algebraic_topology.split_simplicial_object

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

dd1f8496

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

4f4a1c87

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -90,9 +90,9 @@ theorem ext (A₁ A₂ : IndexSet Δ) (h₁ : A₁.1 = A₂.1) (h₂ : A₁.e 
     A₁ = A₂ := by
   rcases A₁ with ⟨Δ₁, ⟨α₁, hα₁⟩⟩
   rcases A₂ with ⟨Δ₂, ⟨α₂, hα₂⟩⟩
-  simp only at h₁ 
+  simp only at h₁
   subst h₁
-  simp only [eq_to_hom_refl, comp_id, index_set.e] at h₂ 
+  simp only [eq_to_hom_refl, comp_id, index_set.e] at h₂
   simp only [h₂]
 #align simplicial_object.splitting.index_set.ext SimplicialObject.Splitting.IndexSet.ext
 -/
@@ -107,7 +107,7 @@ instance : Fintype (IndexSet Δ) :=
       rintro ⟨Δ₁, α₁⟩ ⟨Δ₂, α₂⟩ h₁
       induction Δ₁ using Opposite.rec'
       induction Δ₂ using Opposite.rec'
-      simp only at h₁ 
+      simp only at h₁
       have h₂ : Δ₁ = Δ₂ := by ext1; simpa only [Fin.mk_eq_mk] using h₁.1
       subst h₂
       refine' ext _ _ rfl _
@@ -142,12 +142,12 @@ def EqId : Prop :=
 theorem eqId_iff_eq : A.EqId ↔ A.1 = Δ := by
   constructor
   · intro h
-    dsimp at h 
+    dsimp at h
     rw [h]
     rfl
   · intro h
     rcases A with ⟨Δ', ⟨f, hf⟩⟩
-    simp only at h 
+    simp only at h
     subst h
     refine' ext _ _ rfl _
     · haveI := hf
@@ -186,7 +186,7 @@ theorem eqId_iff_mono : A.EqId ↔ Mono A.e :=
   by
   constructor
   · intro h
-    dsimp at h 
+    dsimp at h
     subst h
     dsimp only [id, e]
     infer_instance

4f4a1c87

bump to nightly-2023-12-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

c30f5587

Diff

@@ -240,34 +240,28 @@ def summand (A : IndexSet Δ) : C :=
 
 variable [HasFiniteCoproducts C]
 
-#print SimplicialObject.Splitting.coprod /-
 /-- The coproduct of the family `summand N Δ` -/
 @[simp]
 def coprod :=
   ∐ summand N Δ
 #align simplicial_object.splitting.coprod SimplicialObject.Splitting.coprod
--/
 
 variable {Δ}
 
-#print SimplicialObject.Splitting.ιCoprod /-
 /-- The inclusion of a summand in the coproduct. -/
 @[simp]
 def ιCoprod (A : IndexSet Δ) : N A.1.unop.len ⟶ coprod N Δ :=
   Sigma.ι _ A
 #align simplicial_object.splitting.ι_coprod SimplicialObject.Splitting.ιCoprod
--/
 
 variable {N}
 
-#print SimplicialObject.Splitting.map /-
 /-- The canonical morphism `coprod N Δ ⟶ X.obj Δ` attached to a sequence
 of objects `N` and a sequence of morphisms `N n ⟶ X _[n]`. -/
 @[simp]
 def map (Δ : SimplexCategoryᵒᵖ) : coprod N Δ ⟶ X.obj Δ :=
   Sigma.desc fun A => φ A.1.unop.len ≫ X.map A.e.op
 #align simplicial_object.splitting.map SimplicialObject.Splitting.map
--/
 
 end Splitting
 
@@ -290,42 +284,36 @@ namespace Splitting
 
 variable {X Y : SimplicialObject C} (s : Splitting X)
 
-#print SimplicialObject.Splitting.map_isIso /-
 instance map_isIso (Δ : SimplexCategoryᵒᵖ) : IsIso (Splitting.map X s.ι Δ) :=
   s.map_is_iso' Δ
 #align simplicial_object.splitting.map_is_iso SimplicialObject.Splitting.map_isIso
--/
 
