Documentation Verification Report

Multiequalizer

📁 Source: Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean

Statistics

MetricCount
DefinitionsHasMulticoequalizer, HasMultiequalizer, desc, isoCoequalizer, multicofork, sigmaπ, π, Multicofork, desc, mk, ext, isColimitToLinearOrder, isoOfπ, ofLinearOrder, ofSigmaCofork, ofπ, toLinearOrder, toSigmaCofork, π, MulticospanIndex, fst, fstPiMap, fstPiMapOfIsLimit, left, multicospan, multiforkEquivPiFork, multiforkEquivPiForkOfIsLimit, multiforkOfParallelHomsEquivFork, ofParallelHoms, ofPiForkFunctor, parallelPairDiagram, parallelPairDiagramOfIsLimit, right, snd, sndPiMap, sndPiMapOfIsLimit, toPiForkFunctor, MulticospanShape, L, R, fst, prod, snd, isoEqualizer, multifork, ι, ιPi, Multifork, mk, ext, isLimitEquivOfIsos, isoOfι, ofPiFork, ofι, toPiFork, ι, MultispanIndex, SymmStruct, iso, fst, fstSigmaMap, fstSigmaMapOfIsColimit, left, multicoforkEquivSigmaCofork, multicoforkEquivSigmaCoforkOfIsColimit, multispan, ofSigmaCoforkFunctor, parallelPairDiagram, parallelPairDiagramOfIsColimit, right, snd, sndSigmaMap, sndSigmaMapOfIsColimit, toLinearOrder, toLinearOrderMultispanIso, toSigmaCoforkFunctor, MultispanShape, L, R, fst, ofLinearOrder, prod, snd, WalkingMulticospan, comp, functorExt, instInhabitedHom, instInhabitedOfL, instSmallCategory, WalkingMultispan, comp, arrowEquiv, equiv, functorExt, inclusionOfLinearOrder, instInhabitedHom, instInhabitedOfL, instSmallCategory, instUniqueHom, instUniqueLOfLinearOrderBool, multicoequalizer, multiequalizer
102
Theoremscondition, condition_assoc, hom_ext, hom_ext_iff, instEpiSigmaπ, instHasCoequalizerFstSigmaMapSndSigmaMap, multicofork_ι_app_right, multicofork_ι_app_right', multicofork_π, ι_sigmaπ, ι_sigmaπ_assoc, π_desc, π_desc_assoc, fac, fac_assoc, hom_ext, mk_desc, condition, condition_assoc, ext_hom_hom, ext_inv_hom, fst_app_right, isoOfπ_hom_hom, isoOfπ_inv_hom, ofSigmaCofork_pt, ofSigmaCofork_ι_app_left, ofSigmaCofork_ι_app_right, ofSigmaCofork_ι_app_right', ofSigmaCofork_π, ofπ_pt, ofπ_ι_app, sigma_condition, sigma_condition_assoc, snd_app_right, snd_app_right_assoc, toSigmaCofork_pt, toSigmaCofork_π, π_comp_hom, π_comp_hom_assoc, π_eq_app_right, fstPiMapOfIsLimit_proj, fstPiMapOfIsLimit_proj_assoc, fstPiMap_π, fstPiMap_π_assoc, multicospan_map, multicospan_obj, multiforkEquivPiForkOfIsLimit_counitIso, multiforkEquivPiForkOfIsLimit_functor, multiforkEquivPiForkOfIsLimit_inverse, multiforkEquivPiForkOfIsLimit_unitIso, multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_counitIso_inv_app_hom, multiforkEquivPiFork_functor_map_hom, multiforkEquivPiFork_functor_obj_pt, multiforkEquivPiFork_functor_obj_π_app, multiforkEquivPiFork_inverse_map_hom, multiforkEquivPiFork_inverse_obj_pt, multiforkEquivPiFork_inverse_obj_π_app, multiforkEquivPiFork_unitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, multiforkOfParallelHomsEquivFork_functor_obj_ι, multiforkOfParallelHomsEquivFork_inverse_obj_ι, ofParallelHoms_fst, ofParallelHoms_left, ofParallelHoms_right, ofParallelHoms_snd, ofPiForkFunctor_map_hom, ofPiForkFunctor_obj, parallelPairDiagramOfIsLimit_map, parallelPairDiagramOfIsLimit_obj, parallelPairDiagram_map, parallelPairDiagram_obj, sndPiMapOfIsLimit_proj, sndPiMapOfIsLimit_proj_assoc, sndPiMap_π, sndPiMap_π_assoc, toPiForkFunctor_map_hom, toPiForkFunctor_obj, prod_L, prod_R, prod_fst, prod_snd, condition, condition_assoc, hom_ext, hom_ext_iff, instHasEqualizerFstPiMapSndPiMap, instMonoιPi, lift_ι, lift_ι_assoc, multifork_ι, multifork_π_app_left, ιPi_π, ιPi_π_assoc, fac, fac_assoc, hom_ext, mk_lift, app_left_eq_ι, app_right_eq_ι_comp_fst, app_right_eq_ι_comp_snd, app_right_eq_ι_comp_snd_assoc, condition, condition_assoc, ext_hom_hom, ext_inv_hom, hom_comp_ι, hom_comp_ι_assoc, isoOfι_hom_hom, isoOfι_inv_hom, ofPiFork_pt, ofPiFork_ι, ofPiFork_π_app_left, ofPiFork_π_app_right, ofι_pt, ofι_π_app, pi_condition, pi_condition_assoc, toPiFork_pt, toPiFork_π_app_one, toPiFork_π_app_zero, ι_ofι, fst_eq_snd, iso_hom_fst, iso_hom_fst_assoc, iso_hom_snd, iso_hom_snd_assoc, inj_fstSigmaMapOfIsColimit, inj_fstSigmaMapOfIsColimit_assoc, inj_sndSigmaMapOfIsColimit, inj_sndSigmaMapOfIsColimit_assoc, multicoforkEquivSigmaCoforkOfIsColimit_counitIso, multicoforkEquivSigmaCoforkOfIsColimit_functor, multicoforkEquivSigmaCoforkOfIsColimit_inverse, multicoforkEquivSigmaCoforkOfIsColimit_unitIso, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, multicoforkEquivSigmaCofork_functor_map_hom, multicoforkEquivSigmaCofork_functor_obj_pt, multicoforkEquivSigmaCofork_functor_obj_ι_app, multicoforkEquivSigmaCofork_inverse_map_hom, multicoforkEquivSigmaCofork_inverse_obj_pt, multicoforkEquivSigmaCofork_inverse_obj_ι_app, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, multicoforkEquivSigmaCofork_unitIso_inv_app_hom, multispan_map_fst, multispan_map_snd, multispan_obj_left, multispan_obj_right, ofSigmaCoforkFunctor_map_hom, ofSigmaCoforkFunctor_obj, parallelPairDiagramOfIsColimit_map, parallelPairDiagramOfIsColimit_obj, toLinearOrderMultispanIso_hom_app, toLinearOrderMultispanIso_inv_app, toLinearOrder_fst, toLinearOrder_left, toLinearOrder_right, toLinearOrder_snd, toSigmaCoforkFunctor_map_hom, toSigmaCoforkFunctor_obj, ι_fstSigmaMap, ι_fstSigmaMap_assoc, ι_sndSigmaMap, ι_sndSigmaMap_assoc, ofLinearOrder_L, ofLinearOrder_R, ofLinearOrder_fst, ofLinearOrder_snd, prod_L, prod_R, prod_fst, prod_snd, comp_eq_comp, id_eq_id, functorExt_hom_app, functorExt_inv_app, comp_eq_comp, id_eq_id, functorExt_hom_app, functorExt_inv_app, inclusionOfLinearOrder_map, inclusionOfLinearOrder_obj, instIsEmptyHomRightLeft, instLocallySmall, instSmallOfLOfR, instSubsingletonHomLeft, instSubsingletonHomRight
188
Total290

CategoryTheory.Limits

Definitions

NameCategoryTheorems
HasMulticoequalizer 📖MathDef
2 mathmath: AlgebraicGeometry.Scheme.GlueData.instHasMulticoequalizerDiagram, CategoryTheory.GlueData.hasColimit_mapGlueData_diagram
HasMultiequalizer 📖MathDef
Multicofork 📖CompOp
22 mathmath: MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, Multicofork.ext_hom_hom, MultispanIndex.ofSigmaCoforkFunctor_obj, MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_pt, Multicofork.isoOfπ_hom_hom, MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt, MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, Multicofork.ext_inv_hom, MultispanIndex.toSigmaCoforkFunctor_obj, MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_inverse, MultispanIndex.toSigmaCoforkFunctor_map_hom, MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, Multicofork.isoOfπ_inv_hom, MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, MultispanIndex.ofSigmaCoforkFunctor_map_hom, MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_functor
MulticospanIndex 📖CompData
MulticospanShape 📖CompData
Multifork 📖CompOp
24 mathmath: MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, MulticospanIndex.multiforkEquivPiFork_functor_map_hom, Multifork.ext_hom_hom, Multifork.isoOfι_hom_hom, Multifork.isoOfι_inv_hom, MulticospanIndex.toPiForkFunctor_map_hom, MulticospanIndex.multiforkEquivPiForkOfIsLimit_functor, MulticospanIndex.multiforkOfParallelHomsEquivFork_inverse_obj_ι, MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, MulticospanIndex.toPiForkFunctor_obj, MulticospanIndex.multiforkEquivPiForkOfIsLimit_inverse, MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, MulticospanIndex.multiforkEquivPiFork_inverse_obj_pt, MulticospanIndex.ofPiForkFunctor_obj, MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, MulticospanIndex.ofPiForkFunctor_map_hom, Multifork.ext_inv_hom, MulticospanIndex.multiforkOfParallelHomsEquivFork_functor_obj_ι, MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom
MultispanIndex 📖CompData
MultispanShape 📖CompData
WalkingMulticospan 📖CompData
113 mathmath: Wedge.mk_pt, MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, Multifork.IsLimit.sectionsEquiv_apply_val, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map', MulticospanIndex.multiforkEquivPiFork_functor_map_hom, Opens.mayerVietorisSquare_X₃, CondensedMod.isDiscrete_tfae, Multifork.ext_hom_hom, Multifork.isoOfι_hom_hom, MulticospanIndex.multicospan_map, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff, MulticospanIndex.sectionsEquiv_symm_apply_val, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, MulticospanIndex.sectionsEquiv_apply_coe, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, Multifork.isoOfι_inv_hom, MulticospanIndex.toPiForkFunctor_map_hom, Multifork.ofι_pt, CategoryTheory.Presheaf.isLocallySurjective_toSheafify, Multiequalizer.multifork_π_app_left, CondensedMod.isDiscrete_iff_isDiscrete_forget, Multifork.toPiFork_pt, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, MulticospanIndex.multiforkEquivPiForkOfIsLimit_functor, Wedge.IsLimit.lift_ι, Wedge.ext_hom_hom, MulticospanIndex.multiforkOfParallelHomsEquivFork_inverse_obj_ι, CategoryTheory.Presheaf.isLocallyInjective_toSheafify, MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, CategoryTheory.Presheaf.isSheaf_iff_of_isGeneratedByOneHypercovers, MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_inv_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, Opens.mayerVietorisSquare_X₂, Multifork.app_right_eq_ι_comp_snd, Wedge.condition, Multifork.app_left_eq_ι, Multifork.condition, WalkingMulticospan.Hom.comp_eq_comp, Wedge.IsLimit.lift_ι_assoc, Opens.coe_mayerVietorisSquare_X₁, Multifork.IsLimit.fac_assoc, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMap_app, Multifork.toPiFork_π_app_one, Multifork.ofPiFork_pt, Multifork.IsLimit.sectionsEquiv_symm_apply_val, CategoryTheory.Presheaf.isSheaf_iff_multifork, CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf, MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso_inv, MulticospanIndex.toPiForkFunctor_obj, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_app, MulticospanIndex.multiforkEquivPiForkOfIsLimit_inverse, MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac_assoc, CondensedSet.isDiscrete_tfae, Multifork.IsLimit.fac, MulticospanIndex.multiforkEquivPiFork_inverse_obj_pt, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, Wedge.ext_inv_hom, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CondensedSet.LocallyConstant.instFaithfulCondensedTypeDiscrete, WalkingMulticospan.functorExt_hom_app, CondensedSet.LocallyConstant.instFullCondensedTypeDiscrete, CategoryTheory.Presheaf.isLocallySurjective_toPlus, Multifork.app_right_eq_ι_comp_snd_assoc, Multifork.ofPiFork_π_app_right, WalkingMulticospan.functorExt_inv_app, MulticospanIndex.ofPiForkFunctor_obj, Multifork.ofι_π_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, Opens.mayerVietorisSquare'_toSquare, Opens.coe_mayerVietorisSquare_X₄, CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf, MulticospanIndex.multicospan_obj, Multifork.hom_comp_ι, MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, Multifork.pi_condition_assoc, MulticospanIndex.ofPiForkFunctor_map_hom, Multifork.ext_inv_hom, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, CategoryTheory.Sheaf.instIsRightAdjointSheafComposeOfHasWeakSheafify, Wedge.condition_assoc, CategoryTheory.Functor.SmallCategories.instPreservesFiniteLimitsSheafSheafPullbackOfRepresentablyFlat, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, MulticospanIndex.multiforkOfParallelHomsEquivFork_functor_obj_ι, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.isSheaf_iff, CategoryTheory.Presheaf.isLocallyInjective_toPlus, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, Multifork.hom_comp_ι_assoc, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, Multifork.app_right_eq_ι_comp_fst, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map, Condensed.instAB4CondensedMod, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, Multifork.toPiFork_π_app_zero, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, Multifork.toSections_fac, WalkingMulticospan.Hom.id_eq_id, Multifork.isLimit_types_iff, MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, Multifork.condition_assoc, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.liftAux_fac, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac, Multifork.pi_condition, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso_hom
WalkingMultispan 📖CompData
132 mathmath: CategoryTheory.GlueData.diagramIso_app_right, WalkingMultispan.functorExt_hom_app, TopCat.GlueData.preimage_image_eq_image, TopCat.GlueData.π_surjective, Multicofork.ofπ_ι_app, TopCat.GlueData.open_image_open, MultispanIndex.toLinearOrderMultispanIso_inv_app, MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, TopCat.GlueData.ι_fromOpenSubsetsGlue, MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Functor.CoconeTypes.isMulticoequalizer_iff, CategoryTheory.GlueData.types_π_surjective, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersion, MultispanIndex.toLinearOrderMultispanIso_hom_app, Multicofork.π_comp_hom_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.isOpen_iff, TopCat.GlueData.ι_fromOpenSubsetsGlue_apply, MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, Cowedge.IsColimit.π_desc_assoc, Multicofork.snd_app_right_assoc, SSet.horn₃₁.desc.multicofork_pt, Multicofork.toSigmaCofork_pt, Multicofork.condition_assoc, MultispanIndex.multispanMapIso_inv_app, MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, Cowedge.IsColimit.π_desc, Cowedge.condition_assoc, MultispanIndex.multispan_map_fst, AlgebraicGeometry.Scheme.GlueData.instPreservesColimitTopCatWalkingMultispanProdJMultispanDiagramForgetToTop, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, SSet.horn₃₁.desc.multicofork_π_two_assoc, Multicofork.ext_hom_hom, SSet.horn₃₁.desc.multicofork_π_zero_assoc, Multicofork.ofSigmaCofork_pt, CategoryTheory.GlueData.diagramIso_app_left, Multicofork.π_eq_app_right, AlgebraicGeometry.Scheme.GlueData.instPreservesColimitWalkingMultispanProdJMultispanDiagramForget, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv, AlgebraicGeometry.Scheme.GlueData.instIsOpenImmersionιLocallyRingedSpaceToLocallyRingedSpaceGlueData, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, MultispanIndex.multispan_obj_right, CategoryTheory.GlueData.diagramIso_inv_app_left, MultispanIndex.ofSigmaCoforkFunctor_obj, Multicofork.map_pt, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', TopCat.GlueData.range_fromOpenSubsetsGlue, MultispanIndex.multispan_map_snd, CategoryTheory.GlueData.diagramIso_inv_app_right, Cowedge.ext_hom_hom, Cowedge.mk_pt, TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbedding, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective, Multicofork.ofπ_pt, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_pt, WalkingMultispan.functorExt_inv_app, Multicofork.map_ι_app, WalkingMultispan.instSubsingletonHomRight, AlgebraicGeometry.PresheafedSpace.GlueData.componentwise_diagram_π_isIso, Multicoequalizer.multicofork_ι_app_right', AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, TopCat.GlueData.fromOpenSubsetsGlue_injective, Multicofork.isoOfπ_hom_hom, TopCat.GlueData.ι_isOpenEmbedding, Multicofork.toSigmaCofork_π, MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt, WalkingMultispan.instLocallySmall, Multicofork.IsColimit.fac_assoc, Multicofork.fst_app_right, SSet.horn₃₂.desc.multicofork_π_zero_assoc, WalkingMultispan.inclusionOfLinearOrder_obj, WalkingMultispan.Hom.id_eq_id, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, TopCat.GlueData.preimage_range, CategoryTheory.OrthogonalReflection.D₂.hasColimitsOfShape, MultispanIndex.multispanMapIso_hom_app, MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, TopCat.GlueData.ι_mono, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv_assoc, AlgebraicGeometry.SheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.image_inter, Multicofork.ext_inv_hom, MultispanIndex.toSigmaCoforkFunctor_obj, SSet.horn₃₁.desc.multicofork_π_three_assoc, Cowedge.ext_inv_hom, TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap, Multicofork.snd_app_right, WalkingMultispan.instSmallOfLOfR, Multicofork.sigma_condition, WalkingMultispan.instIsEmptyHomRightLeft, MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_inverse, AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, CompleteLattice.MulticoequalizerDiagram.multicofork_pt, Multicofork.condition, MultispanIndex.multispan_obj_left, TopCat.GlueData.ι_jointly_surjective, MultispanIndex.toSigmaCoforkFunctor_map_hom, SSet.horn₃₂.desc.multicofork_pt, CategoryTheory.GlueData.hasColimit_multispan_comp, MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, Multicofork.sigma_condition_assoc, Multicoequalizer.multicofork_ι_app_right, Multicofork.IsColimit.isPushout, AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π, Multicofork.isoOfπ_inv_hom, TopCat.GlueData.ι_eq_iff_rel, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π, WalkingMultispan.inclusionOfLinearOrder_map, MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.GlueData.types_ι_jointly_surjective, MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, Multicofork.π_comp_hom, Multicofork.ofSigmaCofork_ι_app_left, SSet.horn₃₂.desc.multicofork_π_three_assoc, WalkingMultispan.Hom.comp_eq_comp, SSet.horn₃₂.desc.multicofork_π_one_assoc, WalkingMultispan.instSubsingletonHomLeft, MultispanIndex.ofSigmaCoforkFunctor_map_hom, TopCat.GlueData.ι_injective, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id, MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.GlueData.diagramIso_hom_app_right, MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_functor, Multicofork.IsColimit.fac, TopCat.GlueData.preimage_image_eq_image', Cowedge.condition, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, CategoryTheory.GlueData.diagramIso_hom_app_left
instUniqueLOfLinearOrderBool 📖CompOp
multicoequalizer 📖CompOp
10 mathmath: Multicoequalizer.condition, Multicoequalizer.π_desc_assoc, Multicoequalizer.ι_sigmaπ_assoc, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι_assoc, Multicoequalizer.ι_sigmaπ, Multicoequalizer.hom_ext_iff, Multicoequalizer.condition_assoc, Multicoequalizer.π_desc, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι, Multicoequalizer.instEpiSigmaπ
multiequalizer 📖CompOp
16 mathmath: Multiequalizer.condition_assoc, Multiequalizer.condition, CategoryTheory.GrothendieckTopology.diagram_obj, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, Concrete.multiequalizerEquiv_apply, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, Multiequalizer.hom_ext_iff, Multiequalizer.lift_ι_assoc, CategoryTheory.Presheaf.isSheaf_iff_multiequalizer, CategoryTheory.GrothendieckTopology.diagram_map, Multiequalizer.ιPi_π, CategoryTheory.Meq.equiv_symm_eq_apply, Multiequalizer.instMonoιPi, Multiequalizer.ιPi_π_assoc, CategoryTheory.Meq.equiv_apply, Multiequalizer.lift_ι

