftIso_unitIso_inv_app_right, mapLeftIso_unitIso_hom_app_left, mapLeftIso_counitIso_hom_app_left, mapLeftIso_inverse_obj_hom, mapLeftIso_unitIso_hom_app_right, mapLeftIso_counitIso_inv_app_left, mapLeftIso_counitIso_hom_app_right, mapLeftIso_functor_obj_hom, mapLeftIso_inverse_map_left, mapLeftIso_functor_obj_right, mapLeftIso_functor_map_right
mapRight 📖	CompOp	41 math math: mapRightIso_counitIso_inv_app_left, CategoryTheory.TwoSquare.EquivalenceJ.inverse_map, mapRightEq_hom_app_right, mapRightIso_counitIso_inv_app_right, mapRight_obj_hom, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, mapRightIso_unitIso_inv_app_right, mapRight_obj_left, mapRightId_inv_app_left, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, mapRightComp_inv_app_right, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, mapRightEq_inv_app_left, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, mapRightComp_hom_app_left, mapRightIso_counitIso_hom_app_right, mapRightIso_unitIso_hom_app_left, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, mapRightId_hom_app_right, mapRightIso_counitIso_hom_app_left, mapRightId_hom_app_left, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, mapRight_map_left, mapRightId_inv_app_right, mapRightComp_hom_app_right, CategoryTheory.TwoSquare.structuredArrowDownwards_map, CategoryTheory.TwoSquare.structuredArrowDownwards_obj, mapRightIso_unitIso_inv_app_left, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, mapRightEq_hom_app_left, mapRightEq_inv_app_right, CategoryTheory.TwoSquare.EquivalenceJ.inverse_obj, mapRight_obj_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, mapRight_map_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, mapRightComp_inv_app_left, mapRightIso_unitIso_hom_app_right
mapRightComp 📖	CompOp	4 math math: mapRightComp_inv_app_right, mapRightComp_hom_app_left, mapRightComp_hom_app_right, mapRightComp_inv_app_left
mapRightEq 📖	CompOp	4 math math: mapRightEq_hom_app_right, mapRightEq_inv_app_left, mapRightEq_hom_app_left, mapRightEq_inv_app_right
mapRightId 📖	CompOp	4 math math: mapRightId_inv_app_left, mapRightId_hom_app_right, mapRightId_hom_app_left, mapRightId_inv_app_right
mapRightIso 📖	CompOp	18 math math: mapRightIso_counitIso_inv_app_left, mapRightIso_counitIso_inv_app_right, mapRightIso_functor_map_left, mapRightIso_inverse_map_right, mapRightIso_unitIso_inv_app_right, mapRightIso_functor_obj_right, mapRightIso_functor_obj_hom, mapRightIso_inverse_obj_right, mapRightIso_functor_map_right, mapRightIso_functor_obj_left, mapRightIso_counitIso_hom_app_right, mapRightIso_unitIso_hom_app_left, mapRightIso_counitIso_hom_app_left, mapRightIso_inverse_obj_hom, mapRightIso_unitIso_inv_app_left, mapRightIso_inverse_obj_left, mapRightIso_inverse_map_left, mapRightIso_unitIso_hom_app_right
mapSnd 📖	CompOp	2 math math: mapSnd_inv_app, mapSnd_hom_app
natTrans 📖	CompOp	1 math math: natTrans_app
opEquiv 📖	CompOp	4 math math: opEquiv_counitIso, opEquiv_functor, opEquiv_unitIso, opEquiv_inverse
opFunctor 📖	CompOp	9 math math: opFunctor_obj, opEquiv_counitIso, opFunctor_map, opFunctorCompSnd_hom_app, opFunctorCompFst_hom_app, opFunctorCompFst_inv_app, opEquiv_functor, opEquiv_unitIso, opFunctorCompSnd_inv_app
opFunctorCompFst 📖	CompOp	2 math math: opFunctorCompFst_hom_app, opFunctorCompFst_inv_app
opFunctorCompSnd 📖	CompOp	2 math math: opFunctorCompSnd_hom_app, opFunctorCompSnd_inv_app
post 📖	CompOp	9 math math: instEssSurjCompPostOfFull, post_obj_right, instFaithfulCompPost, post_map_left, isEquivalence_post, post_obj_left, instFullCompPostOfFaithful, post_map_right, post_obj_hom
postIso 📖	CompOp	—
preLeft 📖	CompOp	13 math math: instFaithfulCompPreLeft, preLeft_obj_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, instFullCompPreLeft, isEquivalence_preLeft, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, instEssSurjCompPreLeft, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_right, preLeft_map_left, preLeft_obj_left, preLeft_map_right, preLeft_obj_hom, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_right
preLeftIso 📖	CompOp	—
preRight 📖	CompOp	9 math math: preRight_obj_left, preRight_map_left, preRight_map_right, preRight_obj_right, preRight_obj_hom, instFullCompPreRight, instFaithfulCompPreRight, isEquivalence_preRight, instEssSurjCompPreRight
preRightIso 📖	CompOp	—
right 📖	CompOp	1014 math math: CommRingCat.tensorProd_map_right, CategoryTheory.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.CostructuredArrow.homMk'_id, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst, CategoryTheory.Functor.LeftExtension.coconeAtFunctor_map_hom, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.Over.prodLeftIsoPullback_hom_snd_assoc, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.Limits.HasImage.of_arrow_iso, CategoryTheory.StructuredArrow.projectSubobject_mk, CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.WithTerminal.mkCommaObject_right, CategoryTheory.StructuredArrow.map_map_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.Functor.leibnizPullback_obj_map, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p, CategoryTheory.WithInitial.equivComma_functor_obj_right_obj, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, snd_obj, mapLeftEq_inv_app_right, mapLeftIso_inverse_map_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.Functor.LeftExtension.precomp₂_obj_hom_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_right, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_e, opFunctor_obj, CategoryTheory.Limits.multicospanIndexEnd_fst, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst, CategoryTheory.StructuredArrow.map_obj_right, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_map, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.OverPresheafAux.unitAux_hom, CategoryTheory.CosimplicialObject.id_right_app, CategoryTheory.Over.iteratedSliceBackward_map, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_map_left_left, CategoryTheory.Over.associator_inv_left_snd, CategoryTheory.Functor.mapArrow_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, CategoryTheory.Under.postComp_inv_app_right, CategoryTheory.Bicategory.LeftExtension.w_assoc, map_obj_hom, CategoryTheory.CosimplicialObject.augment_right, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_map_right, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_hom, CategoryTheory.SimplicialObject.comp_right, CategoryTheory.StructuredArrow.homMk'_comp, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.Under.forgetMapInitial_inv_app, CategoryTheory.Arrow.hom_inv_id_right_assoc, CategoryTheory.CostructuredArrow.w_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.MonoOver.isIso_left_iff_subobjectMk_eq, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_id, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_id, mapLeft_map_left, CategoryTheory.SmallObject.πObj_ιIteration_app_right, CategoryTheory.WithInitial.coconeEquiv_functor_obj_pt, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_left_as, CategoryTheory.Under.epi_right_of_epi, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_right_as, CategoryTheory.Limits.IsImage.ofArrowIso_lift, CategoryTheory.StructuredArrow.mapIso_inverse_obj_hom, CategoryTheory.Under.postCongr_inv_app_right, CategoryTheory.Under.mono_right_of_mono, CategoryTheory.Over.whiskerLeft_left, CategoryTheory.CosimplicialObject.Augmented.leftOp_right, CategoryTheory.Limits.image.map_id, CategoryTheory.Bicategory.LeftExtension.ofCompId_right, CategoryTheory.MonoOver.isIso_iff_subobjectMk_eq, CategoryTheory.Functor.RightExtension.postcompose₂_obj_right, CategoryTheory.Functor.LeftExtension.postcomp₁_map_right_app, CategoryTheory.CostructuredArrow.IsUniversal.existsUnique, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.CostructuredArrow.w_prod_fst, CategoryTheory.SimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₃, CategoryTheory.StructuredArrow.map₂_obj_right, CommRingCat.mkUnder_ext_iff, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, mapLeftIso_functor_map_left, CategoryTheory.CostructuredArrow.toOver_obj_right, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd_assoc, CategoryTheory.Bicategory.LeftLift.w_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.isIso_hom_app, CategoryTheory.TwoSquare.EquivalenceJ.inverse_map, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, mapRightEq_hom_app_right, CategoryTheory.CostructuredArrow.eq_mk, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isPullback, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_right, mapRightIso_counitIso_inv_app_right, CategoryTheory.MorphismProperty.Comma.comp_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, CategoryTheory.StructuredArrow.map₂_map_right, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_inv, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_right_as, CommRingCat.toAlgHom_comp, instIsIsoRight, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_hom, CategoryTheory.Limits.image.map_comp, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, CategoryTheory.WithInitial.ofCommaObject_obj, CategoryTheory.Functor.LeftExtension.precomp_map_right, CategoryTheory.WithTerminal.equivComma_inverse_obj_obj, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_right, CategoryTheory.SimplicialObject.Augmented.w₀, CategoryTheory.Functor.RightExtension.coneAt_π_app, mapRightIso_functor_map_left, mapLeftIso_counitIso_inv_app_right, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, map_map_right, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.Limits.Cocone.underPost_ι_app, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, CategoryTheory.Over.braiding_inv_left, CategoryTheory.Functor.RightExtension.postcomp₁_map_right, CategoryTheory.Over.prodLeftIsoPullback_inv_snd, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_right, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_symm_apply, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.SimplicialObject.Augmented.toArrow_map_left, mapRight_obj_hom, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, mapRightIso_inverse_map_right, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, CategoryTheory.Limits.coker_map, CategoryTheory.StructuredArrow.eta_hom_right, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₃₄, CategoryTheory.SmallObject.functorialFactorizationData_i_app, CategoryTheory.CostructuredArrow.prodFunctor_map, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_right, CategoryTheory.Abelian.coim_map, CategoryTheory.CostructuredArrow.map₂_obj_right, CategoryTheory.StructuredArrow.prodInverse_map, CategoryTheory.MorphismProperty.under_iff, CategoryTheory.StructuredArrow.eta_inv_right, CategoryTheory.Over.leftUnitor_hom_left, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp, CategoryTheory.WithTerminal.equivComma_functor_obj_right, CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback_app, CategoryTheory.Over.tensorObj_ext_iff, mapRightIso_unitIso_inv_app_right, CategoryTheory.RetractArrow.i_w, CategoryTheory.CostructuredArrow.toOver_map_right, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_right, CategoryTheory.Functor.LeftExtension.precomp_obj_hom_app, CategoryTheory.WithTerminal.ofCommaObject_obj, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, mapSnd_inv_app, CategoryTheory.StructuredArrow.eq_mk, fromProd_obj_right, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_right_as, mapRightIso_functor_obj_right, CategoryTheory.Limits.multicospanIndexEnd_right, CategoryTheory.NatTrans.instIsClosedUnderLimitsOfShapeOverFunctorEquifiberedHomDiscretePUnitOfHasCoproductsOfShapeHom, opFunctor_map, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext_iff, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t_assoc, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_fiber, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₂, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, CategoryTheory.CostructuredArrow.homMk'_mk_id, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, CategoryTheory.WithInitial.equivComma_functor_obj_right_map, CategoryTheory.Functor.RightExtension.precomp_map_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd_assoc, CategoryTheory.Limits.multicospanShapeEnd_snd, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.isLeftKanExtension, CategoryTheory.StructuredArrow.id_right, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eq, CategoryTheory.Under.pushout_map, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_right_as, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_left_as, rightIso_hom, CategoryTheory.CosimplicialObject.Augmented.const_obj_right, CategoryTheory.Limits.image.map_ι, CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, CategoryTheory.CostructuredArrow.homMk'_right, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₃, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv_assoc, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CategoryTheory.StructuredArrow.preEquivalence_unitIso, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_right, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_left, CategoryTheory.Over.whiskerRight_left_fst, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, comp_right, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂_obj_right_map, CategoryTheory.Arrow.square_from_iso_invert, CategoryTheory.MonoOver.pullback_obj_arrow, CategoryTheory.Limits.multispanShapeCoend_snd, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_right_hom, CategoryTheory.WithTerminal.commaFromOver_obj_right, CategoryTheory.Over.prodLeftIsoPullback_inv_fst, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp_assoc, CategoryTheory.Abelian.im_map, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_right, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.Under.postAdjunctionRight_unit_app_right, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp_assoc, CategoryTheory.Bicategory.LeftExtension.whiskering_map, CategoryTheory.Over.opEquivOpUnder_inverse_obj, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.StructuredArrow.prodFunctor_map, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_right, CategoryTheory.Over.prodLeftIsoPullback_inv_snd_assoc, mapLeftIso_inverse_obj_right, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, CategoryTheory.Pseudofunctor.presheafHom_obj, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_obj, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.Over.iteratedSliceBackward_forget, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, mapLeftId_hom_app_right, post_obj_right, preRight_map_left, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_obj_right, CategoryTheory.Under.map_obj_right, preLeft_obj_right, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_left, CategoryTheory.StructuredArrow.mapIso_inverse_obj_right, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_base, CategoryTheory.WithInitial.mkCommaObject_right_obj, CategoryTheory.Under.post_obj, mapRightComp_inv_app_right, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_hom, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.CostructuredArrow.map_obj_right, CategoryTheory.CosimplicialObject.comp_right_app, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₃, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst, CategoryTheory.Over.prodLeftIsoPullback_hom_snd, CategoryTheory.CostructuredArrow.mkPrecomp_right, CategoryTheory.StructuredArrow.IsUniversal.existsUnique, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, CategoryTheory.IsGrothendieckAbelian.exists_isIso_of_functor_from_monoOver, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.Over.whiskerRight_left_snd_assoc, CategoryTheory.Arrow.w_mk_right, CategoryTheory.Under.eqToHom_right, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.ChosenPullbacksAlong.Over.snd_eq_snd', CategoryTheory.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₃, CategoryTheory.Limits.ker.ι_app, CategoryTheory.Over.associator_hom_left_fst, CategoryTheory.SmallObject.functor_map, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, SSet.Augmented.stdSimplex_map_right, CategoryTheory.StructuredArrow.preEquivalence_inverse, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₂, CategoryTheory.StructuredArrow.preEquivalence_functor, CategoryTheory.CostructuredArrow.toStructuredArrow'_obj, CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk', CategoryTheory.StructuredArrow.homMk'_mk_comp, CategoryTheory.NatTrans.instIsClosedUnderColimitsOfShapeUnderFunctorCoequifiberedHomDiscretePUnitOfHasProductsOfShapeHom, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_inv_right_app, CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc, CategoryTheory.SmallObject.objMap_comp_assoc, CategoryTheory.Limits.ker_obj, CategoryTheory.SmallObject.functorialFactorizationData_Z_obj, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, CategoryTheory.SimplicialObject.Augmented.const_obj_right, CategoryTheory.MonoOver.image_map, CategoryTheory.Under.mapPushoutAdj_unit_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_obj, CategoryTheory.Limits.instHasImageHomMk, CategoryTheory.Limits.ImageMap.factor_map_assoc, CategoryTheory.Over.opEquivOpUnder_inverse_map, CategoryTheory.Under.post_map, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_right, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, AlgebraicGeometry.opensDiagram_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left, map_obj_right, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.Square.toArrowArrowFunctor_map_right_right, coneOfPreserves_pt_right, CategoryTheory.StructuredArrow.eqToHom_right, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_map, CategoryTheory.Functor.leibnizPushout_obj_map, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_id, CategoryTheory.Functor.essImage_underPost, CategoryTheory.Over.tensorHom_left_snd_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, CategoryTheory.SmallObject.