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Result

Found 144 declarations mentioning CategoryTheory.Limits.MultispanIndex.

• CategoryTheory.Limits.MultispanIndex 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  (J : CategoryTheory.Limits.MultispanShape) (C : Type u) [CategoryTheory.Category.{v, u} C] : Type (max (max (max u v) w) w')
• CategoryTheory.Limits.HasMulticoequalizer 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) : Prop
• CategoryTheory.Limits.Multicofork 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) : Type (max (max (max w w') u) v)
• CategoryTheory.Limits.MultispanIndex.SymmStruct 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} (I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C) : Type (max v w)
• CategoryTheory.Limits.MultispanIndex.left 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {J : CategoryTheory.Limits.MultispanShape} {C : Type u} [CategoryTheory.Category.{v, u} C] (self : CategoryTheory.Limits.MultispanIndex J C) : J.L → C
• CategoryTheory.Limits.MultispanIndex.right 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {J : CategoryTheory.Limits.MultispanShape} {C : Type u} [CategoryTheory.Category.{v, u} C] (self : CategoryTheory.Limits.MultispanIndex J C) : J.R → C
• CategoryTheory.Limits.multicoequalizer 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] : C
• CategoryTheory.Limits.MultispanIndex.multispan 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) : CategoryTheory.Functor (CategoryTheory.Limits.WalkingMultispan J) C
• CategoryTheory.Limits.MultispanIndex.toLinearOrder 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} (I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C) [LinearOrder ι] : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.ofLinearOrder ι) C
• CategoryTheory.Limits.Multicoequalizer.multicofork 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] : CategoryTheory.Limits.Multicofork I
• CategoryTheory.Limits.Multicofork.toLinearOrder 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} [LinearOrder ι] {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (c : CategoryTheory.Limits.Multicofork I) : CategoryTheory.Limits.Multicofork I.toLinearOrder
• CategoryTheory.Limits.MultispanIndex.fst 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {J : CategoryTheory.Limits.MultispanShape} {C : Type u} [CategoryTheory.Category.{v, u} C] (self : CategoryTheory.Limits.MultispanIndex J C) (a : J.L) : self.left a ⟶ self.right (J.fst a)
• CategoryTheory.Limits.MultispanIndex.snd 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {J : CategoryTheory.Limits.MultispanShape} {C : Type u} [CategoryTheory.Category.{v, u} C] (self : CategoryTheory.Limits.MultispanIndex J C) (a : J.L) : self.left a ⟶ self.right (J.snd a)
• CategoryTheory.Limits.MultispanIndex.multispan_obj_left 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) (a : J.L) : I.multispan.obj (CategoryTheory.Limits.WalkingMultispan.left a) = I.left a
• CategoryTheory.Limits.MultispanIndex.multispan_obj_right 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) (b : J.R) : I.multispan.obj (CategoryTheory.Limits.WalkingMultispan.right b) = I.right b
• CategoryTheory.Limits.MultispanIndex.parallelPairDiagram 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] : CategoryTheory.Functor CategoryTheory.Limits.WalkingParallelPair C
• CategoryTheory.Limits.Multicoequalizer.π 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] (b : J.R) : I.right b ⟶ CategoryTheory.Limits.multicoequalizer I
• CategoryTheory.Limits.Multicofork.ofLinearOrder 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} [LinearOrder ι] {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (c : CategoryTheory.Limits.Multicofork I.toLinearOrder) (h : I.SymmStruct) : CategoryTheory.Limits.Multicofork I
• CategoryTheory.Limits.MultispanIndex.toLinearOrder_right 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} (I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C) [LinearOrder ι] (i : (CategoryTheory.Limits.MultispanShape.ofLinearOrder ι).R) : I.toLinearOrder.right i = I.right i
• CategoryTheory.Limits.Multicofork.π 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) (b : J.R) : I.right b ⟶ K.pt
• CategoryTheory.Limits.MultispanIndex.SymmStruct.iso 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (self : I.SymmStruct) (i j : ι) : I.left (i, j) ≅ I.left (j, i)
• CategoryTheory.Limits.MultispanIndex.mk 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {J : CategoryTheory.Limits.MultispanShape} {C : Type u} [CategoryTheory.Category.{v, u} C] (left : J.L → C) (right : J.R → C) (fst : (a : J.L) → left a ⟶ right (J.fst a)) (snd : (a : J.L) → left a ⟶ right (J.snd a)) : CategoryTheory.Limits.MultispanIndex J C
• CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (d : CategoryTheory.Limits.Cofan I.right) (hc : CategoryTheory.Limits.IsColimit c) : CategoryTheory.Functor CategoryTheory.Limits.WalkingParallelPair C
• CategoryTheory.Limits.Multicoequalizer.sigmaπ 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] : ∐ I.right ⟶ CategoryTheory.Limits.multicoequalizer I
• CategoryTheory.Limits.MultispanIndex.fstSigmaMap 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] : ∐ I.left ⟶ ∐ I.right
• CategoryTheory.Limits.MultispanIndex.sndSigmaMap 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] : ∐ I.left ⟶ ∐ I.right