CategoryTheory.Limits.Multicoequalizer

Definitions

NameCategoryTheorems
desc 📖CompOp
2 mathmath: π_desc_assoc, π_desc
isoCoequalizer 📖CompOp
multicofork 📖CompOp
2 mathmath: multicofork_π, multicofork_ι_app_right
sigmaπ 📖CompOp
3 mathmath: ι_sigmaπ_assoc, ι_sigmaπ, instEpiSigmaπ
π 📖CompOp
13 mathmath: condition, π_desc_assoc, ι_sigmaπ_assoc, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι_assoc, ι_sigmaπ, multicofork_π, multicofork_ι_app_right', AlgebraicGeometry.Scheme.Pullback.gluing_ι, hom_ext_iff, condition_assoc, π_desc, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι, multicofork_ι_app_right

Theorems

NameKindAssumesProvesValidatesDepends On
condition 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.multicoequalizer
CategoryTheory.Limits.MultispanIndex.fst
π
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Limits.Multicofork.condition
condition_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.multicoequalizer
π
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
condition
hom_ext 📖CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.multicoequalizer
π
CategoryTheory.Limits.colimit.hom_ext
CategoryTheory.Limits.colimit.w
CategoryTheory.Category.assoc
hom_ext_iff 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.multicoequalizer
π
hom_ext
instEpiSigmaπ 📖mathematicalCategoryTheory.Epi
CategoryTheory.Limits.sigmaObj
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.multicoequalizer
sigmaπ
CategoryTheory.epi_comp
instHasCoequalizerFstSigmaMapSndSigmaMap
CategoryTheory.Limits.coequalizer.π_epi
CategoryTheory.epi_of_strongEpi
CategoryTheory.strongEpi_of_isIso
CategoryTheory.Iso.isIso_inv
instHasCoequalizerFstSigmaMapSndSigmaMap 📖mathematicalCategoryTheory.Limits.HasCoequalizer
CategoryTheory.Limits.sigmaObj
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanIndex.fstSigmaMap
CategoryTheory.Limits.MultispanIndex.sndSigmaMap
CategoryTheory.Limits.PreservesColimitsOfShape.preservesColimit
CategoryTheory.Functor.instPreservesColimitsOfShapeOfIsLeftAdjoint
CategoryTheory.Functor.isLeftAdjoint_of_isEquivalence
CategoryTheory.Equivalence.isEquivalence_functor
multicofork_ι_app_right 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cocone.pt
multicofork
CategoryTheory.Limits.Cocone.ι
CategoryTheory.Limits.WalkingMultispan.right
π
multicofork_ι_app_right' 📖mathematicalCategoryTheory.Limits.colimit.ι
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Limits.WalkingMultispan.right
π
multicofork_π 📖mathematicalCategoryTheory.Limits.Multicofork.π
multicofork
π
ι_sigmaπ 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.sigmaObj
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.multicoequalizer
CategoryTheory.Limits.Sigma.ι
sigmaπ
π
instHasCoequalizerFstSigmaMapSndSigmaMap
sigmaπ.eq_1
CategoryTheory.Category.assoc
CategoryTheory.Iso.comp_inv_eq
isoCoequalizer.eq_1
CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom
CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app
ι_sigmaπ_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.sigmaObj
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.Sigma.ι
CategoryTheory.Limits.multicoequalizer
sigmaπ
π
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
ι_sigmaπ
π_desc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Limits.multicoequalizer
π
desc
CategoryTheory.Limits.colimit.ι_desc
π_desc_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Limits.multicoequalizer
π
desc
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
π_desc

CategoryTheory.Limits.Multicofork

Definitions

NameCategoryTheorems
ext 📖CompOp
2 mathmath: ext_hom_hom, ext_inv_hom
isColimitToLinearOrder 📖CompOp
isoOfπ 📖CompOp
2 mathmath: isoOfπ_hom_hom, isoOfπ_inv_hom
ofLinearOrder 📖CompOp
ofSigmaCofork 📖CompOp
8 mathmath: ofSigmaCofork_ι_app_right', ofSigmaCofork_π, ofSigmaCofork_pt, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_obj, ofSigmaCofork_ι_app_right, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, ofSigmaCofork_ι_app_left, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom
ofπ 📖CompOp
4 mathmath: ofπ_ι_app, ofπ_pt, isoOfπ_hom_hom, isoOfπ_inv_hom
toLinearOrder 📖CompOp
toSigmaCofork 📖CompOp
5 mathmath: toSigmaCofork_pt, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, toSigmaCofork_π, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_obj, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom
π 📖CompOp
41 mathmath: SSet.horn₃₁.desc.multicofork_π_two, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, π_comp_hom_assoc, SSet.horn₃₂.desc.multicofork_π_one, IsColimit.isPushout.multicofork_π_eq_inr, ofSigmaCofork_ι_app_right', CategoryTheory.Limits.Cowedge.IsColimit.π_desc_assoc, snd_app_right_assoc, condition_assoc, CategoryTheory.Limits.Cowedge.IsColimit.π_desc, CategoryTheory.Limits.Cowedge.condition_assoc, SSet.horn₃₁.desc.multicofork_π_two_assoc, ofSigmaCofork_π, SSet.horn₃₁.desc.multicofork_π_zero_assoc, π_eq_app_right, ofSigmaCofork_ι_app_right, CategoryTheory.Limits.Multicoequalizer.multicofork_π, map_ι_app, CategoryTheory.Limits.Cowedge.mk_π, isoOfπ_hom_hom, toSigmaCofork_π, IsColimit.fac_assoc, fst_app_right, SSet.horn₃₂.desc.multicofork_π_zero_assoc, SSet.horn₃₁.desc.multicofork_π_three_assoc, SSet.horn₃₁.desc.multicofork_π_zero, SSet.horn₃₂.desc.multicofork_π_three, snd_app_right, sigma_condition, condition, sigma_condition_assoc, IsColimit.isPushout, IsColimit.isPushout.multicofork_π_eq_inl, isoOfπ_inv_hom, π_comp_hom, SSet.horn₃₂.desc.multicofork_π_zero, SSet.horn₃₂.desc.multicofork_π_three_assoc, SSet.horn₃₂.desc.multicofork_π_one_assoc, SSet.horn₃₁.desc.multicofork_π_three, IsColimit.fac, CategoryTheory.Limits.Cowedge.condition

Theorems

NameKindAssumesProvesValidatesDepends On
condition 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Limits.MultispanIndex.fst
π
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
snd_app_right
fst_app_right
condition_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
π
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
condition
ext_hom_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Iso.hom
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
ext
CategoryTheory.Limits.Cocone.pt
ext_inv_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Iso.inv
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
ext
CategoryTheory.Limits.Cocone.pt
fst_app_right 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.Cocone.ι
CategoryTheory.Limits.WalkingMultispan.left
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
π
CategoryTheory.Limits.Cocone.w
isoOfπ_hom_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
ofπ
CategoryTheory.Limits.Cocone.pt
π
condition
CategoryTheory.Iso.hom
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
isoOfπ
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
condition
isoOfπ_inv_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
ofπ
CategoryTheory.Limits.Cocone.pt
π
condition
CategoryTheory.Iso.inv
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
isoOfπ
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
condition
ofSigmaCofork_pt 📖mathematicalCategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
ofSigmaCofork
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit
ofSigmaCofork_ι_app_left 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cocone.pt
ofSigmaCofork
CategoryTheory.Limits.Cocone.ι
CategoryTheory.Limits.WalkingMultispan.left
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit
CategoryTheory.Limits.WalkingParallelPair.one
CategoryTheory.Limits.Cofork.π
ofSigmaCofork_ι_app_right 📖mathematicalπ
ofSigmaCofork
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit
CategoryTheory.Limits.WalkingParallelPair.one
CategoryTheory.Limits.Cofork.π
ofSigmaCofork_π
ofSigmaCofork_ι_app_right' 📖mathematicalπ
ofSigmaCofork
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit
CategoryTheory.Limits.WalkingParallelPair.one
CategoryTheory.Limits.Cofork.π
ofSigmaCofork_π
ofSigmaCofork_π 📖mathematicalπ
ofSigmaCofork
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit
CategoryTheory.Limits.WalkingParallelPair.one
CategoryTheory.Limits.Cofork.π
ofπ_pt 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
ofπ
ofπ_ι_app 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cocone.ι
ofπ
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Limits.WalkingMultispan.left
sigma_condition 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit
CategoryTheory.Limits.Cofan.IsColimit.desc
π
CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cofan.IsColimit.hom_ext
CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit_assoc
CategoryTheory.Limits.Cofan.IsColimit.fac
condition
CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit_assoc
sigma_condition_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Limits.Cofan.IsColimit.desc
π
CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
sigma_condition
snd_app_right 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.Cocone.ι
CategoryTheory.Limits.WalkingMultispan.left
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
π
CategoryTheory.Limits.Cocone.w
snd_app_right_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Limits.WalkingMultispan.left
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cocone.pt
CategoryTheory.NatTrans.app
CategoryTheory.Limits.Cocone.ι
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
π
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
snd_app_right
toSigmaCofork_pt 📖mathematicalCategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit
toSigmaCofork
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
toSigmaCofork_π 📖mathematicalCategoryTheory.Limits.Cofork.π
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.R
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit
toSigmaCofork
CategoryTheory.Limits.Cofan.IsColimit.desc
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
π
π_comp_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
π
CategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.CoconeMorphism.w
π_comp_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
π
CategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
π_comp_hom
π_eq_app_right 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.Cocone.ι
CategoryTheory.Limits.WalkingMultispan.right
π

CategoryTheory.Limits.Multicofork.IsColimit

Definitions

NameCategoryTheorems
desc 📖CompOp
2 mathmath: fac_assoc, fac
mk 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
fac 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Limits.Multicofork.π
desc
CategoryTheory.Limits.IsColimit.fac
fac_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Limits.Multicofork.π
desc
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
fac
hom_ext 📖CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Limits.Multicofork.π
CategoryTheory.Limits.IsColimit.hom_ext
CategoryTheory.Limits.Multicofork.fst_app_right
CategoryTheory.Limits.Multicofork.condition
CategoryTheory.Category.assoc
mk_desc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Limits.MultispanIndex.multispan
CategoryTheory.Limits.Multicofork.π
CategoryTheory.Limits.IsColimit.desc