ε_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂_map_right_app, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.Limits.image.map_homMk'_ι, CategoryTheory.Under.map_obj_hom, CategoryTheory.CommaMorphism.w_assoc, CommRingCat.Under.tensorProdEqualizer_ι, CategoryTheory.CostructuredArrow.map_map_right, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_right_as, AlgebraicGeometry.opensDiagramι_app, CategoryTheory.Arrow.w, CategoryTheory.StructuredArrow.homMk'_left, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd', AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_zero, CategoryTheory.Functor.essImage.of_underPost, equivProd_unitIso_hom_app_right, CategoryTheory.SmallObject.iterationObjRightIso_hom, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_right_as, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, CategoryTheory.SmallObject.objMap_id, preRight_map_right, CategoryTheory.Limits.coker_obj, CategoryTheory.Over.μ_pullback_left_fst_snd', CategoryTheory.Square.toArrowArrowFunctor'_map_right_left, map_map_left, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.CostructuredArrow.w_prod_snd, mapRightIso_functor_obj_hom, CategoryTheory.Limits.imageSubobjectIso_comp_image_map, CommRingCat.toAlgHom_id, toIdPUnitEquiv_unitIso_inv_app_right, post_map_left, CategoryTheory.StructuredArrow.mono_iff_mono_right, CategoryTheory.CommaMorphism.w, CategoryTheory.Limits.multispanIndexCoend_snd, CategoryTheory.RetractArrow.r_w, CategoryTheory.Functor.LeftExtension.postcompose₂_obj_hom_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁_assoc, CategoryTheory.Under.mono_iff_mono_right, CategoryTheory.WithInitial.liftFromUnder_obj_obj, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_map_right_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_right, CategoryTheory.MorphismProperty.instHasPullbackHomDiscretePUnitOfHasPullbacksAlong, CategoryTheory.ChosenPullbacksAlong.iso_pullback_obj, CategoryTheory.SimplicialObject.augment_right, CategoryTheory.SimplicialObject.augment_hom_zero, CategoryTheory.SmallObject.ιObj_naturality, CategoryTheory.Under.postEquiv_counitIso, coconeOfPreserves_pt_right, CategoryTheory.CosimplicialObject.Augmented.drop_obj, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, CommRingCat.mkUnder_right, CategoryTheory.Under.postComp_hom_app_right, preRight_obj_right, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, CategoryTheory.SimplicialObject.Augmented.rightOp_right_map, SSet.Truncated.rightExtensionInclusion_right_as, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Arrow.comp_right_assoc, mapLeftIso_unitIso_inv_app_right, CategoryTheory.WithTerminal.ofCommaMorphism_app, CategoryTheory.Functor.LeftExtension.postcomp₁_obj_hom_app, CategoryTheory.CategoryOfElements.fromStructuredArrow_obj, CategoryTheory.Arrow.inv_hom_id_right, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_left_as, CategoryTheory.Arrow.w_mk_right_assoc, CategoryTheory.Square.toArrowArrowFunctor_obj_right_right, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.CostructuredArrow.mk_right, CategoryTheory.ComposableArrows.arrowEquiv_symm_apply, CategoryTheory.Over.map_obj_hom, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Over.associator_hom_left_snd_fst, CategoryTheory.CostructuredArrow.toOver_map_left, CategoryTheory.Arrow.mk_right, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', CategoryTheory.MorphismProperty.Comma.comp_right_assoc, CategoryTheory.Functor.mapArrow_map_left, CategoryTheory.MorphismProperty.over_iso_iff, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, CategoryTheory.underToAlgebra_obj_A, CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp_obj, AlgEquiv.toUnder_inv_right_apply, eqToHom_right, CategoryTheory.Functor.LeftExtension.postcompose₂_obj_right_obj, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_hom, CategoryTheory.StructuredArrow.toCostructuredArrow_map, CategoryTheory.Limits.ImageMap.factor_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd, CategoryTheory.WithInitial.equivComma_inverse_map_app, left_hom_inv_right, CategoryTheory.Arrow.isIso_hom_iff_isIso_of_isIso, unopFunctor_obj, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_obj, mapLeftComp_inv_app_right, CategoryTheory.CostructuredArrow.map₂_map_right, toIdPUnitEquiv_unitIso_hom_app_right, CategoryTheory.RetractArrow.retract_right_assoc, CommRingCat.toAlgHom_apply, CategoryTheory.StructuredArrow.toUnder_map_right, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_left, CategoryTheory.StructuredArrow.IsUniversal.hom_desc, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_right_as, mapRightIso_inverse_obj_right, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.Limits.Cocone.fromStructuredArrow_obj_pt, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd_assoc, CategoryTheory.CostructuredArrow.pre_obj_right, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst_assoc, CategoryTheory.TwoSquare.isIso_lanBaseChange_app_iff, CategoryTheory.Over.pullback_map_left, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, CategoryTheory.Under.forgetMapInitial_hom_app, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst, mapRightIso_functor_map_right, limitAuxiliaryCone_π_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.Pseudofunctor.presheafHom_map, CategoryTheory.MorphismProperty.costructuredArrow_iso_iff, SSet.Augmented.stdSimplex_obj_right, CategoryTheory.Limits.multispanIndexCoend_left, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.Over.sections_obj, CategoryTheory.Functor.RightExtension.precomp_obj_right, CategoryTheory.MorphismProperty.Comma.ext_iff, AlgebraicGeometry.opensDiagram_obj, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_right_hom, CategoryTheory.CostructuredArrow.toStructuredArrow'_map, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_right, CategoryTheory.Abelian.coim_obj, CategoryTheory.Functor.mapArrow_map_right, CategoryTheory.MorphismProperty.overObj_iff, AlgebraicGeometry.opensCone_π_app, CategoryTheory.Over.tensorHom_left, CategoryTheory.CostructuredArrow.w, CategoryTheory.RetractArrow.retract_right, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_right_as, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, CategoryTheory.StructuredArrow.homMk'_id, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isIso_hom, CategoryTheory.Functor.RightExtension.mk_right_as, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_right, CategoryTheory.WithInitial.mkCommaObject_right_map, inv_right, CategoryTheory.Under.opEquivOpOver_functor_obj, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_left_as, toIdPUnitEquiv_functor_obj, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Over.associator_inv_left_fst_snd, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_hom_right_app, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.WithInitial.commaFromUnder_obj_right, CategoryTheory.WithInitial.equivComma_inverse_obj_map, CategoryTheory.MorphismProperty.Over.w_assoc, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, CategoryTheory.SimplicialObject.Augmented.rightOp_right_obj, CategoryTheory.Functor.RightExtension.postcomp₁_map_left_app, CategoryTheory.SmallObject.πObj_ιIteration_app_right_assoc, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_right, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.MorphismProperty.ofHoms_homFamily, CategoryTheory.Over.associator_hom_left_snd_snd_assoc, commAlgCatEquivUnder_counitIso, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_right_as, CategoryTheory.StructuredArrow.post_map, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp, CategoryTheory.Functor.LeftExtension.postcomp₁_obj_right_map, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π_assoc, CategoryTheory.Under.equivalenceOfIsInitial_unitIso, CategoryTheory.Limits.im_obj, CategoryTheory.SmallObject.πObj_naturality_assoc, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_right_inv, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_right_app, CategoryTheory.Over.μ_pullback_left_fst_fst', CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Over.whiskerRight_left, CategoryTheory.CostructuredArrow.homMk'_left, CategoryTheory.StructuredArrow.homMk'_right, CategoryTheory.Abelian.coimageImageComparisonFunctor_obj, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₃, CategoryTheory.StructuredArrow.pre_map_left, inv_left_hom_right, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Limits.imageSubobjectMap_arrow, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_right_as, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.CostructuredArrow.prodFunctor_obj, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isIso_hom_app, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, commAlgCatEquivUnder_inverse_obj_carrier, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_F, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.Bicategory.LeftLift.ofIdComp_right, CategoryTheory.Arrow.id_right, CategoryTheory.StructuredArrow.map_map_left, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.Functor.LeftExtension.precomp_obj_right, CategoryTheory.Over.w, CategoryTheory.StructuredArrow.mapIso_functor_obj_right, mapLeftEq_hom_app_right, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp_assoc, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_m, CategoryTheory.StructuredArrow.prodFunctor_obj, AlgHom.toUnder_right, mapLeft_obj_right, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left_inv, CategoryTheory.CosimplicialObject.augment_hom_zero, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst_assoc, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_right, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁, Alexandrov.lowerCone_π_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtension.isIso_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_right, CategoryTheory.Arrow.mk_eq, CategoryTheory.MorphismProperty.Under.w, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_hom, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.StructuredArrow.mono_right_of_mono, AlgEquiv.toUnder_hom_right_apply, AlgebraicGeometry.Scheme.kerFunctor_map, CategoryTheory.MorphismProperty.Comma.prop, CategoryTheory.CostructuredArrow.homMk'_mk_comp, CategoryTheory.Over.associator_inv_left_fst_fst, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_map_right_right, mapLeftIso_inverse_obj_hom, CategoryTheory.CostructuredArrow.right_eq_id, CategoryTheory.StructuredArrow.comp_right, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_right_as, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.Over.snd_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.Limits.ImageMap.map_ι, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst_assoc, CategoryTheory.Functor.leibnizPushout_obj_obj, CategoryTheory.Over.over_right, mapRightIso_counitIso_hom_app_right, CategoryTheory.Arrow.isIso_hom_iff_isIso_hom_of_isIso, commAlgCatEquivUnder_unitIso, CategoryTheory.Over.tensorHom_left_fst, equivProd_inverse_obj_right, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₄, CategoryTheory.Over.whiskerRight_left_snd, CategoryTheory.MorphismProperty.structuredArrowObj_iff, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₄, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, CategoryTheory.MorphismProperty.mem_toSet_iff, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isRightKanExtension, opFunctorCompFst_hom_app, CategoryTheory.underToAlgebra_obj_a, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, CategoryTheory.CommSq.of_arrow, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst, CategoryTheory.Under.mk_right, opFunctorCompFst_inv_app, CategoryTheory.CostructuredArrow.toStructuredArrow_obj, unopFunctor_map, CategoryTheory.Arrow.isIso_of_isIso, CategoryTheory.Arrow.rightFunc_obj, CategoryTheory.Over.tensorHom_left_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd_assoc, CategoryTheory.Under.postMap_app, CategoryTheory.Over.prodLeftIsoPullback_inv_fst_assoc, CategoryTheory.Abelian.im_obj, CategoryTheory.RetractArrow.instIsSplitEpiRightRArrow, CategoryTheory.Functor.toUnder_obj_right, CategoryTheory.Under.hom_right_inv_right, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_hom_left, CategoryTheory.Arrow.iso_w, mapLeftIso_unitIso_hom_app_right, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_obj, CategoryTheory.Limits.Cocone.fromStructuredArrow_map_hom, CategoryTheory.Functor.RightExtension.postcomp₁_obj_right, CategoryTheory.Over.whiskerLeft_left_fst, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_counit_app, CategoryTheory.SmallObject.πFunctorObj_eq, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, CategoryTheory.MonoOver.inf_map_app, mapRightId_hom_app_right, CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp_map, CategoryTheory.SmallObject.objMap_comp, CategoryTheory.Functor.LeftExtension.postcompose₂_map_left, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Functor.LeftExtension.postcomp₁_obj_right_obj, CategoryTheory.Arrow.inv_left_hom_right, toPUnitIdEquiv_inverse_obj_right_as, CategoryTheory.Functor.RightExtension.postcompose₂_obj_hom_app, CategoryTheory.Functor.RightExtension.precomp_obj_hom_app, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_right, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, CategoryTheory.algebraEquivUnder_counitIso, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, CategoryTheory.Functor.RightExtension.precomp_map_right, CategoryTheory.ChosenPullbacksAlong.Over.lift_left, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₂, CategoryTheory.Under.postCongr_hom_app_right, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, CategoryTheory.Abelian.coimageImageComparisonFunctor_map, mapLeftIso_counitIso_hom_app_right, CategoryTheory.CostructuredArrow.map_map_left, CategoryTheory.CostructuredArrow.map₂_map_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε_assoc, CategoryTheory.WithInitial.equivComma_inverse_obj_obj, CategoryTheory.Over.isPullback_of_binaryFan_isLimit, CategoryTheory.MorphismProperty.commaObj_iff, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_right, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_hom_right, CategoryTheory.Over.whiskerLeft_left_fst_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_left, CategoryTheory.Under.pushout_obj, CategoryTheory.MorphismProperty.Over.w, CategoryTheory.Square.toArrowArrowFunctor_obj_right_hom, CategoryTheory.Square.toArrowArrowFunctor_obj_right_left, CategoryTheory.Functor.RightExtension.postcompose₂_map_left_app, CategoryTheory.RetractArrow.op_r_left, CategoryTheory.StructuredArrow.mk_right, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_right_as, CategoryTheory.StructuredArrow.preEquivalenceInverse_map_right_right, mapLeft_map_right, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, CategoryTheory.CostructuredArrow.IsUniversal.fac, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₄, unopFunctorCompFst_inv_app, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_right_inv, CategoryTheory.MonoOver.subobjectMk_le_mk_of_hom, equivProd_unitIso_inv_app_right, CategoryTheory.Over.whiskerLeft_left_snd_assoc, CategoryTheory.SmallObject.SuccStruct.toSuccArrow_right, CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, CategoryTheory.Square.toArrowArrowFunctor_obj_left_right, CategoryTheory.TwoSquare.EquivalenceJ.functor_obj, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.StructuredArrow.w, CategoryTheory.Functor.RightExtension.postcompose₂_map_right, commAlgCatEquivUnder_inverse_map, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left, CategoryTheory.Under.forget_obj, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_id, CategoryTheory.Functor.LeftExtension.precomp_map_left, mapLeftIso_functor_obj_hom, CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_I, CategoryTheory.MorphismProperty.comma_iso_iff, CategoryTheory.StructuredArrow.pre_map_right, CategoryTheory.StructuredArrow.w_prod_fst_assoc, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₂₄, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.Functor.LeftExtension.precomp₂_obj_right, CategoryTheory.SmallObject.functorMap_π, CategoryTheory.StructuredArrow.mapIso_functor_obj_hom, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_left, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π, Alexandrov.projSup_obj, CategoryTheory.underToAlgebra_map_f, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, CategoryTheory.Functor.LeftExtension.coconeAt_pt, CategoryTheory.SimplicialObject.Augmented.point_obj, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_isImage, CategoryTheory.