-#print SimplicialObject.Splitting.iso /-
 /-- The isomorphism on simplices given by the axiom `splitting.map_is_iso'` -/
 @[simps]
 def iso (Δ : SimplexCategoryᵒᵖ) : coprod s.n Δ ≅ X.obj Δ :=
   asIso (Splitting.map X s.ι Δ)
 #align simplicial_object.splitting.iso SimplicialObject.Splitting.iso
--/
 
-#print SimplicialObject.Splitting.ιSummand /-
 /-- Via the isomorphism `s.iso Δ`, this is the inclusion of a summand
 in the direct sum decomposition given by the splitting `s : splitting X`. -/
 def ιSummand {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) : s.n A.1.unop.len ⟶ X.obj Δ :=
   Splitting.ιCoprod s.n A ≫ (s.Iso Δ).Hom
 #align simplicial_object.splitting.ι_summand SimplicialObject.Splitting.ιSummand
--/
 
-#print SimplicialObject.Splitting.ιSummand_eq /-
+#print SimplicialObject.Splitting.cofan_inj_eq /-
 @[reassoc]
-theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
+theorem cofan_inj_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A = s.ι A.1.unop.len ≫ X.map A.e.op :=
   by
   dsimp only [ι_summand, iso.hom]
   erw [colimit.ι_desc, cofan.mk_ι_app]
-#align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.ιSummand_eq
+#align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.cofan_inj_eq
 -/
 
-#print SimplicialObject.Splitting.ιSummand_id /-
-theorem ιSummand_id (n : ℕ) : s.ιSummand (IndexSet.id (op [n])) = s.ι n := by
+#print SimplicialObject.Splitting.cofan_inj_id /-
+theorem cofan_inj_id (n : ℕ) : s.ιSummand (IndexSet.id (op [n])) = s.ι n := by
   erw [ι_summand_eq, X.map_id, comp_id]; rfl
-#align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.ιSummand_id
+#align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.cofan_inj_id
 -/
 
 #print SimplicialObject.Splitting.φ /-
@@ -338,12 +326,12 @@ def φ (f : X ⟶ Y) (n : ℕ) : s.n n ⟶ Y _[n] :=
 #align simplicial_object.splitting.φ SimplicialObject.Splitting.φ
 -/
 
-#print SimplicialObject.Splitting.ιSummand_comp_app /-
+#print SimplicialObject.Splitting.cofan_inj_comp_app /-
 @[simp, reassoc]
-theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
+theorem cofan_inj_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ f.app Δ = s.φ f A.1.unop.len ≫ Y.map A.e.op := by
   simp only [ι_summand_eq_assoc, φ, nat_trans.naturality, assoc]
-#align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_app
+#align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.cofan_inj_comp_app
 -/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
@@ -404,16 +392,16 @@ def ofIso (e : X ≅ Y) : Splitting Y where
 #align simplicial_object.splitting.of_iso SimplicialObject.Splitting.ofIso
 -/
 
-#print SimplicialObject.Splitting.ιSummand_epi_naturality /-
+#print SimplicialObject.Splitting.cofan_inj_epi_naturality /-
 @[reassoc]
-theorem ιSummand_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ₁ ⟶ Δ₂)
+theorem cofan_inj_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ₁ ⟶ Δ₂)
     [Epi p.unop] : s.ιSummand A ≫ X.map p = s.ιSummand (A.epi_comp p) :=
   by
   dsimp [ι_summand]
   erw [colimit.ι_desc, colimit.ι_desc, cofan.mk_ι_app, cofan.mk_ι_app]
   dsimp only [index_set.epi_comp, index_set.e]
   rw [op_comp, X.map_comp, assoc, Quiver.Hom.op_unop]
-#align simplicial_object.splitting.ι_summand_epi_naturality SimplicialObject.Splitting.ιSummand_epi_naturality
+#align simplicial_object.splitting.ι_summand_epi_naturality SimplicialObject.Splitting.cofan_inj_epi_naturality
 -/
 
 end Splitting
@@ -531,12 +519,12 @@ theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ :
 #align simplicial_object.split.comp_f SimplicialObject.Split.comp_f
 -/
 