CategoryTheory.Limits.MulticospanIndex

Definitions

NameCategoryTheorems
fst 📖CompOp
18 mathmath: CategoryTheory.Limits.Multiequalizer.condition_assoc, CategoryTheory.Limits.multicospanIndexEnd_fst, CategoryTheory.GrothendieckTopology.Cover.index_fst, CategoryTheory.Limits.Multiequalizer.condition, ofParallelHoms_fst, CategoryTheory.PreOneHypercover.multicospanIndex_fst, multicospan_map, sectionsEquiv_apply_coe, fstPiMapOfIsLimit_proj, fstPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.Multifork.condition, fstPiMap_π_assoc, multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_fst, sections.property, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, fstPiMap_π, CategoryTheory.Limits.Multifork.condition_assoc
fstPiMap 📖CompOp
14 mathmath: multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, multiforkEquivPiFork_functor_map_hom, CategoryTheory.Limits.Multiequalizer.instHasEqualizerFstPiMapSndPiMap, parallelPairDiagram_map, multiforkEquivPiFork_inverse_map_hom, multiforkEquivPiFork_functor_obj_pt, multiforkEquivPiFork_counitIso_inv_app_hom, fstPiMap_π_assoc, multiforkEquivPiFork_functor_obj_π_app, multiforkEquivPiFork_inverse_obj_π_app, multiforkEquivPiFork_inverse_obj_pt, fstPiMap_π, multiforkEquivPiFork_unitIso_hom_app_hom
fstPiMapOfIsLimit 📖CompOp
30 mathmath: multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, multiforkEquivPiFork_functor_map_hom, toPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.toPiFork_pt, multiforkEquivPiForkOfIsLimit_functor, multiforkEquivPiFork_inverse_map_hom, fstPiMapOfIsLimit_proj, multiforkEquivPiForkOfIsLimit_counitIso, multiforkEquivPiFork_functor_obj_pt, fstPiMapOfIsLimit_proj_assoc, multiforkEquivPiFork_counitIso_inv_app_hom, parallelPairDiagramOfIsLimit_map, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.Multifork.ofPiFork_pt, multiforkEquivPiFork_functor_obj_π_app, toPiForkFunctor_obj, multiforkEquivPiForkOfIsLimit_inverse, multiforkEquivPiFork_inverse_obj_π_app, multiforkEquivPiFork_inverse_obj_pt, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, ofPiForkFunctor_obj, multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.Multifork.pi_condition_assoc, ofPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.ofPiFork_ι, CategoryTheory.Limits.Multifork.toPiFork_π_app_zero, multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Limits.Multifork.pi_condition
left 📖CompOp
74 mathmath: CategoryTheory.Limits.Multiequalizer.condition_assoc, CategoryTheory.GrothendieckTopology.Cover.index_left, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac, multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Limits.Multiequalizer.condition, sndPiMapOfIsLimit_proj, multiforkEquivPiFork_functor_map_hom, multicospan_map, sndPiMap_π_assoc, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply, CategoryTheory.Limits.Multiequalizer.instHasEqualizerFstPiMapSndPiMap, parallelPairDiagram_map, toPiForkFunctor_map_hom, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, CategoryTheory.Limits.Multiequalizer.hom_ext_iff, CategoryTheory.Limits.Multifork.toPiFork_pt, multiforkEquivPiForkOfIsLimit_functor, CategoryTheory.Limits.Wedge.IsLimit.lift_ι, ofParallelHoms_left, sndPiMap_π, parallelPairDiagram_obj, multiforkEquivPiFork_inverse_map_hom, fstPiMapOfIsLimit_proj, multiforkEquivPiForkOfIsLimit_counitIso, multiforkEquivPiFork_functor_obj_pt, fstPiMapOfIsLimit_proj_assoc, multiforkEquivPiFork_counitIso_inv_app_hom, parallelPairDiagramOfIsLimit_map, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.Wedge.condition, CategoryTheory.Limits.Multifork.condition, CategoryTheory.Limits.Wedge.IsLimit.lift_ι_assoc, CategoryTheory.PreOneHypercover.multicospanIndex_left, fstPiMap_π_assoc, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.Multifork.ofPiFork_pt, multiforkEquivPiFork_functor_obj_π_app, toPiForkFunctor_obj, CategoryTheory.Limits.Multiequalizer.ιPi_π, multiforkEquivPiForkOfIsLimit_inverse, multiforkEquivPiFork_inverse_obj_π_app, multiforkEquivPiFork_inverse_obj_pt, sndPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.multicospanIndexEnd_left, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, CategoryTheory.GrothendieckTopology.diagramNatTrans_app, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, ofPiForkFunctor_obj, parallelPairDiagramOfIsLimit_obj, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_left, multicospan_obj, CategoryTheory.Meq.equiv_symm_eq_apply, CategoryTheory.Limits.Multifork.hom_comp_ι, multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.Multifork.pi_condition_assoc, ofPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.ofPiFork_ι, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, CategoryTheory.Limits.Multiequalizer.instMonoιPi, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CategoryTheory.Limits.Multifork.hom_comp_ι_assoc, CategoryTheory.Limits.Multiequalizer.ιPi_π_assoc, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, CategoryTheory.Meq.equiv_apply, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, CategoryTheory.Limits.Multifork.toPiFork_π_app_zero, fstPiMap_π, multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Limits.Multifork.condition_assoc, CategoryTheory.Limits.Multifork.pi_condition
multicospan 📖CompOp
109 mathmath: CategoryTheory.Limits.Wedge.mk_pt, multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_apply_val, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map', multiforkEquivPiFork_functor_map_hom, Opens.mayerVietorisSquare_X₃, CondensedMod.isDiscrete_tfae, CategoryTheory.Limits.Multifork.ext_hom_hom, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, multicospan_map, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff, sectionsEquiv_symm_apply_val, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, sectionsEquiv_apply_coe, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, toPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.ofι_pt, CategoryTheory.Presheaf.isLocallySurjective_toSheafify, CategoryTheory.Limits.Multiequalizer.multifork_π_app_left, CondensedMod.isDiscrete_iff_isDiscrete_forget, CategoryTheory.Limits.Multifork.toPiFork_pt, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, multiforkEquivPiForkOfIsLimit_functor, CategoryTheory.Limits.Wedge.IsLimit.lift_ι, CategoryTheory.Limits.Wedge.ext_hom_hom, multiforkOfParallelHomsEquivFork_inverse_obj_ι, CategoryTheory.Presheaf.isLocallyInjective_toSheafify, multiforkEquivPiFork_inverse_map_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, CategoryTheory.Presheaf.isSheaf_iff_of_isGeneratedByOneHypercovers, multiforkEquivPiForkOfIsLimit_counitIso, multiforkEquivPiFork_functor_obj_pt, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_inv_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', multiforkEquivPiFork_counitIso_inv_app_hom, Opens.mayerVietorisSquare_X₂, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.Wedge.condition, CategoryTheory.Limits.Multifork.app_left_eq_ι, CategoryTheory.Limits.Multifork.condition, CategoryTheory.Limits.Wedge.IsLimit.lift_ι_assoc, Opens.coe_mayerVietorisSquare_X₁, CategoryTheory.Limits.Multifork.IsLimit.fac_assoc, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMap_app, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.Multifork.ofPiFork_pt, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_symm_apply_val, CategoryTheory.Presheaf.isSheaf_iff_multifork, CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf, multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso_inv, toPiForkFunctor_obj, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_app, multiforkEquivPiForkOfIsLimit_inverse, multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac_assoc, CondensedSet.isDiscrete_tfae, CategoryTheory.Limits.Multifork.IsLimit.fac, multiforkEquivPiFork_inverse_obj_pt, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, CategoryTheory.Limits.Wedge.ext_inv_hom, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CondensedSet.LocallyConstant.instFaithfulCondensedTypeDiscrete, CondensedSet.LocallyConstant.instFullCondensedTypeDiscrete, CategoryTheory.Presheaf.isLocallySurjective_toPlus, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, ofPiForkFunctor_obj, CategoryTheory.Limits.Multifork.ofι_π_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, Opens.mayerVietorisSquare'_toSquare, Opens.coe_mayerVietorisSquare_X₄, CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf, multicospan_obj, CategoryTheory.Limits.Multifork.hom_comp_ι, multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.Multifork.pi_condition_assoc, ofPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.ext_inv_hom, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, CategoryTheory.Sheaf.instIsRightAdjointSheafComposeOfHasWeakSheafify, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.Functor.SmallCategories.instPreservesFiniteLimitsSheafSheafPullbackOfRepresentablyFlat, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, multiforkOfParallelHomsEquivFork_functor_obj_ι, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.isSheaf_iff, CategoryTheory.Presheaf.isLocallyInjective_toPlus, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, CategoryTheory.Limits.Multifork.hom_comp_ι_assoc, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map, Condensed.instAB4CondensedMod, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, CategoryTheory.Limits.Multifork.toPiFork_π_app_zero, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, CategoryTheory.Limits.Multifork.toSections_fac, CategoryTheory.Limits.Multifork.isLimit_types_iff, multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Limits.Multifork.condition_assoc, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.liftAux_fac, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac, CategoryTheory.Limits.Multifork.pi_condition, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso_hom
multiforkEquivPiFork 📖CompOp
10 mathmath: multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, multiforkEquivPiFork_functor_map_hom, multiforkEquivPiFork_inverse_map_hom, multiforkEquivPiFork_functor_obj_pt, multiforkEquivPiFork_counitIso_inv_app_hom, multiforkEquivPiFork_functor_obj_π_app, multiforkEquivPiFork_inverse_obj_π_app, multiforkEquivPiFork_inverse_obj_pt, multiforkEquivPiFork_unitIso_hom_app_hom
multiforkEquivPiForkOfIsLimit 📖CompOp
4 mathmath: multiforkEquivPiForkOfIsLimit_functor, multiforkEquivPiForkOfIsLimit_counitIso, multiforkEquivPiForkOfIsLimit_inverse, multiforkEquivPiForkOfIsLimit_unitIso
multiforkOfParallelHomsEquivFork 📖CompOp
2 mathmath: multiforkOfParallelHomsEquivFork_inverse_obj_ι, multiforkOfParallelHomsEquivFork_functor_obj_ι
ofParallelHoms 📖CompOp
6 mathmath: ofParallelHoms_fst, multiforkOfParallelHomsEquivFork_inverse_obj_ι, ofParallelHoms_left, ofParallelHoms_right, multiforkOfParallelHomsEquivFork_functor_obj_ι, ofParallelHoms_snd
ofPiForkFunctor 📖CompOp
9 mathmath: multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, multiforkEquivPiForkOfIsLimit_counitIso, multiforkEquivPiFork_counitIso_inv_app_hom, multiforkEquivPiForkOfIsLimit_inverse, ofPiForkFunctor_obj, multiforkEquivPiForkOfIsLimit_unitIso, ofPiForkFunctor_map_hom, multiforkEquivPiFork_unitIso_hom_app_hom
parallelPairDiagram 📖CompOp
2 mathmath: parallelPairDiagram_map, parallelPairDiagram_obj
parallelPairDiagramOfIsLimit 📖CompOp
2 mathmath: parallelPairDiagramOfIsLimit_map, parallelPairDiagramOfIsLimit_obj
right 📖CompOp
53 mathmath: CategoryTheory.Limits.Multiequalizer.condition_assoc, multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Limits.Multiequalizer.condition, sndPiMapOfIsLimit_proj, multiforkEquivPiFork_functor_map_hom, multicospan_map, sndPiMap_π_assoc, CategoryTheory.Limits.Multiequalizer.instHasEqualizerFstPiMapSndPiMap, parallelPairDiagram_map, CategoryTheory.Limits.multicospanIndexEnd_right, CategoryTheory.PreOneHypercover.multicospanIndex_right, toPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.toPiFork_pt, multiforkEquivPiForkOfIsLimit_functor, sndPiMap_π, ofParallelHoms_right, parallelPairDiagram_obj, multiforkEquivPiFork_inverse_map_hom, fstPiMapOfIsLimit_proj, multiforkEquivPiForkOfIsLimit_counitIso, multiforkEquivPiFork_functor_obj_pt, fstPiMapOfIsLimit_proj_assoc, multiforkEquivPiFork_counitIso_inv_app_hom, parallelPairDiagramOfIsLimit_map, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.Multifork.condition, fstPiMap_π_assoc, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.Multifork.ofPiFork_pt, multiforkEquivPiFork_functor_obj_π_app, toPiForkFunctor_obj, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_right, multiforkEquivPiForkOfIsLimit_inverse, multiforkEquivPiFork_inverse_obj_π_app, multiforkEquivPiFork_inverse_obj_pt, sndPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, ofPiForkFunctor_obj, parallelPairDiagramOfIsLimit_obj, CategoryTheory.GrothendieckTopology.Cover.index_right, multicospan_obj, multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.Multifork.pi_condition_assoc, ofPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.ofPiFork_ι, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, CategoryTheory.Limits.Multifork.toPiFork_π_app_zero, fstPiMap_π, multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Limits.Multifork.condition_assoc, CategoryTheory.Limits.Multifork.pi_condition
snd 📖CompOp
17 mathmath: CategoryTheory.Limits.Multiequalizer.condition_assoc, CategoryTheory.Limits.Multiequalizer.condition, sndPiMapOfIsLimit_proj, multicospan_map, sndPiMap_π_assoc, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.PreOneHypercover.multicospanIndex_snd, sndPiMap_π, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.Multifork.condition, sndPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, CategoryTheory.GrothendieckTopology.Cover.index_snd, sections.property, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_snd, ofParallelHoms_snd, CategoryTheory.Limits.Multifork.condition_assoc
sndPiMap 📖CompOp
14 mathmath: multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, multiforkEquivPiFork_functor_map_hom, sndPiMap_π_assoc, CategoryTheory.Limits.Multiequalizer.instHasEqualizerFstPiMapSndPiMap, parallelPairDiagram_map, sndPiMap_π, multiforkEquivPiFork_inverse_map_hom, multiforkEquivPiFork_functor_obj_pt, multiforkEquivPiFork_counitIso_inv_app_hom, multiforkEquivPiFork_functor_obj_π_app, multiforkEquivPiFork_inverse_obj_π_app, multiforkEquivPiFork_inverse_obj_pt, multiforkEquivPiFork_unitIso_hom_app_hom
sndPiMapOfIsLimit 📖CompOp
30 mathmath: multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, sndPiMapOfIsLimit_proj, multiforkEquivPiFork_functor_map_hom, toPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.toPiFork_pt, multiforkEquivPiForkOfIsLimit_functor, multiforkEquivPiFork_inverse_map_hom, multiforkEquivPiForkOfIsLimit_counitIso, multiforkEquivPiFork_functor_obj_pt, multiforkEquivPiFork_counitIso_inv_app_hom, parallelPairDiagramOfIsLimit_map, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.Multifork.ofPiFork_pt, multiforkEquivPiFork_functor_obj_π_app, toPiForkFunctor_obj, multiforkEquivPiForkOfIsLimit_inverse, multiforkEquivPiFork_inverse_obj_π_app, multiforkEquivPiFork_inverse_obj_pt, sndPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, ofPiForkFunctor_obj, multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.Multifork.pi_condition_assoc, ofPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.ofPiFork_ι, CategoryTheory.Limits.Multifork.toPiFork_π_app_zero, multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Limits.Multifork.pi_condition
toPiForkFunctor 📖CompOp
9 mathmath: multiforkEquivPiFork_counitIso_hom_app_hom, multiforkEquivPiFork_unitIso_inv_app_hom, toPiForkFunctor_map_hom, multiforkEquivPiForkOfIsLimit_functor, multiforkEquivPiForkOfIsLimit_counitIso, multiforkEquivPiFork_counitIso_inv_app_hom, toPiForkFunctor_obj, multiforkEquivPiForkOfIsLimit_unitIso, multiforkEquivPiFork_unitIso_hom_app_hom