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_obj, mapRight_map_left, CategoryTheory.SimplicialObject.Augmented.rightOp_left, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_right_app, mapRightId_inv_app_right, CategoryTheory.Functor.LeftExtension.postcomp₁_map_left, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₂, CategoryTheory.CechNerveTerminalFrom.hasWidePullback, CategoryTheory.MorphismProperty.Over.pullback_map_left, mapRightComp_hom_app_right, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₁, CategoryTheory.RetractArrow.op_i_left, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, CategoryTheory.Limits.HasImageMaps.has_image_map, CategoryTheory.Over.sections_map, mapRightIso_inverse_obj_hom, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_right, CategoryTheory.Functor.mapArrowFunctor_map_app_right, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.Over.μ_pullback_left_snd, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_right, CategoryTheory.Under.mapPushoutAdj_counit_app, CategoryTheory.Over.iteratedSliceBackward_obj, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.CostructuredArrow.homMk'_comp, CategoryTheory.TwoSquare.structuredArrowDownwards_map, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_hom_right, CategoryTheory.Localization.structuredArrowEquiv_symm_apply, CategoryTheory.Functor.LeftExtension.mk_right, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_hom, preLeft_map_left, CategoryTheory.Arrow.epi_right, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_left, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_hom, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_right, CategoryTheory.TwoSquare.structuredArrowDownwards_obj, CommRingCat.Under.equalizerFork_ι, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_right, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, id_right, CategoryTheory.Under.postAdjunctionLeft_counit_app, CategoryTheory.Under.inv_right_hom_right, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Over.braiding_hom_left, CategoryTheory.MonoOver.instMonoHomDiscretePUnitObjOverForget, CategoryTheory.RetractArrow.instIsSplitMonoRightIArrow, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd, CategoryTheory.WithInitial.liftFromUnder_map_app, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, CategoryTheory.StructuredArrow.projectSubobject_factors, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_right_as, CategoryTheory.FunctorToTypes.mem_fromOverSubfunctor_iff, CategoryTheory.SimplicialObject.id_right, CategoryTheory.Over.μ_pullback_left_fst_fst, CategoryTheory.Under.hom_right_inv_right_assoc, mapSnd_hom_app, CategoryTheory.Over.iteratedSliceForward_map, CategoryTheory.MorphismProperty.underObj_iff, CategoryTheory.CostructuredArrow.pre_map_right, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₁, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.MorphismProperty.Under.w_assoc, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.StructuredArrow.preEquivalenceFunctor_map_right, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_hom_right, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_left, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.Limits.image_map_comp_imageSubobjectIso_inv, CategoryTheory.Under.opEquivOpOver_inverse_obj, Types.monoOverEquivalenceSet_unitIso, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π, CategoryTheory.TwoSquare.EquivalenceJ.functor_map, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_obj, CategoryTheory.Square.toArrowArrowFunctor'_map_right_right, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, CategoryTheory.RetractArrow.unop_i_left, CategoryTheory.MorphismProperty.instHasPullbackSndHomDiscretePUnitOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_map, CategoryTheory.cosimplicialToSimplicialAugmented_map, AlgebraicGeometry.Scheme.kerFunctor_obj, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, CategoryTheory.SmallObject.functor_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, mapRightEq_inv_app_right, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.Over.whiskerRight_left_fst_assoc, post_map_right, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.CostructuredArrow.mapIso_functor_obj_right, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.Over.tensorHom_left_snd, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Bicategory.LeftExtension.whiskerHom_right, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.StructuredArrow.toUnder_map_left, CategoryTheory.StructuredArrow.w_prod_snd_assoc, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_hom_left, CategoryTheory.StructuredArrow.prodInverse_obj, CategoryTheory.MorphismProperty.Comma.eqToHom_right, CategoryTheory.CostructuredArrow.preEquivalence.functor_map_left, CategoryTheory.StructuredArrow.preEquivalence_counitIso, CategoryTheory.Functor.RightExtension.postcomp₁_obj_hom_app, CategoryTheory.SmallObject.ιObj_naturality_assoc, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₂, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.Limits.ImageMap.map_ι_assoc, CategoryTheory.Arrow.inv_right, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_right_as, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_left_as, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, CategoryTheory.Arrow.left_hom_inv_right, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_inv_right, CategoryTheory.Square.toArrowArrowFunctor_map_right_left, CategoryTheory.Arrow.hom_inv_id_right, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_right, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_right_as, CategoryTheory.MorphismProperty.Comma.Hom.prop_hom_right, CategoryTheory.Arrow.inv_hom_id_right_assoc, TopologicalSpace.Opens.overEquivalence_inverse_obj_right_as, CategoryTheory.StructuredArrow.proj_obj, CategoryTheory.Functor.LeftExtension.coconeAt_ι_app, equivProd_functor_map, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_left_as, CategoryTheory.Over.lift_left, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.TwoSquare.EquivalenceJ.inverse_obj, mapLeftIso_inverse_map_left, CategoryTheory.Arrow.w_assoc, CategoryTheory.StructuredArrow.map_obj_hom, CategoryTheory.CostructuredArrow.preEquivalence.inverse_map_left_left, CategoryTheory.SmallObject.functorialFactorizationData_p_app, CategoryTheory.Over.opEquivOpUnder_functor_map, mapRight_obj_right, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_right, CategoryTheory.Limits.multispanIndexCoend_fst, mapLeftIso_functor_obj_right, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, mapLeft_obj_hom, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CategoryTheory.CostructuredArrow.pre_map_left, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_hom, CategoryTheory.Under.inv_right_hom_right_assoc, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_obj, CategoryTheory.ChosenPullbacksAlong.Over.fst_eq_fst', CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.ObjectProperty.LimitOfShape.toStructuredArrow_map, CategoryTheory.Under.opEquivOpOver_functor_map, CategoryTheory.Under.postEquiv_unitIso, CategoryTheory.CostructuredArrow.projectQuotient_factors, CategoryTheory.Over.fst_left, CategoryTheory.Over.prodLeftIsoPullback_hom_fst, CategoryTheory.Over.associator_hom_left_fst_assoc, CategoryTheory.SmallObject.preservesColimit, CategoryTheory.Over.isMonHom_pullbackFst_id_right, CategoryTheory.Over.forgetAdjStar_unit_app_left, preLeft_map_right, CategoryTheory.Functor.leibnizPullback_map_app, CategoryTheory.StructuredArrow.toCostructuredArrow'_map, CategoryTheory.Over.tensorObj_left, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_right_as, CategoryTheory.RetractArrow.unop_r_left, CategoryTheory.StructuredArrow.post_obj, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst, CategoryTheory.StructuredArrow.toCostructuredArrow'_obj, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp, CategoryTheory.Abelian.app_hom, CategoryTheory.SmallObject.hasColimitsOfShape_discrete, post_obj_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd', CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.Bicategory.LeftExtension.w, CategoryTheory.SmallObject.πObj_naturality, CategoryTheory.Under.id_right, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_hom, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_inv_right, unopFunctorCompFst_hom_app, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom_assoc, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, CategoryTheory.StructuredArrow.IsUniversal.fac_assoc, CategoryTheory.Arrow.equivSigma_apply_snd_fst, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.WithInitial.ofCommaMorphism_app, CategoryTheory.Limits.Cocone.equivStructuredArrow_counitIso, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_base, CategoryTheory.SmallObject.instIsIsoRightAppArrowιIteration, toIdPUnitEquiv_inverse_obj_right, colimitAuxiliaryCocone_ι_app, CategoryTheory.Arrow.comp_right, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_left, CategoryTheory.Under.postAdjunctionLeft_unit_app, CategoryTheory.StructuredArrow.IsUniversal.fac, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₂₄, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, ext_iff, CategoryTheory.StructuredArrow.toUnder_obj_right, CategoryTheory.Over.associator_hom_left_snd_snd, CategoryTheory.Over.associator_inv_left_snd_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.MorphismProperty.arrow_iso_iff, CategoryTheory.Functor.leibnizPullback_obj_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, mapRightIso_inverse_map_left, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.Under.w_assoc, CategoryTheory.Limits.image.factor_map, mapLeftId_inv_app_right, CategoryTheory.StructuredArrow.w_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_hom, CategoryTheory.StructuredArrow.map₂_obj_hom, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.Under.opEquivOpOver_inverse_map, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, CategoryTheory.Over.iteratedSliceForward_obj, CategoryTheory.MorphismProperty.Comma.Hom.comp_right, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_hom, rightIso_inv, mapLeftComp_hom_app_right, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.Over.whiskerLeft_left_snd, CategoryTheory.Functor.leibnizPushout_map_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_obj, CategoryTheory.Over.w_assoc, mapRight_map_right, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.StructuredArrow.homMk'_mk_id, CategoryTheory.CostructuredArrow.IsUniversal.fac_assoc, Alexandrov.projSup_map, CategoryTheory.Abelian.coimIsoIm_hom_app, CategoryTheory.Limits.diagonal_pullback_fst, CategoryTheory.Under.w, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst_assoc, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, CategoryTheory.MonoOver.mono_obj_hom, CategoryTheory.Sieve.overEquiv_iff, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd, mapLeftIso_functor_map_right, CategoryTheory.Over.opEquivOpUnder_functor_obj, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CommRingCat.Under.equalizer_comp, equivProd_functor_obj, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_right_as, CategoryTheory.Over.tensorObj_hom, CategoryTheory.StructuredArrow.toCostructuredArrow_obj, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_hom, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_hom, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_right, CategoryTheory.Arrow.iso_w', CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_hom, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, mapRightIso_unitIso_hom_app_right, CategoryTheory.Limits.ker_map, CategoryTheory.Arrow.isIso_right, CategoryTheory.Under.comp_right, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₃₄, CategoryTheory.MorphismProperty.costructuredArrowObj_iff, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Abelian.coimIsoIm_inv_app, CategoryTheory.StructuredArrow.pre_obj_right, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.MorphismProperty.Comma.id_right, CategoryTheory.Arrow.equivSigma_symm_apply_right, CategoryTheory.Bicategory.LeftLift.w, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_obj_right, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₄, CategoryTheory.Functor.structuredArrowMapCone_π_app, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Localization.structuredArrowEquiv_apply
rightIso 📖	CompOp	2 math math: rightIso_hom, rightIso_inv
snd 📖	CompOp	31 math math: snd_obj, coneOfPreserves_π_app_right, limitAuxiliaryCone_pt, mapSnd_inv_app, equivProd_counitIso_hom_app, natTrans_app, coneOfPreserves_pt_right, colimitAuxiliaryCocone_pt, coconeOfPreserves_pt_right, preservesColimitsOfShape_snd, snd_map, equivProd_counitIso_inv_app, coconeOfPreserves_ι_app_right, limitAuxiliaryCone_π_app, unopFunctorCompSnd_inv_app, coconeOfPreserves_ι_app_left, opFunctorCompSnd_hom_app, opFunctorCompFst_hom_app, opFunctorCompFst_inv_app, initial_snd, coneOfPreserves_pt_hom, unopFunctorCompFst_inv_app, final_snd, opFunctorCompSnd_inv_app, mapSnd_hom_app, unopFunctorCompSnd_hom_app, toIdPUnitEquiv_functor_iso, unopFunctorCompFst_hom_app, colimitAuxiliaryCocone_ι_app, map_snd, coneOfPreserves_π_app_left
toIdPUnitEquiv 📖	CompOp	10 math math: toIdPUnitEquiv_inverse_map_right, toIdPUnitEquiv_unitIso_inv_app_right, toIdPUnitEquiv_unitIso_hom_app_right, toIdPUnitEquiv_functor_map, toIdPUnitEquiv_inverse_obj_left_as, toIdPUnitEquiv_functor_obj, toIdPUnitEquiv_counitIso_hom_app, toIdPUnitEquiv_counitIso_inv_app, toIdPUnitEquiv_functor_iso, toIdPUnitEquiv_inverse_obj_right
toPUnitIdEquiv 📖	CompOp	10 math math: toPUnitIdEquiv_functor_map, toPUnitIdEquiv_counitIso_hom_app, toPUnitIdEquiv_functor_obj, toPUnitIdEquiv_unitIso_inv_app_left, toPUnitIdEquiv_inverse_map_left, toPUnitIdEquiv_functor_iso, toPUnitIdEquiv_unitIso_hom_app_left, toPUnitIdEquiv_inverse_obj_right_as, toPUnitIdEquiv_inverse_obj_left, toPUnitIdEquiv_counitIso_inv_app
unopFunctor 📖	CompOp	9 math math: opEquiv_counitIso, unopFunctor_obj, unopFunctorCompSnd_inv_app, unopFunctor_map, opEquiv_unitIso, unopFunctorCompFst_inv_app, opEquiv_inverse, unopFunctorCompSnd_hom_app, unopFunctorCompFst_hom_app
unopFunctorCompFst 📖	CompOp	2 math math: unopFunctorCompFst_inv_app, unopFunctorCompFst_hom_app
unopFunctorCompSnd 📖	CompOp	2 math math: unopFunctorCompSnd_inv_app, unopFunctorCompSnd_hom_app

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.CategoryStruct.comp CategoryTheory.Comma CategoryTheory.Category.toCategoryStruct CategoryTheory.commaCategory left	—	—
comp_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.CategoryStruct.comp CategoryTheory.Comma CategoryTheory.Category.toCategoryStruct CategoryTheory.commaCategory right	—	—
eqToHom_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.eqToHom CategoryTheory.Comma CategoryTheory.Category.toCategoryStruct CategoryTheory.commaCategory left	—	—
eqToHom_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.eqToHom CategoryTheory.Comma CategoryTheory.Category.toCategoryStruct CategoryTheory.commaCategory right	—	—
equivProd_counitIso_hom_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.prod' CategoryTheory.Functor.comp CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory fromProd CategoryTheory.Functor.prod' fst snd CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.counitIso equivProd CategoryTheory.Prod.mkHom CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.id	—	—
equivProd_counitIso_inv_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.prod' CategoryTheory.Functor.comp CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory fromProd CategoryTheory.Functor.prod' fst snd CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.counitIso equivProd CategoryTheory.Prod.mkHom CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.id	—	—
equivProd_functor_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.prod' CategoryTheory.Equivalence.functor equivProd CategoryTheory.Prod.mkHom CategoryTheory.Category.toCategoryStruct left right CategoryTheory.CommaMorphism.left CategoryTheory.CommaMorphism.right	—	—
equivProd_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.prod' CategoryTheory.Equivalence.functor equivProd left right	—	—
equivProd_inverse_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Discrete.eqToHom CategoryTheory.Functor.obj CategoryTheory.Functor.map CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse equivProd Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct	—	—
equivProd_inverse_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Discrete.eqToHom CategoryTheory.Functor.obj CategoryTheory.Functor.map CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse equivProd Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct	—	—
equivProd_inverse_obj_left 📖	mathematical	—	left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse equivProd	—	—
equivProd_inverse_obj_right 📖	mathematical	—	right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse equivProd	—	—