-#print SimplicialObject.Split.ιSummand_naturality_symm /-
+#print SimplicialObject.Split.cofan_inj_naturality_symm /-
 @[simp, reassoc]
-theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}
+theorem cofan_inj_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}
     (A : Splitting.IndexSet Δ) : S₁.s.ιSummand A ≫ Φ.f.app Δ = Φ.f A.1.unop.len ≫ S₂.s.ιSummand A :=
   by rw [S₁.s.ι_summand_eq, S₂.s.ι_summand_eq, assoc, Φ.F.naturality, ← Φ.comm_assoc]
-#align simplicial_object.split.ι_summand_naturality_symm SimplicialObject.Split.ιSummand_naturality_symm
+#align simplicial_object.split.ι_summand_naturality_symm SimplicialObject.Split.cofan_inj_naturality_symm
 -/
 
 variable (C)
@@ -562,17 +550,17 @@ def evalN (n : ℕ) : Split C ⥤ C where
 #align simplicial_object.split.eval_N SimplicialObject.Split.evalN
 -/
 
-#print SimplicialObject.Split.natTransιSummand /-
+#print SimplicialObject.Split.natTransCofanInj /-
 /-- The inclusion of each summand in the coproduct decomposition of simplices
 in split simplicial objects is a natural transformation of functors
 `simplicial_object.split C ⥤ C` -/
 @[simps]
-def natTransιSummand {Δ : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) :
+def natTransCofanInj {Δ : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) :
     evalN C A.1.unop.len ⟶ forget C ⋙ (evaluation SimplexCategoryᵒᵖ C).obj Δ
     where
   app S := S.s.ιSummand A
-  naturality' S₁ S₂ Φ := (ιSummand_naturality_symm Φ A).symm
-#align simplicial_object.split.nat_trans_ι_summand SimplicialObject.Split.natTransιSummand
+  naturality' S₁ S₂ Φ := (cofan_inj_naturality_symm Φ A).symm
+#align simplicial_object.split.nat_trans_ι_summand SimplicialObject.Split.natTransCofanInj
 -/
 
 end Split

4f4a1c87

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
-import Mathbin.AlgebraicTopology.SimplicialObject
-import Mathbin.CategoryTheory.Limits.Shapes.FiniteProducts
+import AlgebraicTopology.SimplicialObject
+import CategoryTheory.Limits.Shapes.FiniteProducts
 
 #align_import algebraic_topology.split_simplicial_object from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"

4f4a1c87

bump to nightly-2023-09-06-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

f3106448

Diff

@@ -471,8 +471,6 @@ theorem Hom.ext {S₁ S₂ : Split C} (Φ₁ Φ₂ : Hom S₁ S₂) (h : ∀ n :
 #align simplicial_object.split.hom.ext SimplicialObject.Split.Hom.ext
 -/
 
-restate_axiom hom.comm'
-
 attribute [simp, reassoc] hom.comm
 
 end Split

4f4a1c87

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.split_simplicial_object
-! leanprover-community/mathlib commit 4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.SimplicialObject
 import Mathbin.CategoryTheory.Limits.Shapes.FiniteProducts
 
+#align_import algebraic_topology.split_simplicial_object from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"
+
 /-!
 
 # Split simplicial objects

4f4a1c87

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -210,22 +210,27 @@ def epiComp {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ
 #align simplicial_object.splitting.index_set.epi_comp SimplicialObject.Splitting.IndexSet.epiComp
 -/
 
+#print SimplicialObject.Splitting.IndexSet.pull /-
 /-- When `A : index_set Δ` and `θ : Δ → Δ'` is a morphism in `simplex_categoryᵒᵖ`,
 an element in `index_set Δ'` can be defined by using the epi-mono factorisation
 of `θ.unop ≫ A.e`. -/
 def pull : IndexSet Δ' :=
   mk (factorThruImage (θ.unop ≫ A.e))
 #align simplicial_object.splitting.index_set.pull SimplicialObject.Splitting.IndexSet.pull
+-/
 