Theorems

NameKindAssumesProvesValidatesDepends On
fstPiMapOfIsLimit_proj 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.Fan.proj
CategoryTheory.Limits.MulticospanShape.fst
fst
CategoryTheory.Limits.Fan.IsLimit.fac
fstPiMapOfIsLimit_proj_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.Fan.proj
CategoryTheory.Limits.MulticospanShape.fst
fst
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
fstPiMapOfIsLimit_proj
fstPiMap_π 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMap
CategoryTheory.Limits.Pi.π
CategoryTheory.Limits.MulticospanShape.fst
fst
fstPiMapOfIsLimit_proj
fstPiMap_π_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMap
CategoryTheory.Limits.Pi.π
CategoryTheory.Limits.MulticospanShape.fst
fst
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
fstPiMap_π
multicospan_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
left
right
CategoryTheory.CategoryStruct.id
fst
snd
multicospan_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
left
right
multiforkEquivPiForkOfIsLimit_counitIso 📖mathematicalCategoryTheory.Equivalence.counitIso
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
multiforkEquivPiForkOfIsLimit
CategoryTheory.NatIso.ofComponents
CategoryTheory.Functor.comp
ofPiForkFunctor
toPiForkFunctor
CategoryTheory.Functor.id
CategoryTheory.Limits.Fork.ext
CategoryTheory.Functor.obj
CategoryTheory.Iso.refl
multiforkEquivPiForkOfIsLimit_functor 📖mathematicalCategoryTheory.Equivalence.functor
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
multiforkEquivPiForkOfIsLimit
toPiForkFunctor
multiforkEquivPiForkOfIsLimit_inverse 📖mathematicalCategoryTheory.Equivalence.inverse
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
multiforkEquivPiForkOfIsLimit
ofPiForkFunctor
multiforkEquivPiForkOfIsLimit_unitIso 📖mathematicalCategoryTheory.Equivalence.unitIso
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
multiforkEquivPiForkOfIsLimit
CategoryTheory.NatIso.ofComponents
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
toPiForkFunctor
ofPiForkFunctor
CategoryTheory.Limits.Cones.ext
CategoryTheory.Functor.obj
CategoryTheory.Iso.refl
multiforkEquivPiFork_counitIso_hom_app_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.limit.cone
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.limit.isLimit
sndPiMapOfIsLimit
CategoryTheory.Functor.obj
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.category
CategoryTheory.Functor.comp
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
ofPiForkFunctor
toPiForkFunctor
CategoryTheory.Functor.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.counitIso
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.limit
multiforkEquivPiFork_counitIso_inv_app_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.limit.cone
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.limit.isLimit
sndPiMapOfIsLimit
CategoryTheory.Functor.obj
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.category
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
ofPiForkFunctor
toPiForkFunctor
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.counitIso
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.limit
multiforkEquivPiFork_functor_map_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.limit.cone
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.limit.isLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Multifork.toPiFork
CategoryTheory.Functor.map
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.Fork
CategoryTheory.Equivalence.functor
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
multiforkEquivPiFork_functor_obj_pt 📖mathematicalCategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.limit.cone
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.limit.isLimit
sndPiMapOfIsLimit
CategoryTheory.Functor.obj
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.Fork
CategoryTheory.Equivalence.functor
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
multiforkEquivPiFork_functor_obj_π_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.limit.cone
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.limit.isLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Cone.π
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.Fork
CategoryTheory.Equivalence.functor
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
CategoryTheory.Limits.WalkingParallelPair.zero
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.limit
CategoryTheory.Limits.Fan.IsLimit.lift
CategoryTheory.Limits.Multifork.ι
CategoryTheory.Limits.WalkingParallelPair.one
CategoryTheory.CategoryStruct.comp
CategoryTheory.Limits.Multifork.pi_condition
multiforkEquivPiFork_inverse_map_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.Multifork.ofPiFork
CategoryTheory.Limits.limit.cone
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
CategoryTheory.Limits.limit.isLimit
CategoryTheory.Functor.map
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
fstPiMapOfIsLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Multifork
CategoryTheory.Equivalence.inverse
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
CategoryTheory.Limits.limit
multiforkEquivPiFork_inverse_obj_pt 📖mathematicalCategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Functor.obj
CategoryTheory.Limits.Fork
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.limit.cone
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.limit.isLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Multifork
CategoryTheory.Equivalence.inverse
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
CategoryTheory.Limits.limit
multiforkEquivPiFork_inverse_obj_π_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.limit.cone
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.limit.isLimit
sndPiMapOfIsLimit
multicospan
CategoryTheory.Limits.Cone.π
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.Multifork
CategoryTheory.Equivalence.inverse
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.limit
CategoryTheory.CategoryStruct.comp
CategoryTheory.Limits.Fork.ι
CategoryTheory.Limits.Fan.proj
CategoryTheory.Limits.MulticospanShape.fst
fst
fstPiMapOfIsLimit_proj
multiforkEquivPiFork_unitIso_hom_app_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Functor.obj
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.limit.cone
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.limit.isLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
toPiForkFunctor
ofPiForkFunctor
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.unitIso
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
multiforkEquivPiFork_unitIso_inv_app_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Functor.obj
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
CategoryTheory.Functor.comp
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.limit.cone
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
CategoryTheory.Limits.limit.isLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
toPiForkFunctor
ofPiForkFunctor
CategoryTheory.Functor.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.unitIso
CategoryTheory.Limits.piObj
fstPiMap
sndPiMap
multiforkEquivPiFork
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
multiforkOfParallelHomsEquivFork_functor_obj_ι 📖mathematicalCategoryTheory.Limits.Fork.ι
CategoryTheory.Functor.obj
CategoryTheory.Limits.Multifork
ofParallelHoms
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.Fork
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Equivalence.functor
multiforkOfParallelHomsEquivFork
CategoryTheory.Limits.Multifork.ι
CategoryTheory.Limits.MulticospanShape.L
Unique.instInhabited
CategoryTheory.Limits.Fan.IsLimit.fac
multiforkOfParallelHomsEquivFork_inverse_obj_ι 📖mathematicalCategoryTheory.Limits.Multifork.ι
ofParallelHoms
CategoryTheory.Functor.obj
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Equivalence.inverse
multiforkOfParallelHomsEquivFork
CategoryTheory.Limits.Fork.ι
CategoryTheory.Category.comp_id
ofParallelHoms_fst 📖mathematicalfst
ofParallelHoms
ofParallelHoms_left 📖mathematicalleft
ofParallelHoms
ofParallelHoms_right 📖mathematicalright
ofParallelHoms
ofParallelHoms_snd 📖mathematicalsnd
ofParallelHoms
ofPiForkFunctor_map_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.Multifork.ofPiFork
CategoryTheory.Functor.map
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Multifork
ofPiForkFunctor
ofPiForkFunctor_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
ofPiForkFunctor
CategoryTheory.Limits.Multifork.ofPiFork
parallelPairDiagramOfIsLimit_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
parallelPairDiagramOfIsLimit
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
CategoryTheory.CategoryStruct.id
fstPiMapOfIsLimit
sndPiMapOfIsLimit
parallelPairDiagramOfIsLimit_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
parallelPairDiagramOfIsLimit
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
parallelPairDiagram_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
parallelPairDiagram
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
left
CategoryTheory.Limits.MulticospanShape.R
right
CategoryTheory.CategoryStruct.id
fstPiMap
sndPiMap
parallelPairDiagram_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
parallelPairDiagram
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
left
CategoryTheory.Limits.MulticospanShape.R
right
sndPiMapOfIsLimit_proj 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
sndPiMapOfIsLimit
CategoryTheory.Limits.Fan.proj
CategoryTheory.Limits.MulticospanShape.snd
snd
CategoryTheory.Limits.Fan.IsLimit.fac
sndPiMapOfIsLimit_proj_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
sndPiMapOfIsLimit
CategoryTheory.Limits.Fan.proj
CategoryTheory.Limits.MulticospanShape.snd
snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
sndPiMapOfIsLimit_proj
sndPiMap_π 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
left
CategoryTheory.Limits.MulticospanShape.R
right
sndPiMap
CategoryTheory.Limits.Pi.π
CategoryTheory.Limits.MulticospanShape.snd
snd
sndPiMapOfIsLimit_proj
sndPiMap_π_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
left
CategoryTheory.Limits.MulticospanShape.R
right
sndPiMap
CategoryTheory.Limits.Pi.π
CategoryTheory.Limits.MulticospanShape.snd
snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
sndPiMap_π
toPiForkFunctor_map_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.Multifork.toPiFork
CategoryTheory.Functor.map
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.Fork
toPiForkFunctor
toPiForkFunctor_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
multicospan
CategoryTheory.Limits.Fork
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MulticospanShape.R
right
fstPiMapOfIsLimit
sndPiMapOfIsLimit
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
toPiForkFunctor
CategoryTheory.Limits.Multifork.toPiFork

CategoryTheory.Limits.MulticospanShape

Definitions

NameCategoryTheorems
L 📖CompOp
49 mathmath: CategoryTheory.Limits.multicospanShapeEnd_L, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanShape_L, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π_assoc, CategoryTheory.Limits.Multiequalizer.instHasEqualizerFstPiMapSndPiMap, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_map, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.toPiFork_pt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_functor, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj_assoc, CategoryTheory.PreOneHypercover.multicospanShape_L, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_map, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π_assoc, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.Multifork.ofPiFork_pt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_obj, CategoryTheory.Limits.Multiequalizer.ιPi_π, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_inverse, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_pt, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj_assoc, prod_L, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_obj, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.Multifork.pi_condition_assoc, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.ofPiFork_ι, CategoryTheory.Limits.Multiequalizer.instMonoιPi, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_functor_obj_ι, CategoryTheory.Limits.Multiequalizer.ιPi_π_assoc, CategoryTheory.Limits.Multifork.toPiFork_π_app_zero, CategoryTheory.GrothendieckTopology.Cover.shape_L, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Limits.Multifork.pi_condition
R 📖CompOp
45 mathmath: CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π_assoc, CategoryTheory.Limits.Multiequalizer.instHasEqualizerFstPiMapSndPiMap, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_map, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.toPiFork_pt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_functor, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_map, CategoryTheory.PreOneHypercover.multicospanShape_R, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π_assoc, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.Multifork.ofPiFork_pt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Limits.multicospanShapeEnd_R, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_inverse, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, prod_R, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_pt, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_obj, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.Multifork.pi_condition_assoc, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanShape_R, CategoryTheory.Limits.Multifork.ofPiFork_ι, CategoryTheory.Limits.Multifork.toPiFork_π_app_zero, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.GrothendieckTopology.Cover.shape_R, CategoryTheory.Limits.Multifork.pi_condition
fst 📖CompOp
22 mathmath: CategoryTheory.Limits.Multiequalizer.condition_assoc, CategoryTheory.Limits.multicospanIndexEnd_fst, CategoryTheory.GrothendieckTopology.Cover.index_fst, CategoryTheory.Limits.Multiequalizer.condition, CategoryTheory.PreOneHypercover.multicospanIndex_fst, prod_fst, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_apply_coe, CategoryTheory.PreOneHypercover.multicospanShape_fst, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanShape_fst, CategoryTheory.GrothendieckTopology.Cover.shape_fst, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj, CategoryTheory.Limits.multicospanShapeEnd_fst, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.Multifork.condition, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_fst, CategoryTheory.Limits.MulticospanIndex.sections.property, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, CategoryTheory.Meq.condition, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π, CategoryTheory.Limits.Multifork.condition_assoc
prod 📖CompOp
4 mathmath: prod_fst, prod_snd, prod_R, prod_L
snd 📖CompOp
20 mathmath: CategoryTheory.Limits.Multiequalizer.condition_assoc, CategoryTheory.Limits.Multiequalizer.condition, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj, CategoryTheory.GrothendieckTopology.Cover.shape_snd, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π_assoc, CategoryTheory.Limits.multicospanShapeEnd_snd, prod_snd, CategoryTheory.PreOneHypercover.multicospanIndex_snd, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanShape_snd, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.Multifork.condition, CategoryTheory.PreOneHypercover.multicospanShape_snd, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, CategoryTheory.GrothendieckTopology.Cover.index_snd, CategoryTheory.Limits.MulticospanIndex.sections.property, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_snd, CategoryTheory.Meq.condition, CategoryTheory.Limits.Multifork.condition_assoc

Theorems

NameKindAssumesProvesValidatesDepends On
prod_L 📖mathematicalL
prod
prod_R 📖mathematicalR
prod
prod_fst 📖mathematicalfst
prod
prod_snd 📖mathematicalsnd
prod

CategoryTheory.Limits.Multiequalizer

Definitions

NameCategoryTheorems
isoEqualizer 📖CompOp
multifork 📖CompOp
2 mathmath: multifork_π_app_left, multifork_ι
ι 📖CompOp
20 mathmath: condition_assoc, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac, condition, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, hom_ext_iff, multifork_π_app_left, multifork_ι, lift_ι_assoc, CategoryTheory.GrothendieckTopology.diagram_map, CategoryTheory.GrothendieckTopology.diagramPullback_app, ιPi_π, CategoryTheory.GrothendieckTopology.diagramNatTrans_app, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, CategoryTheory.Meq.equiv_symm_eq_apply, ιPi_π_assoc, CategoryTheory.Meq.equiv_apply, lift_ι
ιPi 📖CompOp
3 mathmath: ιPi_π, instMonoιPi, ιPi_π_assoc

Theorems

NameKindAssumesProvesValidatesDepends On
condition 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.multiequalizer
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
ι
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Limits.Multifork.condition
condition_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.multiequalizer
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
ι
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
condition
hom_ext 📖CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.multiequalizer
CategoryTheory.Limits.MulticospanIndex.left
ι
CategoryTheory.Limits.Multifork.IsLimit.hom_ext
hom_ext_iff 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.multiequalizer
CategoryTheory.Limits.MulticospanIndex.left
ι
hom_ext
instHasEqualizerFstPiMapSndPiMap 📖mathematicalCategoryTheory.Limits.HasEqualizer
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fstPiMap
CategoryTheory.Limits.MulticospanIndex.sndPiMap
CategoryTheory.Limits.PreservesLimitsOfShape.preservesLimit
CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint
CategoryTheory.Functor.isRightAdjoint_of_isEquivalence
CategoryTheory.Equivalence.isEquivalence_functor
instMonoιPi 📖mathematicalCategoryTheory.Mono
CategoryTheory.Limits.multiequalizer
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.Limits.MulticospanIndex.left
ιPi
CategoryTheory.mono_comp
instHasEqualizerFstPiMapSndPiMap
CategoryTheory.mono_of_strongMono
CategoryTheory.strongMono_of_isIso
CategoryTheory.Iso.isIso_hom
CategoryTheory.Limits.equalizer.ι_mono
lift_ι 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Limits.multiequalizer
lift
ι
CategoryTheory.Limits.limit.lift_π
lift_ι_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Limits.multiequalizer
lift
ι
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
lift_ι
multifork_ι 📖mathematicalCategoryTheory.Limits.Multifork.ι
multifork
ι
multifork_π_app_left 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.MulticospanIndex.multicospan
multifork
CategoryTheory.Limits.Cone.π
CategoryTheory.Limits.WalkingMulticospan.left
ι
ιPi_π 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.multiequalizer
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.Limits.MulticospanIndex.left
ιPi
CategoryTheory.Limits.Pi.π
ι
instHasEqualizerFstPiMapSndPiMap
ιPi.eq_1
CategoryTheory.Category.assoc
CategoryTheory.Iso.eq_inv_comp
isoEqualizer.eq_1
CategoryTheory.Limits.limit.isoLimitCone_inv_π
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app
ιPi_π_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.multiequalizer
CategoryTheory.Limits.piObj
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.Limits.MulticospanIndex.left
ιPi
CategoryTheory.Limits.Pi.π
ι
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
ιPi_π