equivProd_unitIso_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.unitIso CategoryTheory.prod' equivProd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	—
equivProd_unitIso_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.unitIso CategoryTheory.prod' equivProd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	—
equivProd_unitIso_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.unitIso CategoryTheory.prod' equivProd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	—
equivProd_unitIso_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.unitIso CategoryTheory.prod' equivProd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	—
essSurj_map 📖	mathematical	—	CategoryTheory.Functor.EssSurj CategoryTheory.Comma CategoryTheory.commaCategory map	—	CategoryTheory.NatIso.isIso_app_of_isIso CategoryTheory.Functor.preimage.congr_simp CategoryTheory.NatIso.isIso_inv_app CategoryTheory.Functor.map_preimage CategoryTheory.Category.assoc CategoryTheory.IsIso.inv_hom_id CategoryTheory.Category.comp_id CategoryTheory.IsIso.hom_inv_id_assoc CategoryTheory.Functor.map_comp CategoryTheory.Iso.inv_hom_id CategoryTheory.Functor.map_id
faithful_map 📖	mathematical	—	CategoryTheory.Functor.Faithful CategoryTheory.Comma CategoryTheory.commaCategory map	—	hom_ext CategoryTheory.Functor.map_injective
fromProd_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Discrete.eqToHom CategoryTheory.Functor.obj CategoryTheory.Functor.map CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory fromProd Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct	—	—
fromProd_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Discrete.eqToHom CategoryTheory.Functor.obj CategoryTheory.Functor.map CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory fromProd Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct	—	—
fromProd_obj_hom 📖	mathematical	—	hom CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory fromProd CategoryTheory.Discrete.eqToHom	—	—
fromProd_obj_left 📖	mathematical	—	left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory fromProd	—	—
fromProd_obj_right 📖	mathematical	—	right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory fromProd	—	—
fst_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory fst CategoryTheory.CommaMorphism.left	—	—
fst_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory fst left	—	—
full_map 📖	mathematical	—	CategoryTheory.Functor.Full CategoryTheory.Comma CategoryTheory.commaCategory map	—	CategoryTheory.Functor.map_injective CategoryTheory.cancel_mono CategoryTheory.IsIso.mono_of_iso CategoryTheory.NatIso.isIso_app_of_isIso CategoryTheory.cancel_epi CategoryTheory.IsIso.epi_of_iso CategoryTheory.Functor.map_comp CategoryTheory.Category.assoc CategoryTheory.NatTrans.naturality_assoc CategoryTheory.NatTrans.naturality CategoryTheory.Functor.map_preimage CategoryTheory.CommaMorphism.w hom_ext
hom_ext 📖	—	CategoryTheory.CommaMorphism.left CategoryTheory.CommaMorphism.right	—	—	CategoryTheory.CommaMorphism.ext
hom_ext_iff 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.CommaMorphism.right	—	hom_ext
id_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.CategoryStruct.id CategoryTheory.Comma CategoryTheory.Category.toCategoryStruct CategoryTheory.commaCategory left	—	—
id_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.CategoryStruct.id CategoryTheory.Comma CategoryTheory.Category.toCategoryStruct CategoryTheory.commaCategory right	—	—
instEssSurjCompPostOfFull 📖	mathematical	—	CategoryTheory.Functor.EssSurj CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory post	—	CategoryTheory.Functor.essSurj_of_iso essSurj_map CategoryTheory.Functor.instEssSurjId CategoryTheory.Iso.isIso_hom CategoryTheory.Iso.isIso_inv
instEssSurjCompPreLeft 📖	mathematical	—	CategoryTheory.Functor.EssSurj CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preLeft	—	CategoryTheory.Functor.essSurj_of_iso essSurj_map CategoryTheory.Functor.instEssSurjId CategoryTheory.Functor.Full.id CategoryTheory.Iso.isIso_inv CategoryTheory.IsIso.comp_isIso CategoryTheory.Iso.isIso_hom
instEssSurjCompPreRight 📖	mathematical	—	CategoryTheory.Functor.EssSurj CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preRight	—	CategoryTheory.Functor.essSurj_of_iso essSurj_map CategoryTheory.Functor.instEssSurjId CategoryTheory.Functor.Full.id CategoryTheory.IsIso.comp_isIso CategoryTheory.Iso.isIso_hom CategoryTheory.Iso.isIso_inv
instFaithfulCompPost 📖	mathematical	—	CategoryTheory.Functor.Faithful CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp post	—	CategoryTheory.Functor.Faithful.of_iso faithful_map CategoryTheory.Functor.Faithful.id
instFaithfulCompPreLeft 📖	mathematical	—	CategoryTheory.Functor.Faithful CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preLeft	—	CategoryTheory.Functor.Faithful.of_iso faithful_map CategoryTheory.Functor.Faithful.id
instFaithfulCompPreRight 📖	mathematical	—	CategoryTheory.Functor.Faithful CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preRight	—	CategoryTheory.Functor.Faithful.of_iso faithful_map CategoryTheory.Functor.Faithful.id
instFullCompPostOfFaithful 📖	mathematical	—	CategoryTheory.Functor.Full CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp post	—	CategoryTheory.Functor.Full.of_iso full_map CategoryTheory.Functor.Full.id CategoryTheory.Iso.isIso_hom CategoryTheory.Iso.isIso_inv
instFullCompPreLeft 📖	mathematical	—	CategoryTheory.Functor.Full CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preLeft	—	CategoryTheory.Functor.Full.of_iso full_map CategoryTheory.Functor.Faithful.id CategoryTheory.Functor.Full.id CategoryTheory.Iso.isIso_inv CategoryTheory.IsIso.comp_isIso CategoryTheory.Iso.isIso_hom
instFullCompPreRight 📖	mathematical	—	CategoryTheory.Functor.Full CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preRight	—	CategoryTheory.Functor.Full.of_iso full_map CategoryTheory.Functor.Faithful.id CategoryTheory.Functor.Full.id CategoryTheory.IsIso.comp_isIso CategoryTheory.Iso.isIso_hom CategoryTheory.Iso.isIso_inv
instIsIsoLeft 📖	mathematical	—	CategoryTheory.IsIso left CategoryTheory.CommaMorphism.left	—	CategoryTheory.Functor.map_isIso
instIsIsoRight 📖	mathematical	—	CategoryTheory.IsIso right CategoryTheory.CommaMorphism.right	—	CategoryTheory.Functor.map_isIso
inv_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.inv CategoryTheory.Comma CategoryTheory.commaCategory left instIsIsoLeft	—	CategoryTheory.IsIso.eq_inv_of_hom_inv_id instIsIsoLeft comp_left CategoryTheory.IsIso.hom_inv_id id_left
inv_left_hom_right 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj left right CategoryTheory.Functor.map CategoryTheory.inv CategoryTheory.CommaMorphism.left instIsIsoLeft hom CategoryTheory.CommaMorphism.right	—	instIsIsoLeft CategoryTheory.Functor.map_isIso CategoryTheory.Functor.map_inv CategoryTheory.CommaMorphism.w
inv_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.inv CategoryTheory.Comma CategoryTheory.commaCategory right instIsIsoRight	—	CategoryTheory.IsIso.eq_inv_of_hom_inv_id instIsIsoRight comp_right CategoryTheory.IsIso.hom_inv_id id_right
isEquivalenceMap 📖	mathematical	—	CategoryTheory.Functor.IsEquivalence CategoryTheory.Comma CategoryTheory.commaCategory map	—	faithful_map CategoryTheory.Functor.IsEquivalence.faithful full_map CategoryTheory.Functor.IsEquivalence.full essSurj_map CategoryTheory.Functor.IsEquivalence.essSurj
isEquivalence_post 📖	mathematical	—	CategoryTheory.Functor.IsEquivalence CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp post	—	instFaithfulCompPost instFullCompPostOfFaithful CategoryTheory.Functor.IsEquivalence.faithful instEssSurjCompPostOfFull CategoryTheory.Functor.IsEquivalence.full
isEquivalence_preLeft 📖	mathematical	—	CategoryTheory.Functor.IsEquivalence CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preLeft	—	instFaithfulCompPreLeft CategoryTheory.Functor.IsEquivalence.faithful instFullCompPreLeft CategoryTheory.Functor.IsEquivalence.full instEssSurjCompPreLeft CategoryTheory.Functor.IsEquivalence.essSurj
isEquivalence_preRight 📖	mathematical	—	CategoryTheory.Functor.IsEquivalence CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preRight	—	instFaithfulCompPreRight CategoryTheory.Functor.IsEquivalence.faithful instFullCompPreRight CategoryTheory.Functor.IsEquivalence.full instEssSurjCompPreRight CategoryTheory.Functor.IsEquivalence.essSurj
isoMk_hom_left 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj left right CategoryTheory.CategoryStruct.comp CategoryTheory.Functor.map CategoryTheory.Iso.hom hom	CategoryTheory.CommaMorphism.left CategoryTheory.Comma CategoryTheory.commaCategory isoMk	—	—
isoMk_hom_right 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj left right CategoryTheory.CategoryStruct.comp CategoryTheory.Functor.map CategoryTheory.Iso.hom hom	CategoryTheory.CommaMorphism.right CategoryTheory.Comma CategoryTheory.commaCategory isoMk	—	—
isoMk_inv_left 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj left right CategoryTheory.CategoryStruct.comp CategoryTheory.Functor.map CategoryTheory.Iso.hom hom	CategoryTheory.CommaMorphism.left CategoryTheory.Iso.inv CategoryTheory.Comma CategoryTheory.commaCategory isoMk	—	—
isoMk_inv_right 📖	mathematical	Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj left right CategoryTheory.CategoryStruct.comp CategoryTheory.Functor.map CategoryTheory.Iso.hom hom	CategoryTheory.CommaMorphism.right CategoryTheory.Iso.inv CategoryTheory.Comma CategoryTheory.commaCategory isoMk	—	—
leftIso_hom 📖	mathematical	—	CategoryTheory.Iso.hom left leftIso CategoryTheory.CommaMorphism.left CategoryTheory.Comma CategoryTheory.commaCategory	—	—
leftIso_inv 📖	mathematical	—	CategoryTheory.Iso.inv left leftIso CategoryTheory.CommaMorphism.left CategoryTheory.Comma CategoryTheory.commaCategory	—	—
left_hom_inv_right 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj left right CategoryTheory.Functor.map CategoryTheory.CommaMorphism.left hom CategoryTheory.inv CategoryTheory.CommaMorphism.right instIsIsoRight	—	instIsIsoRight CategoryTheory.Functor.map_isIso CategoryTheory.Functor.map_inv CategoryTheory.CommaMorphism.w_assoc CategoryTheory.IsIso.hom_inv_id CategoryTheory.Category.comp_id
mapFst_hom_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp map fst CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category mapFst CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj left	—	—
mapFst_inv_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp fst map CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category mapFst CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj left	—	—
mapLeftComp_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.comp CategoryTheory.NatTrans.app CategoryTheory.Iso.hom mapLeftComp CategoryTheory.CategoryStruct.id left	—	—
mapLeftComp_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.comp CategoryTheory.NatTrans.app CategoryTheory.Iso.hom mapLeftComp CategoryTheory.CategoryStruct.id right	—	—
mapLeftComp_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapLeft CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv mapLeftComp CategoryTheory.CategoryStruct.id left	—	—
mapLeftComp_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapLeft CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv mapLeftComp CategoryTheory.CategoryStruct.id right	—	—
mapLeftEq_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category mapLeftEq CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	—
mapLeftEq_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category mapLeftEq CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	—
mapLeftEq_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category mapLeftEq CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	—
mapLeftEq_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category mapLeftEq CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	—
mapLeftId_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.hom mapLeftId left	—	—
mapLeftId_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.hom mapLeftId right	—	—
mapLeftId_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id mapLeft CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv mapLeftId left	—	—
mapLeftId_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id mapLeft CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv mapLeftId right	—	—
mapLeftIso_counitIso_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapLeft CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Equivalence.counitIso mapLeftIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
mapLeftIso_counitIso_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapLeft CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Equivalence.counitIso mapLeftIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
mapLeftIso_counitIso_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp mapLeft CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.NatTrans.app CategoryTheory.Equivalence.counitIso mapLeftIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
mapLeftIso_counitIso_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp mapLeft CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.NatTrans.app CategoryTheory.Equivalence.counitIso mapLeftIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
mapLeftIso_functor_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapLeftIso	—	—
mapLeftIso_functor_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapLeftIso	—	—
mapLeftIso_functor_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapLeftIso CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct left right CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category	—	—
mapLeftIso_functor_obj_left 📖	mathematical	—	left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapLeftIso	—	—
mapLeftIso_functor_obj_right 📖	mathematical	—	right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapLeftIso	—	—
mapLeftIso_inverse_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapLeftIso	—	—
mapLeftIso_inverse_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapLeftIso	—	—
mapLeftIso_inverse_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapLeftIso CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct left right CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category	—	—
mapLeftIso_inverse_obj_left 📖	mathematical	—	left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapLeftIso	—	—
mapLeftIso_inverse_obj_right 📖	mathematical	—	right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapLeftIso	—	—
mapLeftIso_unitIso_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp mapLeft CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.NatTrans.app CategoryTheory.Equivalence.unitIso mapLeftIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
mapLeftIso_unitIso_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp mapLeft CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.NatTrans.app CategoryTheory.Equivalence.unitIso mapLeftIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
mapLeftIso_unitIso_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapLeft CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Equivalence.unitIso mapLeftIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
mapLeftIso_unitIso_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapLeft CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Equivalence.unitIso mapLeftIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
mapLeft_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.NatTrans.app hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory mapLeft	—	—
mapLeft_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.NatTrans.app hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory mapLeft	—	—
mapLeft_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct left right CategoryTheory.NatTrans.app	—	—
mapLeft_obj_left 📖	mathematical	—	left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft	—	—
mapLeft_obj_right 📖	mathematical	—	right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapLeft	—	—
mapRightComp_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.comp CategoryTheory.NatTrans.app CategoryTheory.Iso.hom mapRightComp CategoryTheory.CategoryStruct.id left	—	—
mapRightComp_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.comp CategoryTheory.NatTrans.app CategoryTheory.Iso.hom mapRightComp CategoryTheory.CategoryStruct.id right	—	—
mapRightComp_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapRight CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv mapRightComp CategoryTheory.CategoryStruct.id left	—	—
mapRightComp_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapRight CategoryTheory.CategoryStruct.comp CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv mapRightComp CategoryTheory.CategoryStruct.id right	—	—
mapRightEq_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category mapRightEq CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	—
mapRightEq_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category mapRightEq CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	—