+#print SimplicialObject.Splitting.IndexSet.fac_pull /-
 @[reassoc]
 theorem fac_pull : (A.pull θ).e ≫ image.ι (θ.unop ≫ A.e) = θ.unop ≫ A.e :=
   image.fac _
 #align simplicial_object.splitting.index_set.fac_pull SimplicialObject.Splitting.IndexSet.fac_pull
+-/
 
 end IndexSet
 
 variable (N : ℕ → C) (Δ : SimplexCategoryᵒᵖ) (X : SimplicialObject C) (φ : ∀ n, N n ⟶ X _[n])
 
+#print SimplicialObject.Splitting.summand /-
 /-- Given a sequences of objects `N : ℕ → C` in a category `C`, this is
 a family of objects indexed by the elements `A : splitting.index_set Δ`.
 The `Δ`-simplices of a split simplicial objects shall identify to the
@@ -234,6 +239,7 @@ coproduct of objects in such a family. -/
 def summand (A : IndexSet Δ) : C :=
   N A.1.unop.len
 #align simplicial_object.splitting.summand SimplicialObject.Splitting.summand
+-/
 
 variable [HasFiniteCoproducts C]
 
@@ -257,12 +263,14 @@ def ιCoprod (A : IndexSet Δ) : N A.1.unop.len ⟶ coprod N Δ :=
 
 variable {N}
 
+#print SimplicialObject.Splitting.map /-
 /-- The canonical morphism `coprod N Δ ⟶ X.obj Δ` attached to a sequence
 of objects `N` and a sequence of morphisms `N n ⟶ X _[n]`. -/
 @[simp]
 def map (Δ : SimplexCategoryᵒᵖ) : coprod N Δ ⟶ X.obj Δ :=
   Sigma.desc fun A => φ A.1.unop.len ≫ X.map A.e.op
 #align simplicial_object.splitting.map SimplicialObject.Splitting.map
+-/
 
 end Splitting
 
@@ -285,22 +293,29 @@ namespace Splitting
 
 variable {X Y : SimplicialObject C} (s : Splitting X)
 
+#print SimplicialObject.Splitting.map_isIso /-
 instance map_isIso (Δ : SimplexCategoryᵒᵖ) : IsIso (Splitting.map X s.ι Δ) :=
   s.map_is_iso' Δ
 #align simplicial_object.splitting.map_is_iso SimplicialObject.Splitting.map_isIso
+-/
 
+#print SimplicialObject.Splitting.iso /-
 /-- The isomorphism on simplices given by the axiom `splitting.map_is_iso'` -/
 @[simps]
 def iso (Δ : SimplexCategoryᵒᵖ) : coprod s.n Δ ≅ X.obj Δ :=
   asIso (Splitting.map X s.ι Δ)
 #align simplicial_object.splitting.iso SimplicialObject.Splitting.iso
+-/
 
+#print SimplicialObject.Splitting.ιSummand /-
 /-- Via the isomorphism `s.iso Δ`, this is the inclusion of a summand
 in the direct sum decomposition given by the splitting `s : splitting X`. -/
 def ιSummand {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) : s.n A.1.unop.len ⟶ X.obj Δ :=
   Splitting.ιCoprod s.n A ≫ (s.Iso Δ).Hom
 #align simplicial_object.splitting.ι_summand SimplicialObject.Splitting.ιSummand
+-/
 
+#print SimplicialObject.Splitting.ιSummand_eq /-
 @[reassoc]
 theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A = s.ι A.1.unop.len ≫ X.map A.e.op :=
@@ -308,11 +323,15 @@ theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
   dsimp only [ι_summand, iso.hom]
   erw [colimit.ι_desc, cofan.mk_ι_app]
 #align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.ιSummand_eq
+-/
 
+#print SimplicialObject.Splitting.ιSummand_id /-
 theorem ιSummand_id (n : ℕ) : s.ιSummand (IndexSet.id (op [n])) = s.ι n := by
   erw [ι_summand_eq, X.map_id, comp_id]; rfl
 #align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.ιSummand_id
+-/
 