• CategoryTheory.Limits.Multicoequalizer.instEpiSigmaπ 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] : CategoryTheory.Epi (CategoryTheory.Limits.Multicoequalizer.sigmaπ I)
• CategoryTheory.Limits.Multicofork.isoOfπ 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (t : CategoryTheory.Limits.Multicofork I) : t ≅ CategoryTheory.Limits.Multicofork.ofπ I t.pt t.π ⋯
• CategoryTheory.Limits.Multicoequalizer.multicofork_π 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] (b : J.R) : (CategoryTheory.Limits.Multicoequalizer.multicofork I).π b = CategoryTheory.Limits.Multicoequalizer.π I b
• CategoryTheory.Limits.Multicofork.isColimitToLinearOrder 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} [LinearOrder ι] {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (c : CategoryTheory.Limits.Multicofork I) (hc : CategoryTheory.Limits.IsColimit c) (h : I.SymmStruct) : CategoryTheory.Limits.IsColimit c.toLinearOrder
• CategoryTheory.Limits.MultispanIndex.SymmStruct.fst_eq_snd 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (self : I.SymmStruct) (i : ι) : I.fst (i, i) = I.snd (i, i)
• CategoryTheory.Limits.Multicoequalizer.instHasCoequalizerFstSigmaMapSndSigmaMap 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] : CategoryTheory.Limits.HasCoequalizer I.fstSigmaMap I.sndSigmaMap
• CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} (I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C) [LinearOrder ι] : (CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder ι).comp I.multispan ≅ I.toLinearOrder.multispan
• CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right' 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] (b : J.R) : CategoryTheory.Limits.colimit.ι I.multispan (CategoryTheory.Limits.WalkingMultispan.right b) = CategoryTheory.Limits.Multicoequalizer.π I b
• CategoryTheory.Limits.MultispanIndex.multispan_map_fst 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) (a : J.L) : I.multispan.map (CategoryTheory.Limits.WalkingMultispan.Hom.fst a) = I.fst a
• CategoryTheory.Limits.MultispanIndex.multispan_map_snd 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) (a : J.L) : I.multispan.map (CategoryTheory.Limits.WalkingMultispan.Hom.snd a) = I.snd a
• CategoryTheory.Limits.MultispanIndex.toLinearOrder_left 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} (I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C) [LinearOrder ι] (j : (CategoryTheory.Limits.MultispanShape.ofLinearOrder ι).L) : I.toLinearOrder.left j = I.left ↑j
• CategoryTheory.Limits.Multicoequalizer.isoCoequalizer 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] : CategoryTheory.Limits.multicoequalizer I ≅ CategoryTheory.Limits.coequalizer I.fstSigmaMap I.sndSigmaMap
• CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (d : CategoryTheory.Limits.Cofan I.right) (hc : CategoryTheory.Limits.IsColimit c) : c.pt ⟶ d.pt
• CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (d : CategoryTheory.Limits.Cofan I.right) (hc : CategoryTheory.Limits.IsColimit c) : c.pt ⟶ d.pt
• CategoryTheory.Limits.Multicofork.ofπ 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) (P : C) (π : (b : J.R) → I.right b ⟶ P) (w : ∀ (a : J.L), CategoryTheory.CategoryStruct.comp (I.fst a) (π (J.fst a)) = CategoryTheory.CategoryStruct.comp (I.snd a) (π (J.snd a))) : CategoryTheory.Limits.Multicofork I
• CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_obj 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (d : CategoryTheory.Limits.Cofan I.right) (hc : CategoryTheory.Limits.IsColimit c) (x : CategoryTheory.Limits.WalkingParallelPair) : (I.parallelPairDiagramOfIsColimit d hc).obj x = CategoryTheory.Limits.parallelPair.parallelPairObj c.pt d.pt x
• CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (b : J.R) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Sigma.ι I.right b) (CategoryTheory.Limits.Multicoequalizer.sigmaπ I) = CategoryTheory.Limits.Multicoequalizer.π I b
• CategoryTheory.Limits.Multicofork.ofSigmaCofork 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {c : CategoryTheory.Limits.Cofan I.left} {hc : CategoryTheory.Limits.IsColimit c} {d : CategoryTheory.Limits.Cofan I.right} (a : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc)) : CategoryTheory.Limits.Multicofork I
• CategoryTheory.Limits.Multicoequalizer.condition 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] (a : J.L) : CategoryTheory.CategoryStruct.comp (I.fst a) (CategoryTheory.Limits.Multicoequalizer.π I (J.fst a)) = CategoryTheory.CategoryStruct.comp (I.snd a) (CategoryTheory.Limits.Multicoequalizer.π I (J.snd a))
• CategoryTheory.Limits.Multicoequalizer.desc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] (W : C) (k : (b : J.R) → I.right b ⟶ W) (h : ∀ (a : J.L), CategoryTheory.CategoryStruct.comp (I.fst a) (k (J.fst a)) = CategoryTheory.CategoryStruct.comp (I.snd a) (k (J.snd a))) : CategoryTheory.Limits.multicoequalizer I ⟶ W
• CategoryTheory.Limits.Multicofork.ofπ_pt 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) (P : C) (π : (b : J.R) → I.right b ⟶ P) (w : ∀ (a : J.L), CategoryTheory.CategoryStruct.comp (I.fst a) (π (J.fst a)) = CategoryTheory.CategoryStruct.comp (I.snd a) (π (J.snd a))) : (CategoryTheory.Limits.Multicofork.ofπ I P π w).pt = P
• CategoryTheory.Limits.Multicoequalizer.hom_ext 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] {W : C} (i j : CategoryTheory.Limits.multicoequalizer I ⟶ W) (h : ∀ (b : J.R), CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.π I b) i = CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.π I b) j) : i = j