mapRightEq_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category mapRightEq CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	—
mapRightEq_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category mapRightEq CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	—
mapRightId_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.hom mapRightId left	—	—
mapRightId_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.hom mapRightId right	—	—
mapRightId_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id mapRight CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv mapRightId left	—	—
mapRightId_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id mapRight CategoryTheory.CategoryStruct.id CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.NatTrans.app CategoryTheory.Iso.inv mapRightId right	—	—
mapRightIso_counitIso_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapRight CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Equivalence.counitIso mapRightIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
mapRightIso_counitIso_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapRight CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Equivalence.counitIso mapRightIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
mapRightIso_counitIso_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp mapRight CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.NatTrans.app CategoryTheory.Equivalence.counitIso mapRightIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
mapRightIso_counitIso_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp mapRight CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.hom CategoryTheory.NatTrans.app CategoryTheory.Equivalence.counitIso mapRightIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
mapRightIso_functor_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj hom CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapRightIso	—	—
mapRightIso_functor_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj hom CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapRightIso	—	—
mapRightIso_functor_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapRightIso CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct left right CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category	—	—
mapRightIso_functor_obj_left 📖	mathematical	—	left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapRightIso	—	—
mapRightIso_functor_obj_right 📖	mathematical	—	right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.functor mapRightIso	—	—
mapRightIso_inverse_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj hom CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapRightIso	—	—
mapRightIso_inverse_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj hom CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapRightIso	—	—
mapRightIso_inverse_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapRightIso CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct left right CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category	—	—
mapRightIso_inverse_obj_left 📖	mathematical	—	left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapRightIso	—	—
mapRightIso_inverse_obj_right 📖	mathematical	—	right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse mapRightIso	—	—
mapRightIso_unitIso_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp mapRight CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.NatTrans.app CategoryTheory.Equivalence.unitIso mapRightIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
mapRightIso_unitIso_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp mapRight CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.NatTrans.app CategoryTheory.Equivalence.unitIso mapRightIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
mapRightIso_unitIso_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapRight CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Equivalence.unitIso mapRightIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
mapRightIso_unitIso_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp mapRight CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Iso.inv CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Equivalence.unitIso mapRightIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
mapRight_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj hom CategoryTheory.NatTrans.app CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory mapRight	—	—
mapRight_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj hom CategoryTheory.NatTrans.app CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory mapRight	—	—
mapRight_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct left right CategoryTheory.NatTrans.app	—	—
mapRight_obj_left 📖	mathematical	—	left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight	—	—
mapRight_obj_right 📖	mathematical	—	right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory mapRight	—	—
mapSnd_hom_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp map snd CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category mapSnd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj right	—	—
mapSnd_inv_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp snd map CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category mapSnd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj right	—	—
map_fst 📖	mathematical	—	CategoryTheory.Functor.comp CategoryTheory.Comma CategoryTheory.commaCategory map fst	—	—
map_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.comp CategoryTheory.NatTrans.app CategoryTheory.Functor.map hom CategoryTheory.Comma CategoryTheory.commaCategory map	—	—
map_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj left right CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.comp CategoryTheory.NatTrans.app CategoryTheory.Functor.map hom CategoryTheory.Comma CategoryTheory.commaCategory map	—	—
map_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory map CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct left CategoryTheory.Functor.comp right CategoryTheory.NatTrans.app CategoryTheory.Functor.map	—	—
map_obj_left 📖	mathematical	—	left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory map	—	—
map_obj_right 📖	mathematical	—	right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory map	—	—
map_snd 📖	mathematical	—	CategoryTheory.Functor.comp CategoryTheory.Comma CategoryTheory.commaCategory map snd	—	—
natTrans_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp fst snd natTrans hom	—	—
opEquiv_counitIso 📖	mathematical	—	CategoryTheory.Equivalence.counitIso CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory opEquiv CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.comp CategoryTheory.Functor.leftOp unopFunctor opFunctor CategoryTheory.Functor.id CategoryTheory.Iso.refl CategoryTheory.Functor.obj	—	—
opEquiv_functor 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory opEquiv opFunctor	—	—
opEquiv_inverse 📖	mathematical	—	CategoryTheory.Equivalence.inverse CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory opEquiv CategoryTheory.Functor.leftOp unopFunctor	—	—
opEquiv_unitIso 📖	mathematical	—	CategoryTheory.Equivalence.unitIso CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory opEquiv CategoryTheory.NatIso.ofComponents CategoryTheory.Functor.id CategoryTheory.Functor.comp opFunctor CategoryTheory.Functor.leftOp unopFunctor CategoryTheory.Iso.refl CategoryTheory.Functor.obj	—	—
opFunctorCompFst_hom_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite CategoryTheory.Comma CategoryTheory.Category.opposite CategoryTheory.commaCategory CategoryTheory.Functor.comp CategoryTheory.Functor.op CategoryTheory.Functor.leftOp opFunctor fst CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category snd opFunctorCompFst CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct Opposite.op right Opposite.unop	—	—
opFunctorCompFst_inv_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite CategoryTheory.Comma CategoryTheory.Category.opposite CategoryTheory.commaCategory CategoryTheory.Functor.comp CategoryTheory.Functor.op CategoryTheory.Functor.leftOp opFunctor fst CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category snd opFunctorCompFst CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct Opposite.op right Opposite.unop	—	—
opFunctorCompSnd_hom_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite CategoryTheory.Comma CategoryTheory.Category.opposite CategoryTheory.commaCategory CategoryTheory.Functor.comp CategoryTheory.Functor.op CategoryTheory.Functor.leftOp opFunctor snd CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category fst opFunctorCompSnd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct Opposite.op left Opposite.unop	—	—
opFunctorCompSnd_inv_app 📖	mathematical	—	CategoryTheory.NatTrans.app Opposite CategoryTheory.Comma CategoryTheory.Category.opposite CategoryTheory.commaCategory CategoryTheory.Functor.comp CategoryTheory.Functor.op CategoryTheory.Functor.leftOp opFunctor snd CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category fst opFunctorCompSnd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct Opposite.op left Opposite.unop	—	—
opFunctor_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op opFunctor Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop right left CategoryTheory.Functor.obj hom CategoryTheory.CommaMorphism.right CategoryTheory.CommaMorphism.left	—	—
opFunctor_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op opFunctor Opposite.op right left Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop hom	—	—
post_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.comp left right CategoryTheory.Functor.map CategoryTheory.Functor.obj hom CategoryTheory.Comma CategoryTheory.commaCategory post	—	—
post_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.comp left right CategoryTheory.Functor.map CategoryTheory.Functor.obj hom CategoryTheory.Comma CategoryTheory.commaCategory post	—	—
post_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.comp CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory post CategoryTheory.Functor.map left right	—	—
post_obj_left 📖	mathematical	—	left CategoryTheory.Functor.comp CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory post	—	—
post_obj_right 📖	mathematical	—	right CategoryTheory.Functor.comp CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory post	—	—
preLeft_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Functor.obj left CategoryTheory.Functor.comp right hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory preLeft	—	—
preLeft_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Functor.obj left CategoryTheory.Functor.comp right hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory preLeft	—	—
preLeft_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preLeft	—	—
preLeft_obj_left 📖	mathematical	—	left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preLeft	—	—
preLeft_obj_right 📖	mathematical	—	right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preLeft	—	—
preRight_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left left CategoryTheory.Functor.comp CategoryTheory.Functor.obj right hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory preRight	—	—
preRight_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right left CategoryTheory.Functor.comp CategoryTheory.Functor.obj right hom CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory preRight	—	—
preRight_obj_hom 📖	mathematical	—	hom CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preRight	—	—
preRight_obj_left 📖	mathematical	—	left CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preRight	—	—
preRight_obj_right 📖	mathematical	—	right CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.Functor.comp CategoryTheory.commaCategory preRight	—	—
rightIso_hom 📖	mathematical	—	CategoryTheory.Iso.hom right rightIso CategoryTheory.CommaMorphism.right CategoryTheory.Comma CategoryTheory.commaCategory	—	—
rightIso_inv 📖	mathematical	—	CategoryTheory.Iso.inv right rightIso CategoryTheory.CommaMorphism.right CategoryTheory.Comma CategoryTheory.commaCategory	—	—
snd_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.commaCategory snd CategoryTheory.CommaMorphism.right	—	—
snd_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory snd right	—	—
toIdPUnitEquiv_counitIso_hom_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Functor.comp CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.prod' CategoryTheory.Equivalence.inverse CategoryTheory.prod.leftUnitorEquivalence equivProd CategoryTheory.Equivalence.functor CategoryTheory.Functor.id CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.counitIso toIdPUnitEquiv CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	CategoryTheory.Category.comp_id
toIdPUnitEquiv_counitIso_inv_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Functor.id CategoryTheory.Functor.comp CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.prod' CategoryTheory.Equivalence.inverse CategoryTheory.prod.leftUnitorEquivalence equivProd CategoryTheory.Equivalence.functor CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.counitIso toIdPUnitEquiv CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	CategoryTheory.Category.comp_id
toIdPUnitEquiv_functor_iso 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory toIdPUnitEquiv snd	—	—
toIdPUnitEquiv_functor_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.Equivalence.functor toIdPUnitEquiv CategoryTheory.CommaMorphism.right	—	—
toIdPUnitEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.Equivalence.functor toIdPUnitEquiv right	—	—
toIdPUnitEquiv_inverse_map_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse equivProd CategoryTheory.prod.leftUnitorEquivalence CategoryTheory.Functor.map toIdPUnitEquiv	—	—
toIdPUnitEquiv_inverse_obj_left_as 📖	mathematical	—	CategoryTheory.Discrete.as left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse toIdPUnitEquiv	—	—
toIdPUnitEquiv_inverse_obj_right 📖	mathematical	—	right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse toIdPUnitEquiv	—	—
toIdPUnitEquiv_unitIso_hom_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp CategoryTheory.prod' CategoryTheory.Equivalence.functor equivProd CategoryTheory.prod.leftUnitorEquivalence CategoryTheory.Equivalence.inverse CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.unitIso toIdPUnitEquiv CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
toIdPUnitEquiv_unitIso_inv_app_right 📖	mathematical	—	CategoryTheory.CommaMorphism.right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp CategoryTheory.prod' CategoryTheory.Equivalence.functor equivProd CategoryTheory.prod.leftUnitorEquivalence CategoryTheory.Equivalence.inverse CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.unitIso toIdPUnitEquiv CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	CategoryTheory.Category.comp_id
toPUnitIdEquiv_counitIso_hom_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Functor.comp CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.prod' CategoryTheory.Equivalence.inverse CategoryTheory.prod.rightUnitorEquivalence equivProd CategoryTheory.Equivalence.functor CategoryTheory.Functor.id CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.counitIso toPUnitIdEquiv CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	CategoryTheory.Category.comp_id
toPUnitIdEquiv_counitIso_inv_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Functor.id CategoryTheory.Functor.comp CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.prod' CategoryTheory.Equivalence.inverse CategoryTheory.prod.rightUnitorEquivalence equivProd CategoryTheory.Equivalence.functor CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.counitIso toPUnitIdEquiv CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	CategoryTheory.Category.comp_id
toPUnitIdEquiv_functor_iso 📖	mathematical	—	CategoryTheory.Equivalence.functor CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory toPUnitIdEquiv fst	—	—
toPUnitIdEquiv_functor_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.Equivalence.functor toPUnitIdEquiv CategoryTheory.CommaMorphism.left	—	—
toPUnitIdEquiv_functor_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.commaCategory CategoryTheory.Equivalence.functor toPUnitIdEquiv left	—	—
toPUnitIdEquiv_inverse_map_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.prod' CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse equivProd CategoryTheory.prod.rightUnitorEquivalence CategoryTheory.Functor.map toPUnitIdEquiv	—	—
toPUnitIdEquiv_inverse_obj_left 📖	mathematical	—	left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse toPUnitIdEquiv	—	—
toPUnitIdEquiv_inverse_obj_right_as 📖	mathematical	—	CategoryTheory.Discrete.as right CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Equivalence.inverse toPUnitIdEquiv	—	—
toPUnitIdEquiv_unitIso_hom_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.id CategoryTheory.Functor.comp CategoryTheory.prod' CategoryTheory.Equivalence.functor equivProd CategoryTheory.prod.rightUnitorEquivalence CategoryTheory.Equivalence.inverse CategoryTheory.NatTrans.app CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.unitIso toPUnitIdEquiv CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