CategoryTheory.Limits.Multifork

Definitions

NameCategoryTheorems
ext 📖CompOp
2 mathmath: ext_hom_hom, ext_inv_hom
isLimitEquivOfIsos 📖CompOp
isoOfι 📖CompOp
2 mathmath: isoOfι_hom_hom, isoOfι_inv_hom
ofPiFork 📖CompOp
7 mathmath: CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, ofPiFork_pt, ofPiFork_π_app_right, ofPiFork_π_app_left, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_obj, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, ofPiFork_ι
ofι 📖CompOp
5 mathmath: isoOfι_hom_hom, isoOfι_inv_hom, ofι_pt, ofι_π_app, ι_ofι
toPiFork 📖CompOp
6 mathmath: CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, toPiFork_pt, toPiFork_π_app_one, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_obj, toPiFork_π_app_zero
ι 📖CompOp
45 mathmath: IsLimit.sectionsEquiv_apply_val, toSections_val, CategoryTheory.Limits.Wedge.mk_ι, isoOfι_hom_hom, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, isoOfι_inv_hom, CategoryTheory.PreOneHypercover.multifork_ι, CategoryTheory.Limits.Wedge.IsLimit.lift_ι, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_inverse_obj_ι, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, CategoryTheory.Limits.Multiequalizer.multifork_ι, app_right_eq_ι_comp_snd, CategoryTheory.Limits.Wedge.condition, app_left_eq_ι, condition, CategoryTheory.Limits.Wedge.IsLimit.lift_ι_assoc, IsLimit.fac_assoc, toPiFork_π_app_one, IsLimit.sectionsEquiv_symm_apply_val, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac', CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac_assoc, IsLimit.fac, app_right_eq_ι_comp_snd_assoc, ofPiFork_π_app_left, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, hom_comp_ι, pi_condition_assoc, ofPiFork_ι, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_functor_obj_ι, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, hom_comp_ι_assoc, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, app_right_eq_ι_comp_fst, toPiFork_π_app_zero, condition_assoc, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.liftAux_fac, ι_ofι, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac, pi_condition

Theorems

NameKindAssumesProvesValidatesDepends On
app_left_eq_ι 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.Cone.π
CategoryTheory.Limits.WalkingMulticospan.left
ι
app_right_eq_ι_comp_fst 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.Cone.π
CategoryTheory.Limits.WalkingMulticospan.right
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
ι
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.Cone.w
app_right_eq_ι_comp_snd 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.Cone.π
CategoryTheory.Limits.WalkingMulticospan.right
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.right
ι
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Limits.Cone.w
app_right_eq_ι_comp_snd_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.WalkingMulticospan.right
CategoryTheory.NatTrans.app
CategoryTheory.Limits.Cone.π
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.snd
ι
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
app_right_eq_ι_comp_snd
condition 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
ι
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
app_right_eq_ι_comp_fst
app_right_eq_ι_comp_snd
condition_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
ι
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
condition
ext_hom_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Iso.hom
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
ext
CategoryTheory.Limits.Cone.pt
ext_inv_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Iso.inv
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
ext
CategoryTheory.Limits.Cone.pt
hom_comp_ι 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.ConeMorphism.hom
ι
CategoryTheory.Limits.ConeMorphism.w
hom_comp_ι_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.MulticospanIndex.left
ι
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
hom_comp_ι
isoOfι_hom_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
ofι
CategoryTheory.Limits.Cone.pt
ι
condition
CategoryTheory.Iso.hom
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
isoOfι
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
condition
isoOfι_inv_hom 📖mathematicalCategoryTheory.Limits.ConeMorphism.hom
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
ofι
CategoryTheory.Limits.Cone.pt
ι
condition
CategoryTheory.Iso.inv
CategoryTheory.Limits.Multifork
CategoryTheory.Limits.Cone.category
isoOfι
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
condition
ofPiFork_pt 📖mathematicalCategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
ofPiFork
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit
ofPiFork_ι 📖mathematicalι
ofPiFork
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit
CategoryTheory.Limits.WalkingParallelPair.zero
CategoryTheory.Limits.Fork.ι
CategoryTheory.Limits.Fan.proj
ofPiFork_π_app_left 📖mathematicalι
ofPiFork
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit
CategoryTheory.Limits.WalkingParallelPair.zero
CategoryTheory.Limits.Fork.ι
CategoryTheory.Limits.Fan.proj
ofPiFork_ι
ofPiFork_π_app_right 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.MulticospanIndex.multicospan
ofPiFork
CategoryTheory.Limits.Cone.π
CategoryTheory.Limits.WalkingMulticospan.right
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit
CategoryTheory.Limits.WalkingParallelPair.zero
CategoryTheory.Limits.Fork.ι
CategoryTheory.Limits.Fan.proj
ofι_pt 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
ofι
ofι_π_app 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.Cone.π
ofι
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Limits.WalkingMulticospan.right
pi_condition 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.Fan.IsLimit.lift
ι
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit
CategoryTheory.Limits.Fan.IsLimit.hom_ext
CategoryTheory.Category.assoc
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj
CategoryTheory.Limits.Fan.IsLimit.fac_assoc
condition
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj
pi_condition_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.Fan.IsLimit.lift
ι
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
pi_condition
toPiFork_pt 📖mathematicalCategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit
toPiFork
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
toPiFork_π_app_one 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit
toPiFork
CategoryTheory.Limits.Cone.π
CategoryTheory.Limits.WalkingParallelPair.one
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.Fan.IsLimit.lift
ι
toPiFork_π_app_zero 📖mathematicalCategoryTheory.Limits.Fork.ι
CategoryTheory.Limits.Cone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MulticospanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.R
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit
toPiFork
CategoryTheory.Limits.Fan.IsLimit.lift
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
ι
ι_ofι 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
ι
ofι

CategoryTheory.Limits.Multifork.IsLimit

Definitions

NameCategoryTheorems
mk 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
fac 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
lift
CategoryTheory.Limits.Multifork.ι
CategoryTheory.Limits.IsLimit.fac
fac_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.MulticospanShape.fst
CategoryTheory.Limits.MulticospanIndex.right
CategoryTheory.Limits.MulticospanIndex.fst
CategoryTheory.Limits.MulticospanShape.snd
CategoryTheory.Limits.MulticospanIndex.snd
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
lift
CategoryTheory.Limits.Multifork.ι
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
fac
hom_ext 📖CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.Multifork.ι
CategoryTheory.Limits.IsLimit.hom_ext
CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mk_lift 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cone.pt
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
CategoryTheory.Limits.MulticospanIndex.multicospan
CategoryTheory.Limits.MulticospanIndex.left
CategoryTheory.Limits.Multifork.ι
CategoryTheory.Limits.IsLimit.lift