• CategoryTheory.Limits.Multicoequalizer.hom_ext_iff 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} [CategoryTheory.Limits.HasMulticoequalizer I] {W : C} {i j : CategoryTheory.Limits.multicoequalizer I ⟶ W} : i = j ↔ ∀ (b : J.R), CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.π I b) i = CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.π I b) j
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] : CategoryTheory.Limits.Multicofork I ≌ CategoryTheory.Limits.Cofork I.fstSigmaMap I.sndSigmaMap
• CategoryTheory.Limits.Multicofork.toSigmaCofork 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) (K : CategoryTheory.Limits.Multicofork I) : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc)
• CategoryTheory.Limits.Multicofork.condition 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) (a : J.L) : CategoryTheory.CategoryStruct.comp (I.fst a) (K.π (J.fst a)) = CategoryTheory.CategoryStruct.comp (I.snd a) (K.π (J.snd a))
• CategoryTheory.Limits.Multicofork.IsColimit.desc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {K : CategoryTheory.Limits.Multicofork I} (hK : CategoryTheory.Limits.IsColimit K) {T : C} (k : (a : J.R) → I.right a ⟶ T) (hk : ∀ (b : J.L), CategoryTheory.CategoryStruct.comp (I.fst b) (k (J.fst b)) = CategoryTheory.CategoryStruct.comp (I.snd b) (k (J.snd b))) : K.pt ⟶ T
• CategoryTheory.Limits.Multicofork.π_comp_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K₁ K₂ : CategoryTheory.Limits.Multicofork I) (f : K₁ ⟶ K₂) (b : J.R) : CategoryTheory.CategoryStruct.comp (K₁.π b) f.hom = K₂.π b
• CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (self : I.SymmStruct) (i j : ι) : CategoryTheory.CategoryStruct.comp (self.iso i j).hom (I.fst (j, i)) = I.snd (i, j)
• CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (self : I.SymmStruct) (i j : ι) : CategoryTheory.CategoryStruct.comp (self.iso i j).hom (I.snd (j, i)) = I.fst (i, j)
• CategoryTheory.Limits.Multicoequalizer.condition_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] (a : J.L) {Z : C} (h : CategoryTheory.Limits.multicoequalizer I ⟶ Z) : CategoryTheory.CategoryStruct.comp (I.fst a) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.π I (J.fst a)) h) = CategoryTheory.CategoryStruct.comp (I.snd a) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.π I (J.snd a)) h)
• CategoryTheory.Limits.Multicofork.π_eq_app_right 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) (b : J.R) : K.ι.app (CategoryTheory.Limits.WalkingMultispan.right b) = K.π b
• CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (b : J.L) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Sigma.ι I.left b) I.fstSigmaMap = CategoryTheory.CategoryStruct.comp (I.fst b) (CategoryTheory.Limits.Sigma.ι I.right (J.fst b))
• CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (b : J.L) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Sigma.ι I.left b) I.sndSigmaMap = CategoryTheory.CategoryStruct.comp (I.snd b) (CategoryTheory.Limits.Sigma.ι I.right (J.snd b))
• CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (b : J.R) {Z : C} (h : CategoryTheory.Limits.multicoequalizer I ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Sigma.ι I.right b) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.sigmaπ I) h) = CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.π I b) h
• CategoryTheory.Limits.Multicoequalizer.π_desc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] (W : C) (k : (b : J.R) → I.right b ⟶ W) (h : ∀ (a : J.L), CategoryTheory.CategoryStruct.comp (I.fst a) (k (J.fst a)) = CategoryTheory.CategoryStruct.comp (I.snd a) (k (J.snd a))) (b : J.R) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.π I b) (CategoryTheory.Limits.Multicoequalizer.desc I W k h) = k b
• CategoryTheory.Limits.Multicofork.toSigmaCofork_pt 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) (K : CategoryTheory.Limits.Multicofork I) : (CategoryTheory.Limits.Multicofork.toSigmaCofork hc hd K).pt = K.pt
• CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] (b : J.R) : (CategoryTheory.Limits.Multicoequalizer.multicofork I).ι.app (CategoryTheory.Limits.WalkingMultispan.right b) = CategoryTheory.Limits.Multicoequalizer.π I b
• CategoryTheory.Limits.Multicofork.IsColimit.hom_ext 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {K : CategoryTheory.Limits.Multicofork I} (hK : CategoryTheory.Limits.IsColimit K) {T : C} {f g : K.pt ⟶ T} (h : ∀ (a : J.R), CategoryTheory.CategoryStruct.comp (K.π a) f = CategoryTheory.CategoryStruct.comp (K.π a) g) : f = g
• CategoryTheory.Limits.Multicofork.condition_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) (a : J.L) {Z : C} (h : K.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (I.fst a) (CategoryTheory.CategoryStruct.comp (K.π (J.fst a)) h) = CategoryTheory.CategoryStruct.comp (I.snd a) (CategoryTheory.CategoryStruct.comp (K.π (J.snd a)) h)
• CategoryTheory.Limits.Multicofork.ext 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {K K' : CategoryTheory.Limits.Multicofork I} (e : K.pt ≅ K'.pt) (h : ∀ (i : J.R), CategoryTheory.CategoryStruct.comp (K.π i) e.hom = K'.π i := by cat_disch) : K ≅ K'