toPUnitIdEquiv_unitIso_inv_app_left 📖	mathematical	—	CategoryTheory.CommaMorphism.left CategoryTheory.Discrete CategoryTheory.discreteCategory CategoryTheory.Functor.obj CategoryTheory.Comma CategoryTheory.commaCategory CategoryTheory.Functor.comp CategoryTheory.prod' CategoryTheory.Equivalence.functor equivProd CategoryTheory.prod.rightUnitorEquivalence CategoryTheory.Equivalence.inverse CategoryTheory.Functor.id CategoryTheory.NatTrans.app CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category CategoryTheory.Equivalence.unitIso toPUnitIdEquiv CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	CategoryTheory.Category.comp_id
unopFunctorCompFst_hom_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory CategoryTheory.Functor.comp unopFunctor fst CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category snd unopFunctorCompFst CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	—
unopFunctorCompFst_inv_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory CategoryTheory.Functor.comp unopFunctor fst CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category snd unopFunctorCompFst CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct right	—	—
unopFunctorCompSnd_hom_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory CategoryTheory.Functor.comp unopFunctor snd CategoryTheory.Iso.hom CategoryTheory.Functor CategoryTheory.Functor.category fst unopFunctorCompSnd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	—
unopFunctorCompSnd_inv_app 📖	mathematical	—	CategoryTheory.NatTrans.app CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory CategoryTheory.Functor.comp unopFunctor snd CategoryTheory.Iso.inv CategoryTheory.Functor CategoryTheory.Functor.category fst unopFunctorCompSnd CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct left	—	—
unopFunctor_map 📖	mathematical	—	CategoryTheory.Functor.map CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory unopFunctor Opposite.op Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct Opposite.unop right left Quiver.Hom.unop CategoryTheory.Functor.obj hom CategoryTheory.CommaMorphism.right CategoryTheory.CommaMorphism.left	—	—
unopFunctor_obj 📖	mathematical	—	CategoryTheory.Functor.obj CategoryTheory.Comma Opposite CategoryTheory.Category.opposite CategoryTheory.Functor.op CategoryTheory.commaCategory unopFunctor Opposite.op Opposite.unop right left Quiver.Hom.unop CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct hom	—	—

CategoryTheory.CommaMorphism

Definitions

Name	Category	Theorems
inhabited 📖	CompOp	—
left 📖	CompOp	664 math math: CategoryTheory.Limits.kernelSubobjectMap_arrow_assoc, CategoryTheory.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst, CategoryTheory.SimplicialObject.id_left_app, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.Over.prodLeftIsoPullback_hom_snd_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_left, CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, CategoryTheory.Bicategory.RightExtension.w_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_hom_left, CategoryTheory.CostructuredArrow.hom_eq_iff, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.MorphismProperty.Comma.Hom.ext_iff, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_e, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_inv_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_map, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ_assoc, CategoryTheory.Over.iteratedSliceBackward_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_map_left_left, CategoryTheory.Over.associator_inv_left_snd, CategoryTheory.Comma.toPUnitIdEquiv_functor_map, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, CategoryTheory.Over.inv_left_hom_left_assoc, AlgebraicGeometry.Scheme.OpenCover.map_glueMorphismsOverOfLocallyDirected_left_assoc, CategoryTheory.Arrow.mapCechNerve_app, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.RetractArrow.retract_left_assoc, CategoryTheory.CostructuredArrow.w_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.MonoOver.isIso_left_iff_subobjectMk_eq, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, CategoryTheory.RetractArrow.left_r, CategoryTheory.Sieve.overEquiv_pullback, CategoryTheory.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.Comma.mapLeft_map_left, CategoryTheory.OverPresheafAux.restrictedYoneda_map, CategoryTheory.Bicategory.RightLift.w_assoc, CategoryTheory.Over.comp_left_assoc, CategoryTheory.Over.hom_left_inv_left, CategoryTheory.MorphismProperty.Comma.eqToHom_left, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_left, CategoryTheory.Over.whiskerLeft_left, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_left, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.CostructuredArrow.w_prod_fst, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₃, CategoryTheory.Over.epi_iff_epi_left, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, CategoryTheory.Over.OverMorphism.ext_iff, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp, CategoryTheory.Comma.mapLeftIso_functor_map_left, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_π_app_left, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, CategoryTheory.Arrow.comp_left, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd_assoc, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_left, CategoryTheory.TwoSquare.EquivalenceJ.inverse_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isPullback, CategoryTheory.RetractArrow.r_w_assoc, CategoryTheory.Comma.mapLeftEq_hom_app_left, CategoryTheory.Limits.Cone.fromCostructuredArrow_map_hom, AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan, CategoryTheory.Arrow.mapAugmentedCechNerve_left, CategoryTheory.MorphismProperty.CostructuredArrow.homMk_left, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, CategoryTheory.Comma.eqToHom_left, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, CategoryTheory.Over.toUnit_left, CategoryTheory.Comma.mapRightIso_functor_map_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop, CategoryTheory.Over.braiding_inv_left, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, CategoryTheory.Over.prodLeftIsoPullback_inv_snd, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, CategoryTheory.SimplicialObject.Augmented.toArrow_map_left, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, CategoryTheory.toOverUnit_map_left, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.Comma.inv_left, CategoryTheory.WithTerminal.mkCommaMorphism_left_app, CategoryTheory.CostructuredArrow.prodFunctor_map, CategoryTheory.Abelian.coim_map, CategoryTheory.Over.leftUnitor_hom_left, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, CategoryTheory.RetractArrow.i_w, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, CategoryTheory.toOverIsoToOverUnit_inv_app_left, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, CategoryTheory.MorphismProperty.Over.map_map_left, groupHomology.d₁₀ArrowIso_hom_left, CategoryTheory.MonoOver.mkArrowIso_hom_hom_left, CategoryTheory.Comma.opFunctor_map, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, CategoryTheory.ChosenPullbacksAlong.snd'_left, CategoryTheory.MorphismProperty.Comma.isoMk_hom_left, AlgebraicGeometry.Scheme.OpenCover.map_glueMorphismsOverOfLocallyDirected_left, CategoryTheory.Over.rightUnitor_inv_left_fst, CategoryTheory.WithTerminal.commaFromOver_map_left, CategoryTheory.Functor.RightExtension.precomp_map_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd_assoc, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eq, CategoryTheory.Over.mapCongr_inv_app_left, CategoryTheory.MorphismProperty.Over.Hom.ext_iff, CategoryTheory.MorphismProperty.Comma.comp_left_assoc, CategoryTheory.Over.mapCongr_hom_app_left, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, CategoryTheory.Over.postCongr_inv_app_left, CategoryTheory.Over.mapComp_hom_app_left, CategoryTheory.Comma.equivProd_unitIso_hom_app_left, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_left, CategoryTheory.Over.whiskerRight_left_fst, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst_assoc, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_f, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_left, CategoryTheory.Arrow.square_from_iso_invert, CategoryTheory.Over.prodLeftIsoPullback_inv_fst, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.TwoSquare.costructuredArrowRightwards_map, CategoryTheory.CostructuredArrow.mkPrecomp_left, CategoryTheory.Arrow.mono_left, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Over.prodLeftIsoPullback_inv_snd_assoc, CategoryTheory.Over.rightUnitor_inv_left_snd, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, AlgebraicGeometry.instIsClosedImmersionLeftSchemeDiscretePUnitOneOverSpecOf, CategoryTheory.Over.post_map, CategoryTheory.Comma.mapRightId_inv_app_left, CategoryTheory.Over.postCongr_hom_app_left, CategoryTheory.Comma.preRight_map_left, CategoryTheory.CostructuredArrow.post_map, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.RetractArrow.op_r_right, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst, CategoryTheory.Over.prodLeftIsoPullback_hom_snd, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_hom, CategoryTheory.MorphismProperty.Over.isoMk_inv_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.Over.whiskerRight_left_snd_assoc, CategoryTheory.Arrow.w_mk_right, CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctor_lift_left, CategoryTheory.CostructuredArrow.eta_hom_left, CategoryTheory.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Sieve.overEquiv_symm_iff, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₃, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_left, CategoryTheory.Over.associator_hom_left_fst, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_left, CategoryTheory.Comma.comp_left, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, CategoryTheory.WithInitial.mkCommaMorphism_left, CategoryTheory.WithInitial.commaFromUnder_map_left, CategoryTheory.SimplicialObject.Augmented.const_map_left, CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc, CategoryTheory.Over.map_map_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc, CategoryTheory.MorphismProperty.Over.mapId_inv_app_left, groupCohomology.dArrowIso₀₁_inv_left, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, CategoryTheory.MonoOver.image_map, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, CategoryTheory.Comma.mapLeftComp_inv_app_left, CategoryTheory.Limits.ImageMap.factor_map_assoc, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_map_left_left, CategoryTheory.StructuredArrow.mkPostcomp_left, CategoryTheory.StructuredArrow.left_eq_id, CategoryTheory.Over.leftUnitor_inv_left_fst, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Over.inv_left_hom_left, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, AlgebraicGeometry.opensDiagram_map, CategoryTheory.CostructuredArrow.id_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left, HomotopicalAlgebra.cofibrations_over_iff, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_of, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, CategoryTheory.Over.isoMk_inv_left, CategoryTheory.Over.eqToHom_left, CategoryTheory.Comma.equivProd_inverse_map_left, CategoryTheory.MorphismProperty.Comma.isoMk_inv_left, CategoryTheory.Arrow.isoMk_inv_left, CategoryTheory.Over.tensorHom_left_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, w_assoc, CategoryTheory.Over.leftUnitor_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Arrow.w, CategoryTheory.StructuredArrow.homMk'_left, HomotopicalAlgebra.instCofibrationLeftDiscretePUnitOfOver, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd', AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, CategoryTheory.Over.μ_pullback_left_fst_snd', CategoryTheory.Over.comp_left, CategoryTheory.MorphismProperty.Over.forget_comp_forget_map, CategoryTheory.Square.toArrowArrowFunctor'_map_right_left, CategoryTheory.Over.mapId_inv_app_left, CategoryTheory.Comma.map_map_left, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.CostructuredArrow.w_prod_snd, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, CategoryTheory.Comma.post_map_left, w, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_inv_app_left, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, CategoryTheory.Sieve.overEquiv_symm_pullback, CategoryTheory.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.MorphismProperty.Comma.Hom.prop_hom_left, groupCohomology.dArrowIso₀₁_hom_left, CategoryTheory.RetractArrow.r_w, CategoryTheory.Arrow.inv_left, CategoryTheory.SmallObject.ιObj_naturality, CategoryTheory.SmallObject.ιFunctorObj_naturality, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, CategoryTheory.WithTerminal.ofCommaMorphism_app, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, CategoryTheory.SmallObject.functorMapSrc_functorObjTop, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, CategoryTheory.Arrow.w_mk_right_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_obj, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, CategoryTheory.WithInitial.equivComma_functor_map_left, CategoryTheory.OverPresheafAux.restrictedYonedaObj_map, CategoryTheory.Over.associator_hom_left_snd_fst, CategoryTheory.CostructuredArrow.toOver_map_left, CategoryTheory.Over.postComp_inv_app_left, CategoryTheory.Comma.mapRightEq_inv_app_left, CategoryTheory.Functor.mapArrow_map_left, CategoryTheory.subterminalsEquivMonoOverTerminal_inverse_map, CategoryTheory.CostructuredArrow.eta_inv_left, CategoryTheory.Comma.hom_ext_iff, CategoryTheory.RetractArrow.retract_left, CategoryTheory.Arrow.squareToSnd_left, CategoryTheory.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.SimplicialObject.Augmented.hom_ext_iff, CategoryTheory.Limits.ImageMap.factor_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd, CategoryTheory.MonoOver.w, CategoryTheory.WithInitial.equivComma_inverse_map_app, CategoryTheory.Comma.left_hom_inv_right, CategoryTheory.Arrow.isIso_left, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_app, CategoryTheory.Over.iteratedSliceEquivOverMapIso_inv_app_left_left, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_obj, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_left, CategoryTheory.overToCoalgebra_map_f, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_left, CategoryTheory.Over.homMk_left, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_app, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd_assoc, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_f, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst_assoc, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, CategoryTheory.Over.pullback_map_left, CategoryTheory.Arrow.mapAugmentedCechConerve_left, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.Pseudofunctor.presheafHom_map, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_map_left, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.CostructuredArrow.toStructuredArrow'_map, CategoryTheory.RetractArrow.op_i_right, CategoryTheory.Over.tensorHom_left, CategoryTheory.CostructuredArrow.w, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_left_app, CategoryTheory.Over.associator_inv_left_fst_snd, CategoryTheory.SimplicialObject.comp_left_app, CategoryTheory.Square.toArrowArrowFunctor_obj_hom_left, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.CostructuredArrow.grothendieckProj_map, CategoryTheory.MorphismProperty.Over.w_assoc, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, CategoryTheory.Functor.RightExtension.postcomp₁_map_left_app, CategoryTheory.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.Comma.mapRightComp_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, CategoryTheory.RetractArrow.map_r_left, CategoryTheory.Arrow.mapCechConerve_app, CategoryTheory.Comma.toPUnitIdEquiv_inverse_map_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, CategoryTheory.CostructuredArrow.epi_left_of_epi, CategoryTheory.Over.