CategoryTheory.Limits.MultispanIndex

Definitions

NameCategoryTheorems
SymmStruct 📖CompData
fst 📖CompOp
26 mathmath: SymmStruct.iso_hom_snd_assoc, CategoryTheory.Limits.Multicoequalizer.condition, map_fst, SymmStruct.iso_hom_snd, CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inr, ι_fstSigmaMap_assoc, CategoryTheory.Limits.Multicofork.condition_assoc, toLinearOrder_fst, multispan_map_fst, CompleteLattice.MulticoequalizerDiagram.multispanIndex_fst, SymmStruct.iso_hom_fst_assoc, SymmStruct.fst_eq_snd, SymmStruct.iso_hom_fst, inj_fstSigmaMapOfIsColimit_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, CategoryTheory.Limits.Multicofork.fst_app_right, multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.GlueData.diagram_fst, ι_fstSigmaMap, CategoryTheory.Limits.Multicoequalizer.condition_assoc, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, CategoryTheory.Limits.Multicofork.condition, CategoryTheory.Limits.Multicofork.IsColimit.isPushout, CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inl, CategoryTheory.Limits.multispanIndexCoend_fst, inj_fstSigmaMapOfIsColimit
fstSigmaMap 📖CompOp
14 mathmath: TopCat.GlueData.eqvGen_of_π_eq, multicoforkEquivSigmaCofork_functor_obj_ι_app, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, ι_fstSigmaMap_assoc, multicoforkEquivSigmaCofork_functor_map_hom, multicoforkEquivSigmaCofork_functor_obj_pt, multicoforkEquivSigmaCofork_inverse_obj_pt, multicoforkEquivSigmaCofork_inverse_obj_ι_app, ι_fstSigmaMap, CategoryTheory.Limits.Multicoequalizer.instHasCoequalizerFstSigmaMapSndSigmaMap, multicoforkEquivSigmaCofork_inverse_map_hom, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, multicoforkEquivSigmaCofork_unitIso_inv_app_hom
fstSigmaMapOfIsColimit 📖CompOp
30 mathmath: multicoforkEquivSigmaCoforkOfIsColimit_counitIso, multicoforkEquivSigmaCofork_functor_obj_ι_app, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', CategoryTheory.Limits.Multicofork.toSigmaCofork_pt, multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt, ofSigmaCoforkFunctor_obj, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, multicoforkEquivSigmaCofork_functor_obj_pt, inj_fstSigmaMapOfIsColimit_assoc, CategoryTheory.Limits.Multicofork.toSigmaCofork_π, multicoforkEquivSigmaCofork_inverse_obj_pt, multicoforkEquivSigmaCofork_inverse_obj_ι_app, toSigmaCoforkFunctor_obj, parallelPairDiagramOfIsColimit_map, CategoryTheory.Limits.Multicofork.sigma_condition, multicoforkEquivSigmaCoforkOfIsColimit_inverse, toSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, ofSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_unitIso_inv_app_hom, inj_fstSigmaMapOfIsColimit, multicoforkEquivSigmaCoforkOfIsColimit_functor
left 📖CompOp
66 mathmath: TopCat.GlueData.eqvGen_of_π_eq, SymmStruct.iso_hom_snd_assoc, inj_sndSigmaMapOfIsColimit, toLinearOrderMultispanIso_inv_app, multicoforkEquivSigmaCoforkOfIsColimit_counitIso, multicoforkEquivSigmaCofork_functor_obj_ι_app, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, toLinearOrderMultispanIso_hom_app, CategoryTheory.Limits.Multicoequalizer.condition, map_fst, SymmStruct.iso_hom_snd, CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inr, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', ι_fstSigmaMap_assoc, CategoryTheory.Limits.Multicofork.toSigmaCofork_pt, CategoryTheory.Limits.Multicofork.condition_assoc, multispanMapIso_inv_app, multicoforkEquivSigmaCofork_functor_map_hom, SymmStruct.iso_hom_fst_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt, SymmStruct.iso_hom_fst, ι_sndSigmaMap, ofSigmaCoforkFunctor_obj, CompleteLattice.MulticoequalizerDiagram.multispanIndex_left, map_snd, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, CategoryTheory.GlueData.diagram_left, CategoryTheory.Limits.multispanIndexCoend_left, multicoforkEquivSigmaCofork_functor_obj_pt, inj_fstSigmaMapOfIsColimit_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, map_left, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, CategoryTheory.Limits.Multicofork.toSigmaCofork_π, multicoforkEquivSigmaCofork_inverse_obj_pt, CategoryTheory.Limits.Multicofork.fst_app_right, inj_sndSigmaMapOfIsColimit_assoc, multispanMapIso_hom_app, multicoforkEquivSigmaCofork_inverse_obj_ι_app, toSigmaCoforkFunctor_obj, parallelPairDiagramOfIsColimit_map, ι_fstSigmaMap, CategoryTheory.Limits.Multicoequalizer.instHasCoequalizerFstSigmaMapSndSigmaMap, CategoryTheory.Limits.Multicoequalizer.condition_assoc, CategoryTheory.Limits.Multicofork.snd_app_right, CategoryTheory.Limits.Multicofork.sigma_condition, multicoforkEquivSigmaCoforkOfIsColimit_inverse, CategoryTheory.Limits.Multicofork.condition, multispan_obj_left, toSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, CategoryTheory.Limits.Multicofork.IsColimit.isPushout, toLinearOrder_left, CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inl, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, ι_sndSigmaMap_assoc, ofSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_unitIso_inv_app_hom, parallelPairDiagramOfIsColimit_obj, inj_fstSigmaMapOfIsColimit, multicoforkEquivSigmaCoforkOfIsColimit_functor
multicoforkEquivSigmaCofork 📖CompOp
10 mathmath: multicoforkEquivSigmaCofork_functor_obj_ι_app, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, multicoforkEquivSigmaCofork_functor_map_hom, multicoforkEquivSigmaCofork_functor_obj_pt, multicoforkEquivSigmaCofork_inverse_obj_pt, multicoforkEquivSigmaCofork_inverse_obj_ι_app, multicoforkEquivSigmaCofork_inverse_map_hom, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, multicoforkEquivSigmaCofork_unitIso_inv_app_hom
multicoforkEquivSigmaCoforkOfIsColimit 📖CompOp
4 mathmath: multicoforkEquivSigmaCoforkOfIsColimit_counitIso, multicoforkEquivSigmaCoforkOfIsColimit_inverse, multicoforkEquivSigmaCoforkOfIsColimit_unitIso, multicoforkEquivSigmaCoforkOfIsColimit_functor
multispan 📖CompOp
117 mathmath: CategoryTheory.GlueData.diagramIso_app_right, TopCat.GlueData.preimage_image_eq_image, TopCat.GlueData.π_surjective, CategoryTheory.Limits.Multicofork.ofπ_ι_app, TopCat.GlueData.open_image_open, toLinearOrderMultispanIso_inv_app, multicoforkEquivSigmaCoforkOfIsColimit_counitIso, TopCat.GlueData.ι_fromOpenSubsetsGlue, multicoforkEquivSigmaCofork_functor_obj_ι_app, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Functor.CoconeTypes.isMulticoequalizer_iff, CategoryTheory.GlueData.types_π_surjective, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersion, toLinearOrderMultispanIso_hom_app, CategoryTheory.Limits.Multicofork.π_comp_hom_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.isOpen_iff, TopCat.GlueData.ι_fromOpenSubsetsGlue_apply, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.Cowedge.IsColimit.π_desc_assoc, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, SSet.horn₃₁.desc.multicofork_pt, CategoryTheory.Limits.Multicofork.toSigmaCofork_pt, CategoryTheory.Limits.Multicofork.condition_assoc, multispanMapIso_inv_app, multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.Cowedge.IsColimit.π_desc, CategoryTheory.Limits.Cowedge.condition_assoc, multispan_map_fst, AlgebraicGeometry.Scheme.GlueData.instPreservesColimitTopCatWalkingMultispanProdJMultispanDiagramForgetToTop, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, SSet.horn₃₁.desc.multicofork_π_two_assoc, CategoryTheory.Limits.Multicofork.ext_hom_hom, SSet.horn₃₁.desc.multicofork_π_zero_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt, CategoryTheory.GlueData.diagramIso_app_left, CategoryTheory.Limits.Multicofork.π_eq_app_right, AlgebraicGeometry.Scheme.GlueData.instPreservesColimitWalkingMultispanProdJMultispanDiagramForget, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv, AlgebraicGeometry.Scheme.GlueData.instIsOpenImmersionιLocallyRingedSpaceToLocallyRingedSpaceGlueData, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, multispan_obj_right, CategoryTheory.GlueData.diagramIso_inv_app_left, ofSigmaCoforkFunctor_obj, CategoryTheory.Limits.Multicofork.map_pt, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', TopCat.GlueData.range_fromOpenSubsetsGlue, multispan_map_snd, CategoryTheory.GlueData.diagramIso_inv_app_right, CategoryTheory.Limits.Cowedge.ext_hom_hom, CategoryTheory.Limits.Cowedge.mk_pt, TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbedding, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective, CategoryTheory.Limits.Multicofork.ofπ_pt, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, multicoforkEquivSigmaCofork_functor_obj_pt, CategoryTheory.Limits.Multicofork.map_ι_app, CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right', AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, TopCat.GlueData.fromOpenSubsetsGlue_injective, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, TopCat.GlueData.ι_isOpenEmbedding, CategoryTheory.Limits.Multicofork.toSigmaCofork_π, multicoforkEquivSigmaCofork_inverse_obj_pt, CategoryTheory.Limits.Multicofork.IsColimit.fac_assoc, CategoryTheory.Limits.Multicofork.fst_app_right, SSet.horn₃₂.desc.multicofork_π_zero_assoc, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, TopCat.GlueData.preimage_range, multispanMapIso_hom_app, multicoforkEquivSigmaCofork_inverse_obj_ι_app, TopCat.GlueData.ι_mono, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv_assoc, AlgebraicGeometry.SheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.image_inter, CategoryTheory.Limits.Multicofork.ext_inv_hom, toSigmaCoforkFunctor_obj, SSet.horn₃₁.desc.multicofork_π_three_assoc, CategoryTheory.Limits.Cowedge.ext_inv_hom, TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap, CategoryTheory.Limits.Multicofork.snd_app_right, CategoryTheory.Limits.Multicofork.sigma_condition, multicoforkEquivSigmaCoforkOfIsColimit_inverse, AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, CompleteLattice.MulticoequalizerDiagram.multicofork_pt, CategoryTheory.Limits.Multicofork.condition, multispan_obj_left, TopCat.GlueData.ι_jointly_surjective, toSigmaCoforkFunctor_map_hom, SSet.horn₃₂.desc.multicofork_pt, CategoryTheory.GlueData.hasColimit_multispan_comp, multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right, CategoryTheory.Limits.Multicofork.IsColimit.isPushout, AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, TopCat.GlueData.ι_eq_iff_rel, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.GlueData.types_ι_jointly_surjective, multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.Multicofork.π_comp_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, SSet.horn₃₂.desc.multicofork_π_three_assoc, SSet.horn₃₂.desc.multicofork_π_one_assoc, ofSigmaCoforkFunctor_map_hom, TopCat.GlueData.ι_injective, multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.GlueData.diagramIso_hom_app_right, multicoforkEquivSigmaCoforkOfIsColimit_functor, CategoryTheory.Limits.Multicofork.IsColimit.fac, TopCat.GlueData.preimage_image_eq_image', CategoryTheory.Limits.Cowedge.condition, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, CategoryTheory.GlueData.diagramIso_hom_app_left
ofSigmaCoforkFunctor 📖CompOp
9 mathmath: multicoforkEquivSigmaCoforkOfIsColimit_counitIso, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, ofSigmaCoforkFunctor_obj, multicoforkEquivSigmaCoforkOfIsColimit_inverse, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, multicoforkEquivSigmaCoforkOfIsColimit_unitIso, ofSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_unitIso_inv_app_hom
parallelPairDiagram 📖CompOp
parallelPairDiagramOfIsColimit 📖CompOp
2 mathmath: parallelPairDiagramOfIsColimit_map, parallelPairDiagramOfIsColimit_obj
right 📖CompOp
81 mathmath: TopCat.GlueData.eqvGen_of_π_eq, SymmStruct.iso_hom_snd_assoc, inj_sndSigmaMapOfIsColimit, toLinearOrderMultispanIso_inv_app, multicoforkEquivSigmaCoforkOfIsColimit_counitIso, multicoforkEquivSigmaCofork_functor_obj_ι_app, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, toLinearOrderMultispanIso_hom_app, CategoryTheory.Limits.Multicoequalizer.condition, CategoryTheory.Limits.Multicofork.π_comp_hom_assoc, CategoryTheory.Limits.multispanIndexCoend_right, map_fst, SymmStruct.iso_hom_snd, CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inr, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ_assoc, CategoryTheory.Limits.Cowedge.IsColimit.π_desc_assoc, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, ι_fstSigmaMap_assoc, CategoryTheory.Limits.Multicofork.toSigmaCofork_pt, CategoryTheory.Limits.Multicofork.condition_assoc, multispanMapIso_inv_app, multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.Cowedge.IsColimit.π_desc, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_right, CompleteLattice.MulticoequalizerDiagram.multispanIndex_right, SymmStruct.iso_hom_fst_assoc, SSet.horn₃₁.desc.multicofork_π_two_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, SSet.horn₃₁.desc.multicofork_π_zero_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt, SymmStruct.iso_hom_fst, ι_sndSigmaMap, multispan_obj_right, ofSigmaCoforkFunctor_obj, map_snd, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ, multicoforkEquivSigmaCofork_functor_obj_pt, inj_fstSigmaMapOfIsColimit_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, CategoryTheory.Limits.Multicofork.toSigmaCofork_π, multicoforkEquivSigmaCofork_inverse_obj_pt, CategoryTheory.Limits.Multicofork.fst_app_right, inj_sndSigmaMapOfIsColimit_assoc, SSet.horn₃₂.desc.multicofork_π_zero_assoc, multispanMapIso_hom_app, CategoryTheory.Limits.Multicoequalizer.hom_ext_iff, multicoforkEquivSigmaCofork_inverse_obj_ι_app, map_right, toSigmaCoforkFunctor_obj, SSet.horn₃₁.desc.multicofork_π_three_assoc, parallelPairDiagramOfIsColimit_map, ι_fstSigmaMap, CategoryTheory.Limits.Multicoequalizer.instHasCoequalizerFstSigmaMapSndSigmaMap, CategoryTheory.Limits.Multicoequalizer.condition_assoc, CategoryTheory.Limits.Multicofork.snd_app_right, CategoryTheory.Limits.Multicofork.sigma_condition, multicoforkEquivSigmaCoforkOfIsColimit_inverse, CategoryTheory.Limits.Multicofork.condition, toSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, CategoryTheory.Limits.Multicofork.IsColimit.isPushout, CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inl, CategoryTheory.GlueData.diagram_right, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.Multicofork.π_comp_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, ι_sndSigmaMap_assoc, SSet.horn₃₂.desc.multicofork_π_three_assoc, toLinearOrder_right, SSet.horn₃₂.desc.multicofork_π_one_assoc, ofSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_unitIso_inv_app_hom, parallelPairDiagramOfIsColimit_obj, inj_fstSigmaMapOfIsColimit, multicoforkEquivSigmaCoforkOfIsColimit_functor, CategoryTheory.Limits.Multicoequalizer.instEpiSigmaπ
snd 📖CompOp
25 mathmath: SymmStruct.iso_hom_snd_assoc, inj_sndSigmaMapOfIsColimit, CategoryTheory.Limits.Multicoequalizer.condition, SymmStruct.iso_hom_snd, CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inr, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, CategoryTheory.Limits.Multicofork.condition_assoc, toLinearOrder_snd, SymmStruct.iso_hom_fst_assoc, SymmStruct.fst_eq_snd, SymmStruct.iso_hom_fst, ι_sndSigmaMap, CategoryTheory.Limits.multispanIndexCoend_snd, multispan_map_snd, map_snd, CategoryTheory.GlueData.diagram_snd, inj_sndSigmaMapOfIsColimit_assoc, CompleteLattice.MulticoequalizerDiagram.multispanIndex_snd, CategoryTheory.Limits.Multicoequalizer.condition_assoc, CategoryTheory.Limits.Multicofork.snd_app_right, CategoryTheory.Limits.Multicofork.condition, CategoryTheory.Limits.Multicofork.IsColimit.isPushout, CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inl, ι_sndSigmaMap_assoc, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd
sndSigmaMap 📖CompOp
14 mathmath: TopCat.GlueData.eqvGen_of_π_eq, multicoforkEquivSigmaCofork_functor_obj_ι_app, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, multicoforkEquivSigmaCofork_functor_map_hom, ι_sndSigmaMap, multicoforkEquivSigmaCofork_functor_obj_pt, multicoforkEquivSigmaCofork_inverse_obj_pt, multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.Limits.Multicoequalizer.instHasCoequalizerFstSigmaMapSndSigmaMap, multicoforkEquivSigmaCofork_inverse_map_hom, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, ι_sndSigmaMap_assoc, multicoforkEquivSigmaCofork_unitIso_inv_app_hom
sndSigmaMapOfIsColimit 📖CompOp
30 mathmath: inj_sndSigmaMapOfIsColimit, multicoforkEquivSigmaCoforkOfIsColimit_counitIso, multicoforkEquivSigmaCofork_functor_obj_ι_app, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', CategoryTheory.Limits.Multicofork.toSigmaCofork_pt, multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt, ofSigmaCoforkFunctor_obj, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, multicoforkEquivSigmaCofork_functor_obj_pt, CategoryTheory.Limits.Multicofork.toSigmaCofork_π, multicoforkEquivSigmaCofork_inverse_obj_pt, inj_sndSigmaMapOfIsColimit_assoc, multicoforkEquivSigmaCofork_inverse_obj_ι_app, toSigmaCoforkFunctor_obj, parallelPairDiagramOfIsColimit_map, CategoryTheory.Limits.Multicofork.sigma_condition, multicoforkEquivSigmaCoforkOfIsColimit_inverse, toSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, ofSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_unitIso_inv_app_hom, multicoforkEquivSigmaCoforkOfIsColimit_functor
toLinearOrder 📖CompOp
20 mathmath: SSet.horn₃₁.desc.multicofork_π_two, toLinearOrderMultispanIso_inv_app, toLinearOrderMultispanIso_hom_app, SSet.horn₃₂.desc.multicofork_π_one, SSet.horn₃₁.desc.multicofork_pt, toLinearOrder_fst, toLinearOrder_snd, SSet.horn₃₁.desc.multicofork_π_two_assoc, SSet.horn₃₁.desc.multicofork_π_zero_assoc, SSet.horn₃₂.desc.multicofork_π_zero_assoc, SSet.horn₃₁.desc.multicofork_π_three_assoc, SSet.horn₃₁.desc.multicofork_π_zero, SSet.horn₃₂.desc.multicofork_π_three, SSet.horn₃₂.desc.multicofork_pt, toLinearOrder_left, SSet.horn₃₂.desc.multicofork_π_zero, SSet.horn₃₂.desc.multicofork_π_three_assoc, toLinearOrder_right, SSet.horn₃₂.desc.multicofork_π_one_assoc, SSet.horn₃₁.desc.multicofork_π_three
toLinearOrderMultispanIso 📖CompOp
2 mathmath: toLinearOrderMultispanIso_inv_app, toLinearOrderMultispanIso_hom_app
toSigmaCoforkFunctor 📖CompOp
9 mathmath: multicoforkEquivSigmaCoforkOfIsColimit_counitIso, multicoforkEquivSigmaCofork_counitIso_inv_app_hom, multicoforkEquivSigmaCofork_counitIso_hom_app_hom, toSigmaCoforkFunctor_obj, toSigmaCoforkFunctor_map_hom, multicoforkEquivSigmaCofork_unitIso_hom_app_hom, multicoforkEquivSigmaCoforkOfIsColimit_unitIso, multicoforkEquivSigmaCofork_unitIso_inv_app_hom, multicoforkEquivSigmaCoforkOfIsColimit_functor