• CategoryTheory.Limits.Multicofork.IsColimit.fac 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {K : CategoryTheory.Limits.Multicofork I} (hK : CategoryTheory.Limits.IsColimit K) {T : C} (k : (a : J.R) → I.right a ⟶ T) (hk : ∀ (b : J.L), CategoryTheory.CategoryStruct.comp (I.fst b) (k (J.fst b)) = CategoryTheory.CategoryStruct.comp (I.snd b) (k (J.snd b))) (a : J.R) : CategoryTheory.CategoryStruct.comp (K.π a) (CategoryTheory.Limits.Multicofork.IsColimit.desc hK k hk) = k a
• CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} : CategoryTheory.Functor (CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc)) (CategoryTheory.Limits.Multicofork I)
• CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (t : CategoryTheory.Limits.Multicofork I) : t.isoOfπ.hom.hom = CategoryTheory.CategoryStruct.id t.pt
• CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (t : CategoryTheory.Limits.Multicofork I) : t.isoOfπ.inv.hom = CategoryTheory.CategoryStruct.id t.pt
• CategoryTheory.Limits.Multicofork.ofSigmaCofork_pt 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {c : CategoryTheory.Limits.Cofan I.left} {hc : CategoryTheory.Limits.IsColimit c} {d : CategoryTheory.Limits.Cofan I.right} (a : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc)) : (CategoryTheory.Limits.Multicofork.ofSigmaCofork a).pt = a.pt
• CategoryTheory.Limits.Multicofork.fst_app_right 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) (a : J.L) : K.ι.app (CategoryTheory.Limits.WalkingMultispan.left a) = CategoryTheory.CategoryStruct.comp (I.fst a) (K.π (J.fst a))
• CategoryTheory.Limits.Multicofork.snd_app_right 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) (a : J.L) : K.ι.app (CategoryTheory.Limits.WalkingMultispan.left a) = CategoryTheory.CategoryStruct.comp (I.snd a) (K.π (J.snd a))
• CategoryTheory.Limits.Multicoequalizer.π_desc_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasMulticoequalizer I] (W : C) (k : (b : J.R) → I.right b ⟶ W) (h : ∀ (a : J.L), CategoryTheory.CategoryStruct.comp (I.fst a) (k (J.fst a)) = CategoryTheory.CategoryStruct.comp (I.snd a) (k (J.snd a))) (b : J.R) {Z : C} (h✝ : W ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.π I b) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicoequalizer.desc I W k h) h✝) = CategoryTheory.CategoryStruct.comp (k b) h✝
• CategoryTheory.Limits.Multicofork.π_comp_hom_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K₁ K₂ : CategoryTheory.Limits.Multicofork I) (f : K₁ ⟶ K₂) (b : J.R) {Z : C} (h : K₂.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (K₁.π b) (CategoryTheory.CategoryStruct.comp f.hom h) = CategoryTheory.CategoryStruct.comp (K₂.π b) h
• CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (b : J.L) {Z : C} (h : ∐ I.right ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Sigma.ι I.left b) (CategoryTheory.CategoryStruct.comp I.fstSigmaMap h) = CategoryTheory.CategoryStruct.comp (I.fst b) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Sigma.ι I.right (J.fst b)) h)
• CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (b : J.L) {Z : C} (h : ∐ I.right ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Sigma.ι I.left b) (CategoryTheory.CategoryStruct.comp I.sndSigmaMap h) = CategoryTheory.CategoryStruct.comp (I.snd b) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Sigma.ι I.right (J.snd b)) h)
• CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (self : I.SymmStruct) (i j : ι) {Z : C} (h : I.right ((CategoryTheory.Limits.MultispanShape.prod ι).fst (j, i)) ⟶ Z) : CategoryTheory.CategoryStruct.comp (self.iso i j).hom (CategoryTheory.CategoryStruct.comp (I.fst (j, i)) h) = CategoryTheory.CategoryStruct.comp (I.snd (i, j)) h
• CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (self : I.SymmStruct) (i j : ι) {Z : C} (h : I.right ((CategoryTheory.Limits.MultispanShape.prod ι).snd (j, i)) ⟶ Z) : CategoryTheory.CategoryStruct.comp (self.iso i j).hom (CategoryTheory.CategoryStruct.comp (I.snd (j, i)) h) = CategoryTheory.CategoryStruct.comp (I.fst (i, j)) h
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) : CategoryTheory.Limits.Multicofork I ≌ CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc)
• CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) : CategoryTheory.Functor (CategoryTheory.Limits.Multicofork I) (CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc))
• CategoryTheory.Limits.MultispanIndex.toLinearOrder_fst 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} (I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C) [LinearOrder ι] (j : (CategoryTheory.Limits.MultispanShape.ofLinearOrder ι).L) : I.toLinearOrder.fst j = I.fst ↑j
• CategoryTheory.Limits.MultispanIndex.toLinearOrder_snd 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} (I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C) [LinearOrder ι] (j : (CategoryTheory.Limits.MultispanShape.ofLinearOrder ι).L) : I.toLinearOrder.snd j = I.snd ↑j
• CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (d : CategoryTheory.Limits.Cofan I.right) (hc : CategoryTheory.Limits.IsColimit c) (i : J.L) : CategoryTheory.CategoryStruct.comp (c.inj i) (I.fstSigmaMapOfIsColimit d hc) = CategoryTheory.CategoryStruct.comp (I.fst i) (d.inj (J.fst i))
• CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (d : CategoryTheory.Limits.Cofan I.right) (hc : CategoryTheory.Limits.IsColimit c) (i : J.L) : CategoryTheory.CategoryStruct.comp (c.inj i) (I.sndSigmaMapOfIsColimit d hc) = CategoryTheory.CategoryStruct.comp (I.snd i) (d.inj (J.snd i))