+#print SimplicialObject.Splitting.φ /-
 /-- As it is stated in `splitting.hom_ext`, a morphism `f : X ⟶ Y` from a split
 simplicial object to any simplicial object is determined by its restrictions
 `s.φ f n : s.N n ⟶ Y _[n]` to the distinguished summands in each degree `n`. -/
@@ -320,14 +339,18 @@ simplicial object to any simplicial object is determined by its restrictions
 def φ (f : X ⟶ Y) (n : ℕ) : s.n n ⟶ Y _[n] :=
   s.ι n ≫ f.app (op [n])
 #align simplicial_object.splitting.φ SimplicialObject.Splitting.φ
+-/
 
+#print SimplicialObject.Splitting.ιSummand_comp_app /-
 @[simp, reassoc]
 theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ f.app Δ = s.φ f A.1.unop.len ≫ Y.map A.e.op := by
   simp only [ι_summand_eq_assoc, φ, nat_trans.naturality, assoc]
 #align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_app
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
+#print SimplicialObject.Splitting.hom_ext' /-
 theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
     (h : ∀ A : IndexSet Δ, s.ιSummand A ≫ f = s.ιSummand A ≫ g) : f = g :=
   by
@@ -337,7 +360,9 @@ theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[]"
   simpa only [ι_summand_eq, iso_hom, colimit.ι_desc_assoc, cofan.mk_ι_app, assoc] using h A
 #align simplicial_object.splitting.hom_ext' SimplicialObject.Splitting.hom_ext'
+-/
 
+#print SimplicialObject.Splitting.hom_ext /-
 theorem hom_ext (f g : X ⟶ Y) (h : ∀ n : ℕ, s.φ f n = s.φ g n) : f = g :=
   by
   ext Δ
@@ -348,14 +373,18 @@ theorem hom_ext (f g : X ⟶ Y) (h : ∀ n : ℕ, s.φ f n = s.φ g n) : f = g :
   dsimp
   simp only [s.ι_summand_comp_app, h]
 #align simplicial_object.splitting.hom_ext SimplicialObject.Splitting.hom_ext
+-/
 
+#print SimplicialObject.Splitting.desc /-
 /-- The map `X.obj Δ ⟶ Z` obtained by providing a family of morphisms on all the
 terms of decomposition given by a splitting `s : splitting X`  -/
 def desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.n A.1.unop.len ⟶ Z) :
     X.obj Δ ⟶ Z :=
   (s.Iso Δ).inv ≫ Sigma.desc F
 #align simplicial_object.splitting.desc SimplicialObject.Splitting.desc
+-/
 
+#print SimplicialObject.Splitting.ι_desc /-
 @[simp, reassoc]
 theorem ι_desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.n A.1.unop.len ⟶ Z)
     (A : IndexSet Δ) : s.ιSummand A ≫ s.desc Δ F = F A :=
@@ -364,6 +393,7 @@ theorem ι_desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s
   simp only [assoc, iso.hom_inv_id_assoc, ι_coprod]
   erw [colimit.ι_desc, cofan.mk_ι_app]
 #align simplicial_object.splitting.ι_desc SimplicialObject.Splitting.ι_desc
+-/
 
 #print SimplicialObject.Splitting.ofIso /-
 /-- A simplicial object that is isomorphic to a split simplicial object is split. -/
@@ -377,6 +407,7 @@ def ofIso (e : X ≅ Y) : Splitting Y where
 #align simplicial_object.splitting.of_iso SimplicialObject.Splitting.ofIso
 -/
 
+#print SimplicialObject.Splitting.ιSummand_epi_naturality /-
 @[reassoc]
 theorem ιSummand_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ₁ ⟶ Δ₂)
     [Epi p.unop] : s.ιSummand A ≫ X.map p = s.ιSummand (A.epi_comp p) :=
@@ -386,6 +417,7 @@ theorem ιSummand_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : Inde
   dsimp only [index_set.epi_comp, index_set.e]
   rw [op_comp, X.map_comp, assoc, Quiver.Hom.op_unop]
 #align simplicial_object.splitting.ι_summand_epi_naturality SimplicialObject.Splitting.ιSummand_epi_naturality
+-/
 
 end Splitting
 
@@ -426,6 +458,7 @@ structure Hom (S₁ S₂ : Split C) where
 #align simplicial_object.split.hom SimplicialObject.Split.Hom
 -/
 