μ_pullback_left_fst_fst', CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Over.whiskerRight_left, CategoryTheory.CostructuredArrow.homMk'_left, CategoryTheory.Square.toArrowArrowFunctor'_map_left_right, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, CategoryTheory.Arrow.id_left, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₃, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.StructuredArrow.pre_map_left, CategoryTheory.Comma.inv_left_hom_right, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_left, CategoryTheory.Comma.coconeOfPreserves_ι_app_left, ext_iff, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, CategoryTheory.Comma.isoMk_inv_left, CategoryTheory.CostructuredArrow.proj_map, CategoryTheory.RetractArrow.unop_r_right, CategoryTheory.StructuredArrow.map_map_left, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, CategoryTheory.toOverIsoToOverUnit_hom_app_left, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_apply, CategoryTheory.Over.w, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_map, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_map, CategoryTheory.MorphismProperty.Comma.Hom.comp_left, CategoryTheory.OverClass.asOverHom_left, CategoryTheory.CostructuredArrow.comp_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst_assoc, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.CostructuredArrow.homMk_left, CategoryTheory.Over.associator_inv_left_fst_fst, CategoryTheory.MonoOver.isIso_iff_isIso_hom_left, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.Comma.mapLeftId_hom_app_left, CategoryTheory.Over.snd_left, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_map_left_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.CostructuredArrow.prodInverse_map, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst_assoc, CategoryTheory.Comma.mapLeftId_inv_app_left, CategoryTheory.Arrow.inv_hom_id_left_assoc, CategoryTheory.Over.tensorHom_left_fst, CategoryTheory.Over.whiskerRight_left_snd, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver_f, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, HomotopicalAlgebra.instFibrationLeftDiscretePUnitOfOver, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π_assoc, CategoryTheory.Over.isoMk_hom_left, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_hom_app_left, CategoryTheory.CommSq.of_arrow, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, CategoryTheory.Comma.fromProd_map_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst, CategoryTheory.SmallObject.functorMapSrc_functorObjTop_assoc, CategoryTheory.Functor.toOver_map_left, CategoryTheory.Over.star_map_left, CategoryTheory.Comma.unopFunctor_map, CategoryTheory.Over.tensorHom_left_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd_assoc, CategoryTheory.forgetAdjToOver.homEquiv_symm, CategoryTheory.Over.prodLeftIsoPullback_inv_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_hom_left, CategoryTheory.CosimplicialObject.Augmented.const_map_left, CategoryTheory.Over.η_pullback_left, CategoryTheory.MorphismProperty.Comma.comp_left, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, CategoryTheory.Over.id_left, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_hom_left, CategoryTheory.CostructuredArrow.isoMk_inv_left, CategoryTheory.Arrow.iso_w, CategoryTheory.Arrow.comp_left_assoc, CategoryTheory.Over.postComp_hom_app_left, CategoryTheory.CosimplicialObject.Augmented.hom_ext_iff, CategoryTheory.Over.whiskerLeft_left_fst, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_counit_app, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp_map, CategoryTheory.Functor.LeftExtension.postcompose₂_map_left, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, CategoryTheory.MonoOver.mkArrowIso_inv_hom_left, CategoryTheory.Arrow.inv_left_hom_right, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, CategoryTheory.Comma.mapRightId_hom_app_left, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, CategoryTheory.ChosenPullbacksAlong.Over.lift_left, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₂, CategoryTheory.Over.mapId_hom_app_left, CategoryTheory.Comma.mapLeftEq_inv_app_left, CategoryTheory.Square.toArrowArrowFunctor_map_left_left, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, CategoryTheory.Abelian.coimageImageComparisonFunctor_map, CategoryTheory.MonoOver.w_assoc, CategoryTheory.CostructuredArrow.map_map_left, CategoryTheory.RetractArrow.map_i_left, CategoryTheory.MorphismProperty.over_iff, CategoryTheory.CostructuredArrow.map₂_map_left, CategoryTheory.MorphismProperty.Comma.mapRight_map_left, CategoryTheory.Over.isPullback_of_binaryFan_isLimit, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp_assoc, CategoryTheory.Arrow.isoMk_hom_left, CategoryTheory.SimplicialObject.equivalenceRightToLeft_left, CategoryTheory.CosimplicialObject.Augmented.point_map, CategoryTheory.Over.whiskerLeft_left_fst_assoc, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_inv_left_app, CategoryTheory.MorphismProperty.Over.w, CategoryTheory.Functor.RightExtension.postcompose₂_map_left_app, AlgebraicGeometry.isClosedImmersion_equalizer_ι_left, CategoryTheory.RetractArrow.op_r_left, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₄, CategoryTheory.Over.prodComparisonIso_pullback_Spec_inv_left_fst_fst', CategoryTheory.Comma.leftIso_hom, CategoryTheory.Over.whiskerLeft_left_snd_assoc, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.TwoSquare.EquivalenceJ.functor_obj, CategoryTheory.CosimplicialObject.equivalenceRightToLeft_right_app, CategoryTheory.Square.toArrowArrowFunctor'_map_left_left, CategoryTheory.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left, CategoryTheory.WithTerminal.liftFromOver_obj_map, CategoryTheory.Functor.LeftExtension.precomp_map_left, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, HomologicalComplex.Hom.sqFrom_left, CategoryTheory.Arrow.hom_inv_id_left, CategoryTheory.Comma.leftIso_inv, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_left, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_counit_app, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, CategoryTheory.subterminalsEquivMonoOverTerminal_unitIso, CategoryTheory.MorphismProperty.CostructuredArrow.Hom.ext_iff, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.Comma.mapRight_map_left, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_counit_app, CategoryTheory.Arrow.inv_hom_id_left, CategoryTheory.Functor.LeftExtension.postcomp₁_map_left, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₂, CategoryTheory.Functor.RightExtension.coneAtFunctor_map_hom, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_comp, CategoryTheory.Over.rightUnitor_hom_left, CategoryTheory.MorphismProperty.Over.pullback_map_left, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₁, CategoryTheory.RetractArrow.op_i_left, SSet.Augmented.stdSimplex_map_left, CategoryTheory.toOver_map_left, CategoryTheory.Over.sections_map, CategoryTheory.ChosenPullbacksAlong.fst'_left, CategoryTheory.CosimplicialObject.equivalenceLeftToRight_left, CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation, CategoryTheory.Over.μ_pullback_left_snd, CategoryTheory.subterminalsEquivMonoOverTerminal_counitIso, CategoryTheory.Comma.id_left, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_map_left, CategoryTheory.ChosenPullbacksAlong.Over.toUnit_left, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π, CategoryTheory.Over.epi_left_of_epi, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.WithTerminal.equivComma_functor_map_left_app, CategoryTheory.Comma.preLeft_map_left, CategoryTheory.CostructuredArrow.eqToHom_left, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.MorphismProperty.Comma.Hom.hom_left, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.instHomIsOverLeftDiscretePUnit, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, CategoryTheory.Over.braiding_hom_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, CategoryTheory.CostructuredArrow.hom_ext_iff, CategoryTheory.Over.μ_pullback_left_fst_fst, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.Over.iteratedSliceForward_map, CategoryTheory.simplicialToCosimplicialAugmented_map_right, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver'_f, HomologicalComplex.Hom.sqTo_left, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₁, CategoryTheory.SmallObject.ιFunctorObj_naturality_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Over.hom_left_inv_left_assoc, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_left, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.TwoSquare.EquivalenceJ.functor_map, CategoryTheory.RetractArrow.unop_i_left, CategoryTheory.cosimplicialToSimplicialAugmented_map, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, CategoryTheory.Comma.mapRightEq_hom_app_left, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.CosimplicialObject.equivalenceRightToLeft_left, CategoryTheory.Arrow.leftFunc_map, CategoryTheory.Under.costar_map_left, CategoryTheory.Over.whiskerRight_left_fst_assoc, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.Over.tensorHom_left_snd, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.MorphismProperty.Over.isoMk_hom_left, CategoryTheory.StructuredArrow.toUnder_map_left, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_hom_left, CategoryTheory.SimplicialObject.Augmented.drop_map, CategoryTheory.Functor.mapArrowFunctor_map_app_left, CategoryTheory.Pretriangulated.exists_iso_of_arrow_iso, CategoryTheory.CostructuredArrow.preEquivalence.functor_map_left, CategoryTheory.SmallObject.ιObj_naturality_assoc, CategoryTheory.Over.forget_map, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₂, CategoryTheory.RetractArrow.unop_i_right, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, CategoryTheory.Square.toArrowArrowFunctor_map_left_right, CategoryTheory.WithTerminal.liftFromOver_map_app, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, CategoryTheory.Arrow.left_hom_inv_right, CategoryTheory.Square.toArrowArrowFunctor_map_right_left, CategoryTheory.Comma.instIsIsoLeft, CategoryTheory.RetractArrow.left_i, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.RetractArrow.instIsSplitEpiLeftRArrow, CategoryTheory.Comma.equivProd_functor_map, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.Over.lift_left, CategoryTheory.Comma.mapLeftIso_inverse_map_left, CategoryTheory.Arrow.w_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_map_left_left, CategoryTheory.Over.opEquivOpUnder_functor_map, CategoryTheory.Comma.mapLeftComp_hom_app_left, CategoryTheory.Functor.LeftExtension.precomp₂_map_left, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_pullback_map, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, CategoryTheory.SimplicialObject.augmentedCechNerve_map_left_app, AlgebraicGeometry.Scheme.restrictFunctor_map_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, TopCat.Presheaf.generateEquivalenceOpensLe_functor'_map, CategoryTheory.CostructuredArrow.pre_map_left, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_map, HomotopicalAlgebra.weakEquivalences_over_iff, CategoryTheory.CostructuredArrow.ext_iff, CategoryTheory.Over.mkIdTerminal_from_left, CategoryTheory.Square.toArrowArrowFunctor'_obj_hom_left, CategoryTheory.Over.fst_left, CategoryTheory.Over.prodLeftIsoPullback_hom_fst, CategoryTheory.Arrow.hom_ext_iff, CategoryTheory.Over.associator_hom_left_fst_assoc, CategoryTheory.Comma.equivProd_unitIso_inv_app_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.Over.forgetAdjStar_unit_app_left, HomotopicalAlgebra.instWeakEquivalenceLeftDiscretePUnitOfOver, CategoryTheory.CostructuredArrow.epi_iff_epi_left, CategoryTheory.Arrow.homMk_left, CategoryTheory.MorphismProperty.Comma.mapLeft_map_left, CategoryTheory.RetractArrow.i_w_assoc, CategoryTheory.RetractArrow.unop_r_left, CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd', CategoryTheory.toOverUnitPullback_hom_app_left, CategoryTheory.Arrow.hom.congr_left, CategoryTheory.Over.ε_pullback_left, groupHomology.d₁₀ArrowIso_inv_left, CategoryTheory.Over.coprod_map_app, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.WithInitial.ofCommaMorphism_app, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, CategoryTheory.RetractArrow.instIsSplitMonoLeftIArrow, CategoryTheory.MorphismProperty.Over.mapId_hom_app_left, CategoryTheory.CosimplicialObject.comp_left, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, CategoryTheory.Limits.kernelSubobjectMap_arrow, CategoryTheory.Over.associator_hom_left_snd_snd, CategoryTheory.Over.associator_inv_left_snd_assoc, CategoryTheory.Over.coprodObj_map, CategoryTheory.Comma.fst_map, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, CategoryTheory.toOverUnitPullback_inv_app_left, CategoryTheory.Comma.mapRightIso_inverse_map_left, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.Limits.image.factor_map, CategoryTheory.Arrow.hom_inv_id_left_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Arrow.homMk'_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.Under.opEquivOpOver_inverse_map, CategoryTheory.Over.iteratedSliceForward_obj, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_hom_left_app, CategoryTheory.CostructuredArrow.projectQuotient_mk, CategoryTheory.MorphismProperty.Comma.id_left, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.Over.whiskerLeft_left_snd, CategoryTheory.Over.w_assoc, CategoryTheory.Comma.isoMk_hom_left, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, CategoryTheory.Limits.diagonal_pullback_fst, CategoryTheory.Bicategory.RightLift.w, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst_assoc, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd, CategoryTheory.CostructuredArrow.isoMk_hom_left, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, HomotopicalAlgebra.fibrations_over_iff, CategoryTheory.Over.ConstructProducts.conesEquivInverse_map_hom, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, CategoryTheory.Bicategory.RightExtension.w, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, CategoryTheory.Comma.mapRightComp_inv_app_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_map_hom, CategoryTheory.Arrow.iso_w', CategoryTheory.Limits.kernelSubobjectMap_arrow_apply, CategoryTheory.Over.mapComp_inv_app_left, CategoryTheory.CosimplicialObject.id_left, CategoryTheory.Limits.ker_map, CategoryTheory.Over.mono_left_of_mono, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.MonoOver.isIso_iff_isIso_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.MonoOver.instIsIsoLeftDiscretePUnitHomFullSubcategoryOverIsMono, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₄, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_right, CategoryTheory.OverPresheafAux.counitForward_naturality₂, CategoryTheory.Comma.coneOfPreserves_π_app_left
right 📖	CompOp	462 math math: CommRingCat.tensorProd_map_right, CategoryTheory.Functor.LeftExtension.coconeAtFunctor_map_hom, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.StructuredArrow.projectSubobject_mk, CategoryTheory.StructuredArrow.map_map_right, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p, CategoryTheory.StructuredArrow.isoMk_inv_right, CategoryTheory.RetractArrow.right_r, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, CategoryTheory.Comma.mapLeftEq_inv_app_right, CategoryTheory.Comma.mapLeftIso_inverse_map_right, CategoryTheory.MorphismProperty.Comma.Hom.ext_iff, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, CategoryTheory.Bicategory.LeftLift.whiskering_map, CategoryTheory.CosimplicialObject.id_right_app, CategoryTheory.Functor.LeftExtension.precomp₂_map_right, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, CategoryTheory.Under.postComp_inv_app_right, CategoryTheory.Bicategory.LeftExtension.w_assoc, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_map_right, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.Arrow.mapCechNerve_app, CategoryTheory.SimplicialObject.comp_right, CategoryTheory.SimplicialObject.Augmented.point_map, CategoryTheory.Arrow.hom_inv_id_right_assoc, CategoryTheory.Comma.toIdPUnitEquiv_inverse_map_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, CategoryTheory.SmallObject.