• CategoryTheory.Limits.Multicofork.IsColimit.fac_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {K : CategoryTheory.Limits.Multicofork I} (hK : CategoryTheory.Limits.IsColimit K) {T : C} (k : (a : J.R) → I.right a ⟶ T) (hk : ∀ (b : J.L), CategoryTheory.CategoryStruct.comp (I.fst b) (k (J.fst b)) = CategoryTheory.CategoryStruct.comp (I.snd b) (k (J.snd b))) (a : J.R) {Z : C} (h : T ⟶ Z) : CategoryTheory.CategoryStruct.comp (K.π a) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multicofork.IsColimit.desc hK k hk) h) = CategoryTheory.CategoryStruct.comp (k a) h
• CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_map 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (d : CategoryTheory.Limits.Cofan I.right) (hc : CategoryTheory.Limits.IsColimit c) {X✝ Y✝ : CategoryTheory.Limits.WalkingParallelPair} (h : X✝ ⟶ Y✝) : (I.parallelPairDiagramOfIsColimit d hc).map h = CategoryTheory.Limits.parallelPair.parallelPairHom (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc) h
• CategoryTheory.Limits.Multicofork.ext_hom_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {K K' : CategoryTheory.Limits.Multicofork I} (e : K.pt ≅ K'.pt) (h : ∀ (i : J.R), CategoryTheory.CategoryStruct.comp (K.π i) e.hom = K'.π i := by cat_disch) : (CategoryTheory.Limits.Multicofork.ext e h).hom.hom = e.hom
• CategoryTheory.Limits.Multicofork.ext_inv_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {K K' : CategoryTheory.Limits.Multicofork I} (e : K.pt ≅ K'.pt) (h : ∀ (i : J.R), CategoryTheory.CategoryStruct.comp (K.π i) e.hom = K'.π i := by cat_disch) : (CategoryTheory.Limits.Multicofork.ext e h).inv.hom = e.inv
• CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (d : CategoryTheory.Limits.Cofan I.right) (hc : CategoryTheory.Limits.IsColimit c) (i : J.L) {Z : C} (h : d.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (c.inj i) (CategoryTheory.CategoryStruct.comp (I.fstSigmaMapOfIsColimit d hc) h) = CategoryTheory.CategoryStruct.comp (I.fst i) (CategoryTheory.CategoryStruct.comp (d.inj (J.fst i)) h)
• CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (d : CategoryTheory.Limits.Cofan I.right) (hc : CategoryTheory.Limits.IsColimit c) (i : J.L) {Z : C} (h : d.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (c.inj i) (CategoryTheory.CategoryStruct.comp (I.sndSigmaMapOfIsColimit d hc) h) = CategoryTheory.CategoryStruct.comp (I.snd i) (CategoryTheory.CategoryStruct.comp (d.inj (J.snd i)) h)
• CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_obj 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (a : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc)) : (I.ofSigmaCoforkFunctor hc).obj a = CategoryTheory.Limits.Multicofork.ofSigmaCofork a
• CategoryTheory.Limits.Multicofork.toSigmaCofork_π 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) : (CategoryTheory.Limits.Multicofork.toSigmaCofork hc hd K).π = CategoryTheory.Limits.Cofan.IsColimit.desc hd K.π
• CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_obj 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) (K : CategoryTheory.Limits.Multicofork I) : (I.toSigmaCoforkFunctor hc hd).obj K = CategoryTheory.Limits.Multicofork.toSigmaCofork hc hd K
• CategoryTheory.Limits.Multicofork.IsColimit.mk 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) (desc : (E : CategoryTheory.Limits.Multicofork I) → K.pt ⟶ E.pt) (fac : ∀ (E : CategoryTheory.Limits.Multicofork I) (i : J.R), CategoryTheory.CategoryStruct.comp (K.π i) (desc E) = E.π i) (uniq : ∀ (E : CategoryTheory.Limits.Multicofork I) (m : K.pt ⟶ E.pt), (∀ (i : J.R), CategoryTheory.CategoryStruct.comp (K.π i) m = E.π i) → m = desc E) : CategoryTheory.Limits.IsColimit K
• CategoryTheory.Limits.Multicofork.sigma_condition 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) : CategoryTheory.CategoryStruct.comp (I.fstSigmaMapOfIsColimit d hc) (CategoryTheory.Limits.Cofan.IsColimit.desc hd K.π) = CategoryTheory.CategoryStruct.comp (I.sndSigmaMapOfIsColimit d hc) (CategoryTheory.Limits.Cofan.IsColimit.desc hd K.π)
• CategoryTheory.Limits.Multicofork.ofSigmaCofork_π 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (a : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc)) (i : J.R) : (CategoryTheory.Limits.Multicofork.ofSigmaCofork a).π i = CategoryTheory.CategoryStruct.comp (d.inj i) a.π
• CategoryTheory.Limits.Multicofork.snd_app_right_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) (a : J.L) {Z : C} (h : ((CategoryTheory.Functor.const (CategoryTheory.Limits.WalkingMultispan J)).obj K.pt).obj (CategoryTheory.Limits.WalkingMultispan.left a) ⟶ Z) : CategoryTheory.CategoryStruct.comp (K.ι.app (CategoryTheory.Limits.WalkingMultispan.left a)) h = CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp (I.snd a) (K.π (J.snd a))) h
• CategoryTheory.Limits.MultispanIndex.SymmStruct.mk 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} {I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C} (iso : (i j : ι) → I.left (i, j) ≅ I.left (j, i)) (iso_hom_fst : ∀ (i j : ι), CategoryTheory.CategoryStruct.comp (iso i j).hom (I.fst (j, i)) = I.snd (i, j)) (iso_hom_snd : ∀ (i j : ι), CategoryTheory.CategoryStruct.comp (iso i j).hom (I.snd (j, i)) = I.fst (i, j)) (fst_eq_snd : ∀ (i : ι), I.fst (i, i) = I.snd (i, i)) : I.SymmStruct
• CategoryTheory.Limits.Multicofork.ofπ_ι_app 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) (P : C) (π : (b : J.R) → I.right b ⟶ P) (w : ∀ (a : J.L), CategoryTheory.CategoryStruct.comp (I.fst a) (π (J.fst a)) = CategoryTheory.CategoryStruct.comp (I.snd a) (π (J.snd a))) (x : CategoryTheory.Limits.WalkingMultispan J) : (CategoryTheory.Limits.Multicofork.ofπ I P π w).ι.app x = match x with | CategoryTheory.Limits.WalkingMultispan.left a => CategoryTheory.CategoryStruct.comp (I.fst a) (π (J.fst a)) | CategoryTheory.Limits.WalkingMultispan.right a => π a