+#print SimplicialObject.Split.Hom.ext /-
 @[ext]
 theorem Hom.ext {S₁ S₂ : Split C} (Φ₁ Φ₂ : Hom S₁ S₂) (h : ∀ n : ℕ, Φ₁.f n = Φ₂.f n) : Φ₁ = Φ₂ :=
   by
@@ -439,6 +472,7 @@ theorem Hom.ext {S₁ S₂ : Split C} (Φ₁ Φ₂ : Hom S₁ S₂) (h : ∀ n :
   dsimp
   rw [c₁, c₂]
 #align simplicial_object.split.hom.ext SimplicialObject.Split.Hom.ext
+-/
 
 restate_axiom hom.comm'
 
@@ -461,43 +495,58 @@ variable {C}
 
 namespace Split
 
+#print SimplicialObject.Split.congr_F /-
 theorem congr_F {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ = Φ₂) : Φ₁.f = Φ₂.f := by rw [h]
 #align simplicial_object.split.congr_F SimplicialObject.Split.congr_F
+-/
 
+#print SimplicialObject.Split.congr_f /-
 theorem congr_f {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ = Φ₂) (n : ℕ) : Φ₁.f n = Φ₂.f n := by
   rw [h]
 #align simplicial_object.split.congr_f SimplicialObject.Split.congr_f
+-/
 
+#print SimplicialObject.Split.id_F /-
 @[simp]
 theorem id_F (S : Split C) : (𝟙 S : S ⟶ S).f = 𝟙 S.pt :=
   rfl
 #align simplicial_object.split.id_F SimplicialObject.Split.id_F
+-/
 
+#print SimplicialObject.Split.id_f /-
 @[simp]
 theorem id_f (S : Split C) (n : ℕ) : (𝟙 S : S ⟶ S).f n = 𝟙 (S.s.n n) :=
   rfl
 #align simplicial_object.split.id_f SimplicialObject.Split.id_f
+-/
 
+#print SimplicialObject.Split.comp_F /-
 @[simp]
 theorem comp_F {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ : S₂ ⟶ S₃) :
     (Φ₁₂ ≫ Φ₂₃).f = Φ₁₂.f ≫ Φ₂₃.f :=
   rfl
 #align simplicial_object.split.comp_F SimplicialObject.Split.comp_F
+-/
 
+#print SimplicialObject.Split.comp_f /-
 @[simp]
 theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ : S₂ ⟶ S₃) (n : ℕ) :
     (Φ₁₂ ≫ Φ₂₃).f n = Φ₁₂.f n ≫ Φ₂₃.f n :=
   rfl
 #align simplicial_object.split.comp_f SimplicialObject.Split.comp_f
+-/
 
+#print SimplicialObject.Split.ιSummand_naturality_symm /-
 @[simp, reassoc]
 theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}
     (A : Splitting.IndexSet Δ) : S₁.s.ιSummand A ≫ Φ.f.app Δ = Φ.f A.1.unop.len ≫ S₂.s.ιSummand A :=
   by rw [S₁.s.ι_summand_eq, S₂.s.ι_summand_eq, assoc, Φ.F.naturality, ← Φ.comm_assoc]
 #align simplicial_object.split.ι_summand_naturality_symm SimplicialObject.Split.ιSummand_naturality_symm
+-/
 
 variable (C)
 
+#print SimplicialObject.Split.forget /-
 /-- The functor `simplicial_object.split C ⥤ simplicial_object C` which forgets
 the splitting. -/
 @[simps]
@@ -506,7 +555,9 @@ def forget : Split C ⥤ SimplicialObject C
   obj S := S.pt
   map S₁ S₂ Φ := Φ.f
 #align simplicial_object.split.forget SimplicialObject.Split.forget
+-/
 
+#print SimplicialObject.Split.evalN /-
 /-- The functor `simplicial_object.split C ⥤ C` which sends a simplicial object equipped
 with a splitting to its nondegenerate `n`-simplices. -/
 @[simps]
@@ -514,7 +565,9 @@ def evalN (n : ℕ) : Split C ⥤ C where
   obj S := S.s.n n
   map S₁ S₂ Φ := Φ.f n
 #align simplicial_object.split.eval_N SimplicialObject.Split.evalN
+-/
 