πObj_ιIteration_app_right, CategoryTheory.Under.epi_right_of_epi, CategoryTheory.Under.postCongr_inv_app_right, CategoryTheory.Under.mono_right_of_mono, CategoryTheory.Functor.LeftExtension.postcomp₁_map_right_app, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.SimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₃, CategoryTheory.Arrow.mapAugmentedCechConerve_right, CommRingCat.mkUnder_ext_iff, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, CategoryTheory.Square.toArrowArrowFunctor_obj_hom_right, CategoryTheory.Bicategory.LeftLift.w_assoc, CategoryTheory.TwoSquare.EquivalenceJ.inverse_map, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.Comma.mapRightEq_hom_app_right, CategoryTheory.RetractArrow.r_w_assoc, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.MorphismProperty.Comma.comp_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, CategoryTheory.StructuredArrow.map₂_map_right, CategoryTheory.Comma.instIsIsoRight, CategoryTheory.Comma.coneOfPreserves_π_app_right, CategoryTheory.Functor.LeftExtension.precomp_map_right, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, CategoryTheory.Comma.map_map_right, groupCohomology.dArrowIso₀₁_inv_right, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.Functor.RightExtension.postcomp₁_map_right, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_symm_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, CategoryTheory.Comma.mapRightIso_inverse_map_right, CategoryTheory.Limits.coker_map, CategoryTheory.StructuredArrow.eta_hom_right, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₃₄, CategoryTheory.RetractArrow.map_r_right, CategoryTheory.StructuredArrow.prodInverse_map, CategoryTheory.MorphismProperty.under_iff, CategoryTheory.StructuredArrow.eta_inv_right, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.RetractArrow.i_w, CategoryTheory.CostructuredArrow.toOver_map_right, CategoryTheory.CategoryOfElements.to_comma_map_right, CategoryTheory.Comma.opFunctor_map, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, CategoryTheory.Under.homMk_right, CategoryTheory.StructuredArrow.id_right, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.Under.pushout_map, CategoryTheory.Comma.rightIso_hom, CategoryTheory.Limits.image.map_ι, CategoryTheory.CostructuredArrow.homMk'_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_left, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, groupCohomology.dArrowIso₀₁_hom_right, CategoryTheory.Comma.comp_right, CategoryTheory.Arrow.square_from_iso_invert, CategoryTheory.Abelian.im_map, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_right, CategoryTheory.Under.postAdjunctionRight_unit_app_right, CategoryTheory.Bicategory.LeftExtension.whiskering_map, CategoryTheory.Under.map_map_right, CategoryTheory.WithInitial.mkCommaMorphism_right_app, CategoryTheory.StructuredArrow.prodFunctor_map, CategoryTheory.Comma.mapLeftId_hom_app_right, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_base, CategoryTheory.Comma.mapRightComp_inv_app_right, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.CosimplicialObject.comp_right_app, CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_right, CategoryTheory.RetractArrow.op_r_right, CategoryTheory.CostructuredArrow.mkPrecomp_right, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_right, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.Arrow.w_mk_right, CategoryTheory.Under.eqToHom_right, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_inv_right, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₃, CategoryTheory.SmallObject.functor_map, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, SSet.Augmented.stdSimplex_map_right, CategoryTheory.WithTerminal.equivComma_functor_map_right, CategoryTheory.MorphismProperty.Under.isoMk_inv_right, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_inv_right_app, CategoryTheory.MorphismProperty.Comma.isoMk_hom_right, CategoryTheory.Under.isoMk_inv_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, CategoryTheory.Over.opEquivOpUnder_inverse_map, CategoryTheory.MorphismProperty.Under.isoMk_hom_right, CategoryTheory.Under.post_map, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.Square.toArrowArrowFunctor_map_right_right, CategoryTheory.StructuredArrow.eqToHom_right, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_hom_right, CategoryTheory.Functor.LeftExtension.postcompose₂_map_right_app, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, w_assoc, CategoryTheory.CostructuredArrow.map_map_right, AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff, CategoryTheory.Arrow.w, CategoryTheory.Comma.equivProd_unitIso_hom_app_right, CategoryTheory.SmallObject.iterationObjRightIso_hom, CategoryTheory.Comma.preRight_map_right, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_hom_right, CategoryTheory.Square.toArrowArrowFunctor'_map_right_left, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_inv_app_right, CategoryTheory.StructuredArrow.mono_iff_mono_right, w, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.RetractArrow.r_w, CategoryTheory.Under.mono_iff_mono_right, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_map_right_right, CategoryTheory.StructuredArrow.hom_eq_iff, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, CategoryTheory.Under.postComp_hom_app_right, CategoryTheory.Comma.snd_map, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Arrow.comp_right_assoc, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, CategoryTheory.WithTerminal.ofCommaMorphism_app, CategoryTheory.Under.isoMk_hom_right, CategoryTheory.WithTerminal.mkCommaMorphism_right, CategoryTheory.RetractArrow.right_i, CategoryTheory.Arrow.inv_hom_id_right, CategoryTheory.Arrow.isoMk_inv_right, CategoryTheory.Arrow.w_mk_right_assoc, CategoryTheory.SmallObject.functorMap_π_assoc, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_right, CategoryTheory.CosimplicialObject.Augmented.const_map_right, CategoryTheory.Bicategory.LeftExtension.whiskerIdCancel_right, groupHomology.d₁₀ArrowIso_inv_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.MorphismProperty.Comma.comp_right_assoc, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, CategoryTheory.StructuredArrow.isoMk_hom_right, CategoryTheory.Comma.hom_ext_iff, CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp_obj, AlgEquiv.toUnder_inv_right_apply, CategoryTheory.Comma.eqToHom_right, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.SimplicialObject.Augmented.hom_ext_iff, CategoryTheory.StructuredArrow.toCostructuredArrow_map, CategoryTheory.WithInitial.equivComma_inverse_map_app, CategoryTheory.Comma.left_hom_inv_right, CategoryTheory.Comma.mapLeftComp_inv_app_right, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.Comma.coconeOfPreserves_ι_app_right, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_hom_app_right, CategoryTheory.RetractArrow.retract_right_assoc, CommRingCat.toAlgHom_apply, CategoryTheory.StructuredArrow.toUnder_map_right, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_hom_right, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, CategoryTheory.MorphismProperty.Comma.mapLeft_map_right, CategoryTheory.Comma.mapRightIso_functor_map_right, CategoryTheory.WithInitial.equivComma_functor_map_right_app, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, CategoryTheory.Comma.toIdPUnitEquiv_functor_map, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_right, CategoryTheory.MorphismProperty.Comma.Hom.hom_right, CategoryTheory.StructuredArrow.homMk_right, CategoryTheory.RetractArrow.op_i_right, CategoryTheory.SimplicialObject.Augmented.const_map_right, CategoryTheory.Functor.mapArrow_map_right, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_of, CategoryTheory.RetractArrow.retract_right, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, CategoryTheory.Comma.inv_right, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_inv_right, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_hom_right_app, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, CategoryTheory.SmallObject.πObj_ιIteration_app_right_assoc, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_right, CategoryTheory.Under.forget_map, CategoryTheory.StructuredArrow.post_map, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, CategoryTheory.Arrow.mapCechConerve_app, CategoryTheory.SmallObject.πObj_naturality_assoc, CategoryTheory.Bicategory.LeftLift.whiskerHom_right, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_right_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, CategoryTheory.Square.toArrowArrowFunctor'_map_left_right, CategoryTheory.StructuredArrow.homMk'_right, CategoryTheory.Comma.inv_left_hom_right, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Limits.imageSubobjectMap_arrow, CategoryTheory.Limits.imageSubobjectMap_arrow_assoc, CategoryTheory.Over.opEquivOpUnder_counitIso, ext_iff, CategoryTheory.Comma.equivProd_inverse_map_right, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p_assoc, CategoryTheory.RetractArrow.unop_r_right, CategoryTheory.Arrow.id_right, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_left, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.StructuredArrow.mkPostcomp_right, CategoryTheory.Comma.mapLeftEq_hom_app_right, CategoryTheory.SimplicialObject.equivalenceRightToLeft_right, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_m, AlgHom.toUnder_right, CategoryTheory.StructuredArrow.proj_map, CategoryTheory.MorphismProperty.Under.w, CategoryTheory.StructuredArrow.mono_right_of_mono, AlgEquiv.toUnder_hom_right_apply, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_map_right_right, CategoryTheory.CostructuredArrow.right_eq_id, CategoryTheory.StructuredArrow.comp_right, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.Limits.ImageMap.map_ι, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, CategoryTheory.MorphismProperty.Comma.mapRight_map_right, CategoryTheory.Comma.fromProd_map_right, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, CategoryTheory.CommSq.of_arrow, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, CategoryTheory.WithInitial.commaFromUnder_map_right, CategoryTheory.Comma.unopFunctor_map, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_right, CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_inv_right, CategoryTheory.MorphismProperty.Under.Hom.ext_iff, CategoryTheory.RetractArrow.instIsSplitEpiRightRArrow, CategoryTheory.Arrow.hom.congr_right, CategoryTheory.Under.hom_right_inv_right, CategoryTheory.Arrow.iso_w, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, CategoryTheory.MorphismProperty.Comma.isoMk_inv_right, CategoryTheory.Limits.Cocone.fromStructuredArrow_map_hom, CategoryTheory.CosimplicialObject.Augmented.hom_ext_iff, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, CategoryTheory.Comma.mapRightId_hom_app_right, CategoryTheory.TwoSquare.costructuredArrowDownwardsPrecomp_map, CategoryTheory.Arrow.inv_left_hom_right, CategoryTheory.Arrow.homMk_right, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, CategoryTheory.Functor.RightExtension.precomp_map_right, CategoryTheory.Under.postCongr_hom_app_right, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, CategoryTheory.Abelian.coimageImageComparisonFunctor_map, CategoryTheory.WithTerminal.commaFromOver_map_right, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, CategoryTheory.MorphismProperty.Under.forget_comp_forget_map, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_right, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_hom_right, CategoryTheory.RetractArrow.op_r_left, CategoryTheory.StructuredArrow.preEquivalenceInverse_map_right_right, CategoryTheory.Comma.mapLeft_map_right, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₄, CategoryTheory.Comma.equivProd_unitIso_inv_app_right, CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, CategoryTheory.CosimplicialObject.equivalenceRightToLeft_right_app, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.StructuredArrow.w, CategoryTheory.Functor.RightExtension.postcompose₂_map_right, HomologicalComplex.Hom.sqTo_right, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.StructuredArrow.pre_map_right, CategoryTheory.StructuredArrow.w_prod_fst_assoc, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, CategoryTheory.SmallObject.functorMap_π, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_left, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, CategoryTheory.underToAlgebra_map_f, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_right_app, CategoryTheory.Comma.mapRightId_inv_app_right, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₂, CategoryTheory.Comma.mapRightComp_hom_app_right, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₁, CategoryTheory.RetractArrow.op_i_left, CategoryTheory.Comma.isoMk_hom_right, CategoryTheory.Functor.toUnder_map_right, CategoryTheory.Bicategory.LeftLift.whiskerIdCancel_right, CategoryTheory.Functor.mapArrowFunctor_map_app_right, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, HomologicalComplex.Hom.sqFrom_right, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_right, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, CategoryTheory.TwoSquare.structuredArrowDownwards_map, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_hom_right, CategoryTheory.Arrow.epi_right, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_right, CategoryTheory.RetractArrow.map_i_right, CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_hom_right, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.Comma.id_right, CategoryTheory.Under.inv_right_hom_right, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, CategoryTheory.RetractArrow.instIsSplitMonoRightIArrow, CategoryTheory.WithInitial.liftFromUnder_map_app, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.SimplicialObject.id_right, CategoryTheory.Under.hom_right_inv_right_assoc, CategoryTheory.simplicialToCosimplicialAugmented_map_right, CategoryTheory.CostructuredArrow.pre_map_right, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₁, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.MorphismProperty.Under.w_assoc, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.StructuredArrow.preEquivalenceFunctor_map_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_hom_right, CategoryTheory.TwoSquare.EquivalenceJ.functor_map, CategoryTheory.Under.UnderMorphism.ext_iff, CategoryTheory.Square.toArrowArrowFunctor'_map_right_right, CategoryTheory.RetractArrow.unop_i_left, CategoryTheory.cosimplicialToSimplicialAugmented_map, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Arrow.homMk'_right, CategoryTheory.Comma.mapRightEq_inv_app_right, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.Comma.post_map_right, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_inv_right, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.Bicategory.LeftExtension.whiskerHom_right, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.StructuredArrow.w_prod_snd_assoc, CategoryTheory.MorphismProperty.Comma.eqToHom_right, CategoryTheory.Pretriangulated.exists_iso_of_arrow_iso, CategoryTheory.StructuredArrow.ext_iff, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₂, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.RetractArrow.unop_i_right, CategoryTheory.Limits.ImageMap.map_ι_assoc, CategoryTheory.Square.toArrowArrowFunctor'_obj_hom_right, CategoryTheory.Arrow.inv_right, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, CategoryTheory.Square.toArrowArrowFunctor_map_left_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_right_app, groupHomology.d₁₀ArrowIso_hom_right, CategoryTheory.Arrow.left_hom_inv_right, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_inv_right, CategoryTheory.Square.toArrowArrowFunctor_map_right_left, CategoryTheory.Arrow.hom_inv_id_right, CategoryTheory.Under.mkIdInitial_to_right, CategoryTheory.MorphismProperty.Comma.Hom.prop_hom_right, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_right, CategoryTheory.Arrow.inv_hom_id_right_assoc, CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_inv_right, CategoryTheory.Comma.equivProd_functor_map, CategoryTheory.Over.lift_left, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.TwoSquare.EquivalenceJ.inverse_obj, CategoryTheory.Arrow.w_assoc, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_right, CategoryTheory.SimplicialObject.augmentedCechNerve_map_left_app, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, CategoryTheory.Under.inv_right_hom_right_assoc, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.Under.opEquivOpOver_functor_map, CategoryTheory.Arrow.hom_ext_iff, CategoryTheory.CosimplicialObject.equivalenceLeftToRight_right, CategoryTheory.Comma.preLeft_map_right, CategoryTheory.StructuredArrow.toCostructuredArrow'_map, CategoryTheory.RetractArrow.i_w_assoc, CategoryTheory.RetractArrow.unop_r_left, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.Bicategory.LeftExtension.w, CategoryTheory.SmallObject.πObj_naturality, CategoryTheory.Under.id_right, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_inv_right, CategoryTheory.Comma.isoMk_inv_right, CategoryTheory.WithInitial.ofCommaMorphism_app, CategoryTheory.SmallObject.instIsIsoRightAppArrowιIteration, CategoryTheory.Arrow.comp_right, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₂₄, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, CategoryTheory.Under.w_assoc, CategoryTheory.Comma.mapLeftId_inv_app_right, CategoryTheory.StructuredArrow.w_assoc, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, CategoryTheory.MorphismProperty.Comma.Hom.comp_right, CategoryTheory.Comma.rightIso_inv, CategoryTheory.Comma.mapLeftComp_hom_app_right, CategoryTheory.Comma.mapRight_map_right, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, CategoryTheory.Under.w, CategoryTheory.Comma.mapLeftIso_functor_map_right, CategoryTheory.SimplicialObject.augmentedCechNerve_map_right, CategoryTheory.Arrow.mapAugmentedCechNerve_right, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, CategoryTheory.Arrow.isoMk_hom_right, CategoryTheory.StructuredArrow.hom_ext_iff, CategoryTheory.Arrow.iso_w', CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_hom, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_right, CategoryTheory.SimplicialObject.equivalenceLeftToRight_right, CategoryTheory.CosimplicialObject.Augmented.drop_map, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_hom_right, CategoryTheory.Arrow.isIso_right, CategoryTheory.Under.comp_right, CategoryTheory.Arrow.squareToSnd_right, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, CategoryTheory.MorphismProperty.Comma.id_right, CategoryTheory.Bicategory.LeftLift.w, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₄, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_right, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, CategoryTheory.Arrow.rightFunc_map, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	left right	—	—	—
ext_iff 📖	mathematical	—	left right	—	ext
w 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Comma.left CategoryTheory.Comma.right CategoryTheory.Functor.map left CategoryTheory.Comma.hom right	—	—
w_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Comma.left CategoryTheory.Functor.map left CategoryTheory.Comma.right CategoryTheory.Comma.hom right	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' w

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