• CategoryTheory.Limits.Multicofork.IsColimit.mk_desc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) (desc : (E : CategoryTheory.Limits.Multicofork I) → K.pt ⟶ E.pt) (fac : ∀ (E : CategoryTheory.Limits.Multicofork I) (i : J.R), CategoryTheory.CategoryStruct.comp (K.π i) (desc E) = E.π i) (uniq : ∀ (E : CategoryTheory.Limits.Multicofork I) (m : K.pt ⟶ E.pt), (∀ (i : J.R), CategoryTheory.CategoryStruct.comp (K.π i) m = E.π i) → m = desc E) (E : CategoryTheory.Limits.Multicofork I) : (CategoryTheory.Limits.Multicofork.IsColimit.mk K desc fac uniq).desc E = desc E
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_inverse 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) : (I.multicoforkEquivSigmaCoforkOfIsColimit hc hd).inverse = I.ofSigmaCoforkFunctor hc
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_functor 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) : (I.multicoforkEquivSigmaCoforkOfIsColimit hc hd).functor = I.toSigmaCoforkFunctor hc hd
• CategoryTheory.Limits.Multicofork.sigma_condition_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} (K : CategoryTheory.Limits.Multicofork I) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) {Z : C} (h : K.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (I.fstSigmaMapOfIsColimit d hc) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Cofan.IsColimit.desc hd K.π) h) = CategoryTheory.CategoryStruct.comp (I.sndSigmaMapOfIsColimit d hc) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Cofan.IsColimit.desc hd K.π) h)
• CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) {K₁ K₂ : CategoryTheory.Limits.Multicofork I} (f : K₁ ⟶ K₂) : ((I.toSigmaCoforkFunctor hc hd).map f).hom = f.hom
• CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} (I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C) [LinearOrder ι] (X : CategoryTheory.Limits.WalkingMultispan (CategoryTheory.Limits.MultispanShape.ofLinearOrder ι)) : I.toLinearOrderMultispanIso.hom.app X = (match X with | CategoryTheory.Limits.WalkingMultispan.left a => CategoryTheory.Iso.refl (I.left ↑a) | CategoryTheory.Limits.WalkingMultispan.right a => CategoryTheory.Iso.refl (I.right a)).hom
• CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {ι : Type w} (I : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) C) [LinearOrder ι] (X : CategoryTheory.Limits.WalkingMultispan (CategoryTheory.Limits.MultispanShape.ofLinearOrder ι)) : I.toLinearOrderMultispanIso.inv.app X = (match X with | CategoryTheory.Limits.WalkingMultispan.left a => CategoryTheory.Iso.refl (I.left ↑a) | CategoryTheory.Limits.WalkingMultispan.right a => CategoryTheory.Iso.refl (I.right a)).inv
• CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} {I : CategoryTheory.Limits.MultispanIndex J C} {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (a : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc)) (i : J.L) : (CategoryTheory.Limits.Multicofork.ofSigmaCofork a).ι.app (CategoryTheory.Limits.WalkingMultispan.left i) = CategoryTheory.CategoryStruct.comp (c.inj i) (CategoryTheory.CategoryStruct.comp (I.fstSigmaMapOfIsColimit d hc) a.π)
• CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} {K₁ K₂ : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc)} (f : K₁ ⟶ K₂) : ((I.ofSigmaCoforkFunctor hc).map f).hom = f.hom
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_pt 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (K : CategoryTheory.Limits.Multicofork I) : (I.multicoforkEquivSigmaCofork.functor.obj K).pt = K.pt
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (a : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left))) (I.sndSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left)))) : (I.multicoforkEquivSigmaCofork.inverse.obj a).pt = a.pt
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] {K₁ K₂ : CategoryTheory.Limits.Multicofork I} (f : K₁ ⟶ K₂) : (I.multicoforkEquivSigmaCofork.functor.map f).hom = f.hom
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) : (I.multicoforkEquivSigmaCoforkOfIsColimit hc hd).unitIso = CategoryTheory.NatIso.ofComponents (fun K => CategoryTheory.Limits.Cocone.ext (CategoryTheory.Iso.refl ((CategoryTheory.Functor.id (CategoryTheory.Limits.Multicofork I)).obj K).pt) ⋯) ⋯
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (K : CategoryTheory.Limits.Multicofork I) (X : CategoryTheory.Limits.WalkingParallelPair) : (I.multicoforkEquivSigmaCofork.functor.obj K).ι.app X = CategoryTheory.Limits.WalkingParallelPair.rec (CategoryTheory.CategoryStruct.comp (I.sndSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left))) (CategoryTheory.Limits.Cofan.IsColimit.desc (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.right)) K.π)) (CategoryTheory.Limits.Cofan.IsColimit.desc (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.right)) K.π) X
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (a : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left))) (I.sndSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left)))) (x : CategoryTheory.Limits.WalkingMultispan J) : (I.multicoforkEquivSigmaCofork.inverse.obj a).ι.app x = match x with | CategoryTheory.Limits.WalkingMultispan.left a_1 => CategoryTheory.CategoryStruct.comp (I.fst a_1) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Cofan.inj (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (J.fst a_1)) a.π) | CategoryTheory.Limits.WalkingMultispan.right a_1 => CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Cofan.inj (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) a_1) a.π