Theorems

NameKindAssumesProvesValidatesDepends On
inj_fstSigmaMapOfIsColimit 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
left
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanShape.fst
fst
CategoryTheory.Limits.Cofan.IsColimit.fac
inj_fstSigmaMapOfIsColimit_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
left
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanShape.fst
fst
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
inj_fstSigmaMapOfIsColimit
inj_sndSigmaMapOfIsColimit 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
left
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MultispanShape.R
right
sndSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanShape.snd
snd
CategoryTheory.Limits.Cofan.IsColimit.fac
inj_sndSigmaMapOfIsColimit_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
left
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
CategoryTheory.Limits.MultispanShape.R
right
sndSigmaMapOfIsColimit
CategoryTheory.Limits.MultispanShape.snd
snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
inj_sndSigmaMapOfIsColimit
multicoforkEquivSigmaCoforkOfIsColimit_counitIso 📖mathematicalCategoryTheory.Equivalence.counitIso
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
multicoforkEquivSigmaCoforkOfIsColimit
CategoryTheory.NatIso.ofComponents
CategoryTheory.Functor.comp
ofSigmaCoforkFunctor
toSigmaCoforkFunctor
CategoryTheory.Functor.id
CategoryTheory.Limits.Cofork.ext
CategoryTheory.Functor.obj
CategoryTheory.Iso.refl
multicoforkEquivSigmaCoforkOfIsColimit_functor 📖mathematicalCategoryTheory.Equivalence.functor
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
multicoforkEquivSigmaCoforkOfIsColimit
toSigmaCoforkFunctor
multicoforkEquivSigmaCoforkOfIsColimit_inverse 📖mathematicalCategoryTheory.Equivalence.inverse
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
multicoforkEquivSigmaCoforkOfIsColimit
ofSigmaCoforkFunctor
multicoforkEquivSigmaCoforkOfIsColimit_unitIso 📖mathematicalCategoryTheory.Equivalence.unitIso
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
multicoforkEquivSigmaCoforkOfIsColimit
CategoryTheory.NatIso.ofComponents
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
toSigmaCoforkFunctor
ofSigmaCoforkFunctor
CategoryTheory.Limits.Cocones.ext
CategoryTheory.Functor.obj
CategoryTheory.Iso.refl
multicoforkEquivSigmaCofork_counitIso_hom_app_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.colimit.isColimit
sndSigmaMapOfIsColimit
CategoryTheory.Functor.obj
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Functor.comp
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
ofSigmaCoforkFunctor
toSigmaCoforkFunctor
CategoryTheory.Functor.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.counitIso
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.colimit
multicoforkEquivSigmaCofork_counitIso_inv_app_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.colimit.isColimit
sndSigmaMapOfIsColimit
CategoryTheory.Functor.obj
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
ofSigmaCoforkFunctor
toSigmaCoforkFunctor
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.counitIso
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.colimit
multicoforkEquivSigmaCofork_functor_map_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.colimit.isColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Multicofork.toSigmaCofork
CategoryTheory.Functor.map
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.Cofork
CategoryTheory.Equivalence.functor
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
multicoforkEquivSigmaCofork_functor_obj_pt 📖mathematicalCategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.colimit.isColimit
sndSigmaMapOfIsColimit
CategoryTheory.Functor.obj
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.Cofork
CategoryTheory.Equivalence.functor
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
multicoforkEquivSigmaCofork_functor_obj_ι_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.colimit.isColimit
sndSigmaMapOfIsColimit
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.Cocone.ι
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.Cofork
CategoryTheory.Equivalence.functor
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.colimit
CategoryTheory.CategoryStruct.comp
CategoryTheory.Limits.Cofan.IsColimit.desc
CategoryTheory.Limits.Multicofork.π
CategoryTheory.Limits.Multicofork.sigma_condition
multicoforkEquivSigmaCofork_inverse_map_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.Multicofork.ofSigmaCofork
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.isColimit
CategoryTheory.Limits.MultispanShape.R
right
CategoryTheory.Functor.map
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Multicofork
CategoryTheory.Equivalence.inverse
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
CategoryTheory.Limits.colimit
multicoforkEquivSigmaCofork_inverse_obj_pt 📖mathematicalCategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Functor.obj
CategoryTheory.Limits.Cofork
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.colimit.isColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Multicofork
CategoryTheory.Equivalence.inverse
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
CategoryTheory.Limits.colimit
multicoforkEquivSigmaCofork_inverse_obj_ι_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.const
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.colimit.isColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cocone.ι
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.Multicofork
CategoryTheory.Equivalence.inverse
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.colimit
CategoryTheory.CategoryStruct.comp
CategoryTheory.Limits.MultispanShape.fst
fst
CategoryTheory.Limits.Cofork.π
inj_fstSigmaMapOfIsColimit_assoc
multicoforkEquivSigmaCofork_unitIso_hom_app_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Functor.obj
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.colimit.isColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
toSigmaCoforkFunctor
ofSigmaCoforkFunctor
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.unitIso
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
multicoforkEquivSigmaCofork_unitIso_inv_app_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Functor.obj
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Functor.comp
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.colimit.cocone
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
CategoryTheory.Limits.colimit.isColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
toSigmaCoforkFunctor
ofSigmaCoforkFunctor
CategoryTheory.Functor.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.unitIso
CategoryTheory.Limits.sigmaObj
fstSigmaMap
sndSigmaMap
multicoforkEquivSigmaCofork
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
multispan_map_fst 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.WalkingMultispan.left
CategoryTheory.Limits.WalkingMultispan.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.WalkingMultispan.Hom.fst
fst
multispan_map_snd 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.WalkingMultispan.left
CategoryTheory.Limits.WalkingMultispan.right
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.WalkingMultispan.Hom.snd
snd
multispan_obj_left 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.WalkingMultispan.left
left
multispan_obj_right 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.WalkingMultispan.right
right
ofSigmaCoforkFunctor_map_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.Multicofork.ofSigmaCofork
CategoryTheory.Functor.map
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Multicofork
ofSigmaCoforkFunctor
ofSigmaCoforkFunctor_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
ofSigmaCoforkFunctor
CategoryTheory.Limits.Multicofork.ofSigmaCofork
parallelPairDiagramOfIsColimit_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
parallelPairDiagramOfIsColimit
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
CategoryTheory.CategoryStruct.id
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
parallelPairDiagramOfIsColimit_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
parallelPairDiagramOfIsColimit
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
toLinearOrderMultispanIso_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.MultispanShape.ofLinearOrder
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
CategoryTheory.Functor.comp
CategoryTheory.Limits.MultispanShape.prod
CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder
multispan
toLinearOrder
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
toLinearOrderMultispanIso
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingMultispan.left
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
CategoryTheory.Limits.WalkingMultispan.right
CategoryTheory.Iso
CategoryTheory.Iso.refl
left
right
toLinearOrderMultispanIso_inv_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.MultispanShape.ofLinearOrder
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
toLinearOrder
CategoryTheory.Functor.comp
CategoryTheory.Limits.MultispanShape.prod
CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
toLinearOrderMultispanIso
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingMultispan.left
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
CategoryTheory.Limits.WalkingMultispan.right
CategoryTheory.Iso
CategoryTheory.Iso.refl
left
right
toLinearOrder_fst 📖mathematicalfst
CategoryTheory.Limits.MultispanShape.ofLinearOrder
toLinearOrder
CategoryTheory.Limits.MultispanShape.prod
Set
Set.instMembership
setOf
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
toLinearOrder_left 📖mathematicalleft
CategoryTheory.Limits.MultispanShape.ofLinearOrder
toLinearOrder
CategoryTheory.Limits.MultispanShape.prod
Set
Set.instMembership
setOf
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
toLinearOrder_right 📖mathematicalright
CategoryTheory.Limits.MultispanShape.ofLinearOrder
toLinearOrder
CategoryTheory.Limits.MultispanShape.prod
toLinearOrder_snd 📖mathematicalsnd
CategoryTheory.Limits.MultispanShape.ofLinearOrder
toLinearOrder
CategoryTheory.Limits.MultispanShape.prod
Set
Set.instMembership
setOf
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
toSigmaCoforkFunctor_map_hom 📖mathematicalCategoryTheory.Limits.CoconeMorphism.hom
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.Multicofork.toSigmaCofork
CategoryTheory.Functor.map
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.Cofork
toSigmaCoforkFunctor
toSigmaCoforkFunctor_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.Multicofork
CategoryTheory.Limits.Cocone.category
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
multispan
CategoryTheory.Limits.Cofork
CategoryTheory.Limits.Cocone.pt
CategoryTheory.Discrete
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
left
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMapOfIsColimit
sndSigmaMapOfIsColimit
CategoryTheory.Limits.WalkingParallelPair
CategoryTheory.Limits.walkingParallelPairHomCategory
CategoryTheory.Limits.parallelPair
toSigmaCoforkFunctor
CategoryTheory.Limits.Multicofork.toSigmaCofork
ι_fstSigmaMap 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
left
CategoryTheory.Limits.sigmaObj
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.Limits.MultispanShape.R
right
CategoryTheory.Limits.Sigma.ι
fstSigmaMap
CategoryTheory.Limits.MultispanShape.fst
fst
inj_fstSigmaMapOfIsColimit
ι_fstSigmaMap_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
left
CategoryTheory.Limits.sigmaObj
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.Limits.Sigma.ι
CategoryTheory.Limits.MultispanShape.R
right
fstSigmaMap
CategoryTheory.Limits.MultispanShape.fst
fst
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
ι_fstSigmaMap
ι_sndSigmaMap 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
left
CategoryTheory.Limits.sigmaObj
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.Limits.MultispanShape.R
right
CategoryTheory.Limits.Sigma.ι
sndSigmaMap
CategoryTheory.Limits.MultispanShape.snd
snd
inj_sndSigmaMapOfIsColimit
ι_sndSigmaMap_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
left
CategoryTheory.Limits.sigmaObj
CategoryTheory.Limits.MultispanShape.L
CategoryTheory.Limits.Sigma.ι
CategoryTheory.Limits.MultispanShape.R
right
sndSigmaMap
CategoryTheory.Limits.MultispanShape.snd
snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
ι_sndSigmaMap

CategoryTheory.Limits.MultispanIndex.SymmStruct

Definitions

NameCategoryTheorems
iso 📖CompOp
4 mathmath: iso_hom_snd_assoc, iso_hom_snd, iso_hom_fst_assoc, iso_hom_fst

Theorems

NameKindAssumesProvesValidatesDepends On
fst_eq_snd 📖mathematicalCategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.MultispanShape.prod
CategoryTheory.Limits.MultispanIndex.snd
iso_hom_fst 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.prod
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Iso.hom
iso
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.MultispanIndex.snd
iso_hom_fst_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.prod
CategoryTheory.Iso.hom
iso
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.fst
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
iso_hom_fst
iso_hom_snd 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.prod
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Iso.hom
iso
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Limits.MultispanIndex.fst
iso_hom_snd_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.MultispanIndex.left
CategoryTheory.Limits.MultispanShape.prod
CategoryTheory.Iso.hom
iso
CategoryTheory.Limits.MultispanIndex.right
CategoryTheory.Limits.MultispanShape.snd
CategoryTheory.Limits.MultispanIndex.snd
CategoryTheory.Limits.MultispanIndex.fst
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
iso_hom_snd

CategoryTheory.Limits.MultispanShape

Definitions

NameCategoryTheorems
L 📖CompOp
76 mathmath: TopCat.GlueData.preimage_image_eq_image, TopCat.GlueData.π_surjective, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit, TopCat.GlueData.open_image_open, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, TopCat.GlueData.ι_fromOpenSubsetsGlue, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.GlueData.types_π_surjective, AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.isOpen_iff, TopCat.GlueData.ι_fromOpenSubsetsGlue_apply, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap_assoc, CategoryTheory.Limits.Multicofork.toSigmaCofork_pt, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv, CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_obj, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', ofLinearOrder_L, TopCat.GlueData.range_fromOpenSubsetsGlue, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbedding, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_pt, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit_assoc, AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, TopCat.GlueData.fromOpenSubsetsGlue_injective, TopCat.GlueData.ι_isOpenEmbedding, CategoryTheory.Limits.Multicofork.toSigmaCofork_π, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit_assoc, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, TopCat.GlueData.preimage_range, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, TopCat.GlueData.ι_mono, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv_assoc, prod_L, AlgebraicGeometry.SheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.image_inter, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_obj, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_map, CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap, CategoryTheory.Limits.Multicoequalizer.instHasCoequalizerFstSigmaMapSndSigmaMap, CategoryTheory.OrthogonalReflection.D₂.multispanShape_L, CategoryTheory.OrthogonalReflection.instSmallLMultispanShape, TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap, CategoryTheory.Limits.Multicofork.sigma_condition, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_inverse, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, TopCat.GlueData.ι_jointly_surjective, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, CategoryTheory.Limits.multispanShapeCoend_L, TopCat.GlueData.ι_eq_iff_rel, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.GlueData.types_ι_jointly_surjective, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap_assoc, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom, TopCat.GlueData.ι_injective, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_obj, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_functor, TopCat.GlueData.preimage_image_eq_image', AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective
R 📖CompOp
78 mathmath: TopCat.GlueData.preimage_image_eq_image, TopCat.GlueData.π_surjective, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit, TopCat.GlueData.open_image_open, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, TopCat.GlueData.ι_fromOpenSubsetsGlue, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.GlueData.types_π_surjective, AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.isOpen_iff, CategoryTheory.OrthogonalReflection.D₂.multispanShape_R, TopCat.GlueData.ι_fromOpenSubsetsGlue_apply, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ_assoc, CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap_assoc, CategoryTheory.Limits.Multicofork.toSigmaCofork_pt, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv, CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, prod_R, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_obj, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', TopCat.GlueData.range_fromOpenSubsetsGlue, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbedding, CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_pt, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit_assoc, AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, TopCat.GlueData.fromOpenSubsetsGlue_injective, TopCat.GlueData.ι_isOpenEmbedding, CategoryTheory.Limits.Multicofork.toSigmaCofork_π, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit_assoc, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, TopCat.GlueData.preimage_range, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, TopCat.GlueData.ι_mono, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv_assoc, AlgebraicGeometry.SheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.image_inter, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_obj, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_map, CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap, CategoryTheory.Limits.Multicoequalizer.instHasCoequalizerFstSigmaMapSndSigmaMap, TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap, CategoryTheory.Limits.Multicofork.sigma_condition, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_inverse, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, TopCat.GlueData.ι_jointly_surjective, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, TopCat.GlueData.ι_eq_iff_rel, ofLinearOrder_R, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.GlueData.types_ι_jointly_surjective, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap_assoc, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom, TopCat.GlueData.ι_injective, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_obj, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_functor, CategoryTheory.Limits.Multicoequalizer.instEpiSigmaπ, TopCat.GlueData.preimage_image_eq_image', CategoryTheory.Limits.multispanShapeCoend_R, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective
fst 📖CompOp
20 mathmath: CategoryTheory.Limits.Multicoequalizer.condition, CategoryTheory.Limits.MultispanIndex.map_fst, CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap_assoc, CategoryTheory.Limits.Multicofork.condition_assoc, CategoryTheory.Limits.MultispanIndex.multispan_map_fst, CompleteLattice.MulticoequalizerDiagram.multispanIndex_fst, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst_assoc, CategoryTheory.OrthogonalReflection.D₂.multispanShape_fst, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, prod_fst, CategoryTheory.Limits.multispanShapeCoend_fst, CategoryTheory.Limits.Multicofork.fst_app_right, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap, CategoryTheory.Limits.Multicoequalizer.condition_assoc, ofLinearOrder_fst, CategoryTheory.Limits.Multicofork.condition, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit
ofLinearOrder 📖CompOp
26 mathmath: SSet.horn₃₁.desc.multicofork_π_two, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, SSet.horn₃₂.desc.multicofork_π_one, SSet.horn₃₁.desc.multicofork_pt, CategoryTheory.Limits.MultispanIndex.toLinearOrder_fst, CategoryTheory.Limits.MultispanIndex.toLinearOrder_snd, SSet.horn₃₁.desc.multicofork_π_two_assoc, SSet.horn₃₁.desc.multicofork_π_zero_assoc, ofLinearOrder_L, SSet.horn₃₂.desc.multicofork_π_zero_assoc, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_obj, SSet.horn₃₁.desc.multicofork_π_three_assoc, SSet.horn₃₁.desc.multicofork_π_zero, SSet.horn₃₂.desc.multicofork_π_three, ofLinearOrder_fst, SSet.horn₃₂.desc.multicofork_pt, CategoryTheory.Limits.MultispanIndex.toLinearOrder_left, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, ofLinearOrder_R, ofLinearOrder_snd, SSet.horn₃₂.desc.multicofork_π_zero, SSet.horn₃₂.desc.multicofork_π_three_assoc, CategoryTheory.Limits.MultispanIndex.toLinearOrder_right, SSet.horn₃₂.desc.multicofork_π_one_assoc, SSet.horn₃₁.desc.multicofork_π_three
prod 📖CompOp
81 mathmath: CategoryTheory.GlueData.diagramIso_app_right, TopCat.GlueData.preimage_image_eq_image, TopCat.GlueData.π_surjective, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd_assoc, TopCat.GlueData.open_image_open, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, TopCat.GlueData.ι_fromOpenSubsetsGlue, CategoryTheory.GlueData.types_π_surjective, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersion, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.isOpen_iff, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd, TopCat.GlueData.ι_fromOpenSubsetsGlue_apply, AlgebraicGeometry.Scheme.GlueData.instHasMulticoequalizerDiagram, CategoryTheory.Limits.MultispanIndex.toLinearOrder_fst, CategoryTheory.Limits.MultispanIndex.toLinearOrder_snd, AlgebraicGeometry.Scheme.GlueData.instPreservesColimitTopCatWalkingMultispanProdJMultispanDiagramForgetToTop, CompleteLattice.MulticoequalizerDiagram.multispanIndex_right, CompleteLattice.MulticoequalizerDiagram.multispanIndex_fst, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, CategoryTheory.GlueData.diagramIso_app_left, AlgebraicGeometry.Scheme.GlueData.instPreservesColimitWalkingMultispanProdJMultispanDiagramForget, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι_assoc, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv, CategoryTheory.Limits.MultispanIndex.SymmStruct.fst_eq_snd, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst, AlgebraicGeometry.Scheme.GlueData.instIsOpenImmersionιLocallyRingedSpaceToLocallyRingedSpaceGlueData, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, prod_R, CategoryTheory.GlueData.diagramIso_inv_app_left, CompleteLattice.MulticoequalizerDiagram.multispanIndex_left, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', TopCat.GlueData.range_fromOpenSubsetsGlue, CategoryTheory.GlueData.diagramIso_inv_app_right, CategoryTheory.GlueData.diagram_left, CategoryTheory.GlueData.diagram_snd, TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbedding, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, prod_fst, AlgebraicGeometry.PresheafedSpace.GlueData.componentwise_diagram_π_isIso, AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, TopCat.GlueData.fromOpenSubsetsGlue_injective, TopCat.GlueData.ι_isOpenEmbedding, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_obj, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, CompleteLattice.MulticoequalizerDiagram.multispanIndex_snd, AlgebraicGeometry.Scheme.Pullback.gluing_ι, TopCat.GlueData.preimage_range, TopCat.GlueData.ι_mono, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv_assoc, CategoryTheory.GlueData.diagram_fst, prod_L, AlgebraicGeometry.SheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.image_inter, prod_snd, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι, TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap, AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, CompleteLattice.MulticoequalizerDiagram.multicofork_pt, TopCat.GlueData.ι_jointly_surjective, CategoryTheory.GlueData.hasColimit_multispan_comp, CategoryTheory.Limits.MultispanIndex.toLinearOrder_left, AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π, TopCat.GlueData.ι_eq_iff_rel, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π, CategoryTheory.GlueData.diagram_right, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, CategoryTheory.GlueData.types_ι_jointly_surjective, CategoryTheory.Limits.MultispanIndex.toLinearOrder_right, CategoryTheory.GlueData.hasColimit_mapGlueData_diagram, TopCat.GlueData.ι_injective, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id, CategoryTheory.GlueData.diagramIso_hom_app_right, TopCat.GlueData.preimage_image_eq_image', AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, CategoryTheory.GlueData.diagramIso_hom_app_left
snd 📖CompOp
20 mathmath: CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd_assoc, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit, CategoryTheory.Limits.Multicoequalizer.condition, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, CategoryTheory.Limits.multispanShapeCoend_snd, CategoryTheory.Limits.Multicofork.condition_assoc, CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap, CategoryTheory.Limits.multispanIndexCoend_snd, CategoryTheory.OrthogonalReflection.D₂.multispanShape_snd, CategoryTheory.Limits.MultispanIndex.multispan_map_snd, CategoryTheory.Limits.MultispanIndex.map_snd, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit_assoc, CompleteLattice.MulticoequalizerDiagram.multispanIndex_snd, prod_snd, CategoryTheory.Limits.Multicoequalizer.condition_assoc, CategoryTheory.Limits.Multicofork.snd_app_right, CategoryTheory.Limits.Multicofork.condition, ofLinearOrder_snd, CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap_assoc