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] {K₁ K₂ : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left))) (I.sndSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left)))} (f : K₁ ⟶ K₂) : (I.multicoforkEquivSigmaCofork.inverse.map f).hom = f.hom
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (X : CategoryTheory.Limits.Multicofork I) : (I.multicoforkEquivSigmaCofork.unitIso.hom.app X).hom = CategoryTheory.CategoryStruct.id X.pt
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (X : CategoryTheory.Limits.Multicofork I) : (I.multicoforkEquivSigmaCofork.unitIso.inv.app X).hom = CategoryTheory.CategoryStruct.id X.pt
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left} (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right} (hd : CategoryTheory.Limits.IsColimit d) : (I.multicoforkEquivSigmaCoforkOfIsColimit hc hd).counitIso = CategoryTheory.NatIso.ofComponents (fun K => CategoryTheory.Limits.Cofork.ext (CategoryTheory.Iso.refl (((I.ofSigmaCoforkFunctor hc).comp (I.toSigmaCoforkFunctor hc hd)).obj K).pt) ⋯) ⋯
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (X : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left))) (I.sndSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left)))) : (I.multicoforkEquivSigmaCofork.counitIso.hom.app X).hom = CategoryTheory.CategoryStruct.id X.pt
• CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom 📋 Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MultispanShape} (I : CategoryTheory.Limits.MultispanIndex J C) [CategoryTheory.Limits.HasCoproduct I.left] [CategoryTheory.Limits.HasCoproduct I.right] (X : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left))) (I.sndSigmaMapOfIsColimit (CategoryTheory.Limits.colimit.cocone (CategoryTheory.Discrete.functor I.right)) (CategoryTheory.Limits.colimit.isColimit (CategoryTheory.Discrete.functor I.left)))) : (I.multicoforkEquivSigmaCofork.counitIso.inv.app X).hom = CategoryTheory.CategoryStruct.id X.pt
• CategoryTheory.GlueData.diagram 📋 Mathlib.CategoryTheory.GlueData
  {C : Type u₁} [CategoryTheory.Category.{v, u₁} C] (D : CategoryTheory.GlueData C) : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod D.J) C
• CategoryTheory.Limits.MultispanIndex.map 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} (d : CategoryTheory.Limits.MultispanIndex J C) (F : CategoryTheory.Functor C D) : CategoryTheory.Limits.MultispanIndex J D
• CategoryTheory.Limits.Multicofork.map 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} {d : CategoryTheory.Limits.MultispanIndex J C} (c : CategoryTheory.Limits.Multicofork d) (F : CategoryTheory.Functor C D) : CategoryTheory.Limits.Multicofork (d.map F)
• CategoryTheory.Limits.MultispanIndex.map_left 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} (d : CategoryTheory.Limits.MultispanIndex J C) (F : CategoryTheory.Functor C D) (i : J.L) : (d.map F).left i = F.obj (d.left i)
• CategoryTheory.Limits.MultispanIndex.map_right 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} (d : CategoryTheory.Limits.MultispanIndex J C) (F : CategoryTheory.Functor C D) (i : J.R) : (d.map F).right i = F.obj (d.right i)
• CategoryTheory.Limits.MultispanIndex.multispanMapIso 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} (d : CategoryTheory.Limits.MultispanIndex J C) (F : CategoryTheory.Functor C D) : (d.map F).multispan ≅ d.multispan.comp F
• CategoryTheory.Limits.Multicofork.map_pt 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} {d : CategoryTheory.Limits.MultispanIndex J C} (c : CategoryTheory.Limits.Multicofork d) (F : CategoryTheory.Functor C D) : (c.map F).pt = F.obj c.pt
• CategoryTheory.Limits.Multicofork.isColimitMapOfPreserves 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} {d : CategoryTheory.Limits.MultispanIndex J C} (c : CategoryTheory.Limits.Multicofork d) (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.PreservesColimit d.multispan F] (hc : CategoryTheory.Limits.IsColimit c) : CategoryTheory.Limits.IsColimit (c.map F)
• CategoryTheory.Limits.Multicofork.isColimitMapEquiv 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} {d : CategoryTheory.Limits.MultispanIndex J C} (c : CategoryTheory.Limits.Multicofork d) (F : CategoryTheory.Functor C D) : CategoryTheory.Limits.IsColimit (F.mapCocone c) ≃ CategoryTheory.Limits.IsColimit (c.map F)
• CategoryTheory.Limits.MultispanIndex.map_fst 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} (d : CategoryTheory.Limits.MultispanIndex J C) (F : CategoryTheory.Functor C D) (i : J.L) : (d.map F).fst i = F.map (d.fst i)
• CategoryTheory.Limits.MultispanIndex.map_snd 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} (d : CategoryTheory.Limits.MultispanIndex J C) (F : CategoryTheory.Functor C D) (i : J.L) : (d.map F).snd i = F.map (d.snd i)
• CategoryTheory.Limits.MultispanIndex.multispanMapIso_hom_app 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} (d : CategoryTheory.Limits.MultispanIndex J C) (F : CategoryTheory.Functor C D) (X : CategoryTheory.Limits.WalkingMultispan J) : (d.multispanMapIso F).hom.app X = (match X with | CategoryTheory.Limits.WalkingMultispan.left a => CategoryTheory.Iso.refl (F.obj (d.left a)) | CategoryTheory.Limits.WalkingMultispan.right a => CategoryTheory.Iso.refl (F.obj (d.right a))).hom
• CategoryTheory.Limits.MultispanIndex.multispanMapIso_inv_app 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} (d : CategoryTheory.Limits.MultispanIndex J C) (F : CategoryTheory.Functor C D) (X : CategoryTheory.Limits.WalkingMultispan J) : (d.multispanMapIso F).inv.app X = (match X with | CategoryTheory.Limits.WalkingMultispan.left a => CategoryTheory.Iso.refl (F.obj (d.left a)) | CategoryTheory.Limits.WalkingMultispan.right a => CategoryTheory.Iso.refl (F.obj (d.right a))).inv
• CategoryTheory.Limits.Multicofork.map_ι_app 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.Limits.MultispanShape} {d : CategoryTheory.Limits.MultispanIndex J C} (c : CategoryTheory.Limits.Multicofork d) (F : CategoryTheory.Functor C D) (x : CategoryTheory.Limits.WalkingMultispan J) : (c.map F).ι.app x = match x with | CategoryTheory.Limits.WalkingMultispan.left a => CategoryTheory.CategoryStruct.comp (F.map (d.fst a)) (F.map (c.π (J.fst a))) | CategoryTheory.Limits.WalkingMultispan.right a => F.map (c.π a)
• CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork 📋 Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback
  {C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {J : CategoryTheory.Limits.MultispanShape} [Unique J.L] {I : CategoryTheory.Limits.MultispanIndex J C} (h : {J.fst default, J.snd default} = Set.univ) (h' : J.fst default ≠ J.snd default) (s : CategoryTheory.Limits.PushoutCocone (I.fst default) (I.snd default)) : CategoryTheory.Limits.Multicofork I
• CategoryTheory.Limits.Multicofork.IsColimit.isPushout 📋 Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback
  {C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {J : CategoryTheory.Limits.MultispanShape} [Unique J.L] {I : CategoryTheory.Limits.MultispanIndex J C} (c : CategoryTheory.Limits.Multicofork I) (h : {J.fst default, J.snd default} = Set.univ) (h' : J.fst default ≠ J.snd default) (hc : CategoryTheory.Limits.IsColimit c) : CategoryTheory.IsPushout (I.fst default) (I.snd default) (c.π (J.fst default)) (c.π (J.snd default))
• CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inl 📋 Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback
  {C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {J : CategoryTheory.Limits.MultispanShape} [Unique J.L] {I : CategoryTheory.Limits.MultispanIndex J C} (h : {J.fst default, J.snd default} = Set.univ) (h' : J.fst default ≠ J.snd default) (s : CategoryTheory.Limits.PushoutCocone (I.fst default) (I.snd default)) : (CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork h h' s).π (J.fst default) = s.inl
• CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inr 📋 Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback
  {C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {J : CategoryTheory.Limits.MultispanShape} [Unique J.L] {I : CategoryTheory.Limits.MultispanIndex J C} (h : {J.fst default, J.snd default} = Set.univ) (h' : J.fst default ≠ J.snd default) (s : CategoryTheory.Limits.PushoutCocone (I.fst default) (I.snd default)) : (CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork h h' s).π (J.snd default) = s.inr
• CompleteLattice.MulticoequalizerDiagram.multispanIndex 📋 Mathlib.Order.CompleteLattice.MulticoequalizerDiagram
  {T : Type u} [CompleteLattice T] {ι : Type u_1} {x : T} {u : ι → T} {v : ι → ι → T} (d : CompleteLattice.MulticoequalizerDiagram x u v) : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.MultispanShape.prod ι) T
• CategoryTheory.Functor.CoconeTypes.isMulticoequalizer_iff 📋 Mathlib.CategoryTheory.Limits.Types.Multicoequalizer
  {J : CategoryTheory.Limits.MultispanShape} {d : CategoryTheory.Limits.MultispanIndex J (Type u)} (c : d.multispan.CoconeTypes) : c.IsColimit ↔ (∀ (i₁ i₂ : J.R) (x₁ : d.right i₁) (x₂ : d.right i₂), c.ι (CategoryTheory.Limits.WalkingMultispan.right i₁) x₁ = c.ι (CategoryTheory.Limits.WalkingMultispan.right i₂) x₂ → d.multispan.ιColimitType (CategoryTheory.Limits.WalkingMultispan.right i₁) x₁ = d.multispan.ιColimitType (CategoryTheory.Limits.WalkingMultispan.right i₂) x₂) ∧ ∀ (x : c.pt), ∃ i a, c.ι (CategoryTheory.Limits.WalkingMultispan.right i) a = x
• CategoryTheory.Limits.multispanIndexCoend 📋 Mathlib.CategoryTheory.Limits.Shapes.End
  {J : Type u} [CategoryTheory.Category.{v, u} J] {C : Type u'} [CategoryTheory.Category.{v', u'} C] (F : CategoryTheory.Functor Jᵒᵖ (CategoryTheory.Functor J C)) : CategoryTheory.Limits.MultispanIndex (CategoryTheory.Limits.multispanShapeCoend J) C
• CategoryTheory.OrthogonalReflection.D₂.multispanIndex 📋 Mathlib.CategoryTheory.Presentable.OrthogonalReflection
  {C : Type u} [CategoryTheory.Category.{v, u} C] (W : CategoryTheory.MorphismProperty C) (Z : C) [CategoryTheory.Limits.HasCoproduct CategoryTheory.OrthogonalReflection.D₁.obj₁] [CategoryTheory.Limits.HasCoproduct CategoryTheory.OrthogonalReflection.D₁.obj₂] [CategoryTheory.Limits.HasPushouts C] : CategoryTheory.Limits.MultispanIndex (CategoryTheory.OrthogonalReflection.D₂.multispanShape W Z) C

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using the Loogle command from the command palette. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO. Please review the Lean FRO Terms of Use and Privacy Policy.

This is Loogle revision 9f11169 serving mathlib revision ce5dd8c