Theorems

NameKindAssumesProvesValidatesDepends On
ofLinearOrder_L 📖mathematicalL
ofLinearOrder
Set.Elem
setOf
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ofLinearOrder_R 📖mathematicalR
ofLinearOrder
ofLinearOrder_fst 📖mathematicalfst
ofLinearOrder
Set
Set.instMembership
setOf
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ofLinearOrder_snd 📖mathematicalsnd
ofLinearOrder
Set
Set.instMembership
setOf
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
prod_L 📖mathematicalL
prod
prod_R 📖mathematicalR
prod
prod_fst 📖mathematicalfst
prod
prod_snd 📖mathematicalsnd
prod

CategoryTheory.Limits.WalkingMulticospan

Definitions

NameCategoryTheorems
functorExt 📖CompOp
2 mathmath: functorExt_hom_app, functorExt_inv_app
instInhabitedHom 📖CompOp
instInhabitedOfL 📖CompOp
instSmallCategory 📖CompOp
113 mathmath: CategoryTheory.Limits.Wedge.mk_pt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_apply_val, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map', CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, Opens.mayerVietorisSquare_X₃, CondensedMod.isDiscrete_tfae, CategoryTheory.Limits.Multifork.ext_hom_hom, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, CategoryTheory.Limits.MulticospanIndex.multicospan_map, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_symm_apply_val, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_apply_coe, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.ofι_pt, CategoryTheory.Presheaf.isLocallySurjective_toSheafify, CategoryTheory.Limits.Multiequalizer.multifork_π_app_left, CondensedMod.isDiscrete_iff_isDiscrete_forget, CategoryTheory.Limits.Multifork.toPiFork_pt, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_functor, CategoryTheory.Limits.Wedge.IsLimit.lift_ι, CategoryTheory.Limits.Wedge.ext_hom_hom, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_inverse_obj_ι, CategoryTheory.Presheaf.isLocallyInjective_toSheafify, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, CategoryTheory.Presheaf.isSheaf_iff_of_isGeneratedByOneHypercovers, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_inv_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, Opens.mayerVietorisSquare_X₂, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.Wedge.condition, CategoryTheory.Limits.Multifork.app_left_eq_ι, CategoryTheory.Limits.Multifork.condition, Hom.comp_eq_comp, CategoryTheory.Limits.Wedge.IsLimit.lift_ι_assoc, Opens.coe_mayerVietorisSquare_X₁, CategoryTheory.Limits.Multifork.IsLimit.fac_assoc, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMap_app, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.Multifork.ofPiFork_pt, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_symm_apply_val, CategoryTheory.Presheaf.isSheaf_iff_multifork, CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso_inv, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_obj, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_inverse, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac_assoc, CondensedSet.isDiscrete_tfae, CategoryTheory.Limits.Multifork.IsLimit.fac, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_pt, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, CategoryTheory.Limits.Wedge.ext_inv_hom, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CondensedSet.LocallyConstant.instFaithfulCondensedTypeDiscrete, functorExt_hom_app, CondensedSet.LocallyConstant.instFullCondensedTypeDiscrete, CategoryTheory.Presheaf.isLocallySurjective_toPlus, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, functorExt_inv_app, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_obj, CategoryTheory.Limits.Multifork.ofι_π_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, Opens.mayerVietorisSquare'_toSquare, Opens.coe_mayerVietorisSquare_X₄, CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf, CategoryTheory.Limits.MulticospanIndex.multicospan_obj, CategoryTheory.Limits.Multifork.hom_comp_ι, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Limits.Multifork.pi_condition_assoc, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, CategoryTheory.Limits.Multifork.ext_inv_hom, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, CategoryTheory.Sheaf.instIsRightAdjointSheafComposeOfHasWeakSheafify, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.Functor.SmallCategories.instPreservesFiniteLimitsSheafSheafPullbackOfRepresentablyFlat, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_functor_obj_ι, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.isSheaf_iff, CategoryTheory.Presheaf.isLocallyInjective_toPlus, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, CategoryTheory.Limits.Multifork.hom_comp_ι_assoc, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map, Condensed.instAB4CondensedMod, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, CategoryTheory.Limits.Multifork.toPiFork_π_app_zero, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, CategoryTheory.Limits.Multifork.toSections_fac, Hom.id_eq_id, CategoryTheory.Limits.Multifork.isLimit_types_iff, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Limits.Multifork.condition_assoc, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.liftAux_fac, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac, CategoryTheory.Limits.Multifork.pi_condition, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso_hom

Theorems

NameKindAssumesProvesValidatesDepends On
functorExt_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMulticospan
instSmallCategory
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
functorExt
CategoryTheory.Functor.obj
CategoryTheory.Iso
functorExt_inv_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMulticospan
instSmallCategory
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
functorExt
CategoryTheory.Functor.obj
CategoryTheory.Iso

CategoryTheory.Limits.WalkingMulticospan.Hom

Definitions

NameCategoryTheorems
comp 📖CompOp
1 mathmath: comp_eq_comp

Theorems

NameKindAssumesProvesValidatesDepends On
comp_eq_comp 📖mathematicalcomp
CategoryTheory.CategoryStruct.comp
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory
id_eq_id 📖mathematicalid
CategoryTheory.CategoryStruct.id
CategoryTheory.Limits.WalkingMulticospan
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory

CategoryTheory.Limits.WalkingMultispan

Definitions

NameCategoryTheorems
arrowEquiv 📖CompOp
equiv 📖CompOp
functorExt 📖CompOp
2 mathmath: functorExt_hom_app, functorExt_inv_app
inclusionOfLinearOrder 📖CompOp
4 mathmath: CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, inclusionOfLinearOrder_obj, inclusionOfLinearOrder_map
instInhabitedHom 📖CompOp
instInhabitedOfL 📖CompOp
instSmallCategory 📖CompOp
131 mathmath: CategoryTheory.GlueData.diagramIso_app_right, functorExt_hom_app, TopCat.GlueData.preimage_image_eq_image, TopCat.GlueData.π_surjective, CategoryTheory.Limits.Multicofork.ofπ_ι_app, TopCat.GlueData.open_image_open, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, TopCat.GlueData.ι_fromOpenSubsetsGlue, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Functor.CoconeTypes.isMulticoequalizer_iff, CategoryTheory.GlueData.types_π_surjective, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersion, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, CategoryTheory.Limits.Multicofork.π_comp_hom_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.isOpen_iff, TopCat.GlueData.ι_fromOpenSubsetsGlue_apply, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.Cowedge.IsColimit.π_desc_assoc, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, SSet.horn₃₁.desc.multicofork_pt, CategoryTheory.Limits.Multicofork.toSigmaCofork_pt, CategoryTheory.Limits.Multicofork.condition_assoc, CategoryTheory.Limits.MultispanIndex.multispanMapIso_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, CategoryTheory.Limits.Cowedge.IsColimit.π_desc, CategoryTheory.Limits.Cowedge.condition_assoc, CategoryTheory.Limits.MultispanIndex.multispan_map_fst, AlgebraicGeometry.Scheme.GlueData.instPreservesColimitTopCatWalkingMultispanProdJMultispanDiagramForgetToTop, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, SSet.horn₃₁.desc.multicofork_π_two_assoc, CategoryTheory.Limits.Multicofork.ext_hom_hom, SSet.horn₃₁.desc.multicofork_π_zero_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt, CategoryTheory.GlueData.diagramIso_app_left, CategoryTheory.Limits.Multicofork.π_eq_app_right, AlgebraicGeometry.Scheme.GlueData.instPreservesColimitWalkingMultispanProdJMultispanDiagramForget, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv, AlgebraicGeometry.Scheme.GlueData.instIsOpenImmersionιLocallyRingedSpaceToLocallyRingedSpaceGlueData, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, CategoryTheory.Limits.MultispanIndex.multispan_obj_right, CategoryTheory.GlueData.diagramIso_inv_app_left, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_obj, CategoryTheory.Limits.Multicofork.map_pt, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', TopCat.GlueData.range_fromOpenSubsetsGlue, CategoryTheory.Limits.MultispanIndex.multispan_map_snd, CategoryTheory.GlueData.diagramIso_inv_app_right, CategoryTheory.Limits.Cowedge.ext_hom_hom, CategoryTheory.Limits.Cowedge.mk_pt, TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbedding, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective, CategoryTheory.Limits.Multicofork.ofπ_pt, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_pt, functorExt_inv_app, CategoryTheory.Limits.Multicofork.map_ι_app, instSubsingletonHomRight, AlgebraicGeometry.PresheafedSpace.GlueData.componentwise_diagram_π_isIso, CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right', AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, TopCat.GlueData.fromOpenSubsetsGlue_injective, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, TopCat.GlueData.ι_isOpenEmbedding, CategoryTheory.Limits.Multicofork.toSigmaCofork_π, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt, instLocallySmall, CategoryTheory.Limits.Multicofork.IsColimit.fac_assoc, CategoryTheory.Limits.Multicofork.fst_app_right, SSet.horn₃₂.desc.multicofork_π_zero_assoc, inclusionOfLinearOrder_obj, Hom.id_eq_id, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, TopCat.GlueData.preimage_range, CategoryTheory.OrthogonalReflection.D₂.hasColimitsOfShape, CategoryTheory.Limits.MultispanIndex.multispanMapIso_hom_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, TopCat.GlueData.ι_mono, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv_assoc, AlgebraicGeometry.SheafedSpace.GlueData.ιIsOpenImmersion, TopCat.GlueData.image_inter, CategoryTheory.Limits.Multicofork.ext_inv_hom, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_obj, SSet.horn₃₁.desc.multicofork_π_three_assoc, CategoryTheory.Limits.Cowedge.ext_inv_hom, TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap, CategoryTheory.Limits.Multicofork.snd_app_right, CategoryTheory.Limits.Multicofork.sigma_condition, instIsEmptyHomRightLeft, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_inverse, AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, CompleteLattice.MulticoequalizerDiagram.multicofork_pt, CategoryTheory.Limits.Multicofork.condition, CategoryTheory.Limits.MultispanIndex.multispan_obj_left, TopCat.GlueData.ι_jointly_surjective, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom, SSet.horn₃₂.desc.multicofork_pt, CategoryTheory.GlueData.hasColimit_multispan_comp, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right, CategoryTheory.Limits.Multicofork.IsColimit.isPushout, AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, TopCat.GlueData.ι_eq_iff_rel, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π, inclusionOfLinearOrder_map, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.GlueData.types_ι_jointly_surjective, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.Multicofork.π_comp_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, SSet.horn₃₂.desc.multicofork_π_three_assoc, Hom.comp_eq_comp, SSet.horn₃₂.desc.multicofork_π_one_assoc, instSubsingletonHomLeft, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom, TopCat.GlueData.ι_injective, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.GlueData.diagramIso_hom_app_right, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_functor, CategoryTheory.Limits.Multicofork.IsColimit.fac, TopCat.GlueData.preimage_image_eq_image', CategoryTheory.Limits.Cowedge.condition, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, CategoryTheory.GlueData.diagramIso_hom_app_left
instUniqueHom 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
functorExt_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
instSmallCategory
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
functorExt
CategoryTheory.Functor.obj
CategoryTheory.Iso
functorExt_inv_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Limits.WalkingMultispan
instSmallCategory
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
functorExt
CategoryTheory.Functor.obj
CategoryTheory.Iso
inclusionOfLinearOrder_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.MultispanShape.ofLinearOrder
instSmallCategory
CategoryTheory.Limits.MultispanShape.prod
inclusionOfLinearOrder
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
left
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
right
CategoryTheory.CategoryStruct.id
Hom.fst
Hom.snd
inclusionOfLinearOrder_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Limits.MultispanShape.ofLinearOrder
instSmallCategory
CategoryTheory.Limits.MultispanShape.prod
inclusionOfLinearOrder
left
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
right
instIsEmptyHomRightLeft 📖mathematicalIsEmpty
Quiver.Hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
instSmallCategory
right
left
instLocallySmall 📖mathematicalCategoryTheory.LocallySmall
CategoryTheory.Limits.WalkingMultispan
instSmallCategory
small_subsingleton
instSubsingletonHomLeft
small_of_surjective
small_sum
small_subtype
UnivLE.small
univLE_of_max
UnivLE.self
IsEmpty.instSubsingleton
instIsEmptyHomRightLeft
instSubsingletonHomRight
instSmallOfLOfR 📖mathematicalSmall
CategoryTheory.Limits.WalkingMultispan
small_of_surjective
small_sum
instSubsingletonHomLeft 📖mathematicalQuiver.Hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
instSmallCategory
left
Unique.instSubsingleton
IsEmpty.instSubsingleton
instSubsingletonHomRight 📖mathematicalQuiver.Hom
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
instSmallCategory
right
Unique.instSubsingleton
IsEmpty.instSubsingleton

CategoryTheory.Limits.WalkingMultispan.Hom

Definitions

NameCategoryTheorems
comp 📖CompOp
1 mathmath: comp_eq_comp

Theorems

NameKindAssumesProvesValidatesDepends On
comp_eq_comp 📖mathematicalcomp
CategoryTheory.CategoryStruct.comp
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.WalkingMultispan.instSmallCategory
id_eq_id 📖mathematicalid
CategoryTheory.CategoryStruct.id
CategoryTheory.Limits.WalkingMultispan
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.WalkingMultispan.instSmallCategory

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