+#print SimplicialObject.Split.natTransιSummand /-
 /-- The inclusion of each summand in the coproduct decomposition of simplices
 in split simplicial objects is a natural transformation of functors
 `simplicial_object.split C ⥤ C` -/
@@ -525,6 +578,7 @@ def natTransιSummand {Δ : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) :
   app S := S.s.ιSummand A
   naturality' S₁ S₂ Φ := (ιSummand_naturality_symm Φ A).symm
 #align simplicial_object.split.nat_trans_ι_summand SimplicialObject.Split.natTransιSummand
+-/
 
 end Split

4f4a1c87

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -372,7 +372,7 @@ def ofIso (e : X ≅ Y) : Splitting Y where
   n := s.n
   ι n := s.ι n ≫ e.Hom.app (op [n])
   map_is_iso' Δ := by
-    convert(inferInstance : is_iso ((s.iso Δ).Hom ≫ e.hom.app Δ))
+    convert (inferInstance : is_iso ((s.iso Δ).Hom ≫ e.hom.app Δ))
     tidy
 #align simplicial_object.splitting.of_iso SimplicialObject.Splitting.ofIso
 -/

4f4a1c87

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -57,7 +57,7 @@ namespace Splitting
 #print SimplicialObject.Splitting.IndexSet /-
 /-- The index set which appears in the definition of split simplicial objects. -/
 def IndexSet (Δ : SimplexCategoryᵒᵖ) :=
-  ΣΔ' : SimplexCategoryᵒᵖ, { α : Δ.unop ⟶ Δ'.unop // Epi α }
+  Σ Δ' : SimplexCategoryᵒᵖ, { α : Δ.unop ⟶ Δ'.unop // Epi α }
 #align simplicial_object.splitting.index_set SimplicialObject.Splitting.IndexSet
 -/
 
@@ -93,9 +93,9 @@ theorem ext (A₁ A₂ : IndexSet Δ) (h₁ : A₁.1 = A₂.1) (h₂ : A₁.e 
     A₁ = A₂ := by
   rcases A₁ with ⟨Δ₁, ⟨α₁, hα₁⟩⟩
   rcases A₂ with ⟨Δ₂, ⟨α₂, hα₂⟩⟩
-  simp only at h₁
+  simp only at h₁ 
   subst h₁
-  simp only [eq_to_hom_refl, comp_id, index_set.e] at h₂
+  simp only [eq_to_hom_refl, comp_id, index_set.e] at h₂ 
   simp only [h₂]
 #align simplicial_object.splitting.index_set.ext SimplicialObject.Splitting.IndexSet.ext
 -/
@@ -110,7 +110,7 @@ instance : Fintype (IndexSet Δ) :=
       rintro ⟨Δ₁, α₁⟩ ⟨Δ₂, α₂⟩ h₁
       induction Δ₁ using Opposite.rec'
       induction Δ₂ using Opposite.rec'
-      simp only at h₁
+      simp only at h₁ 
       have h₂ : Δ₁ = Δ₂ := by ext1; simpa only [Fin.mk_eq_mk] using h₁.1
       subst h₂
       refine' ext _ _ rfl _
@@ -145,12 +145,12 @@ def EqId : Prop :=
 theorem eqId_iff_eq : A.EqId ↔ A.1 = Δ := by
   constructor
   · intro h
-    dsimp at h
+    dsimp at h 
     rw [h]
     rfl
   · intro h
     rcases A with ⟨Δ', ⟨f, hf⟩⟩
-    simp only at h
+    simp only at h 
     subst h
     refine' ext _ _ rfl _
     · haveI := hf
@@ -189,7 +189,7 @@ theorem eqId_iff_mono : A.EqId ↔ Mono A.e :=
   by
   constructor
   · intro h
-    dsimp at h
+    dsimp at h 
     subst h
     dsimp only [id, e]
     infer_instance

4f4a1c87

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -44,7 +44,7 @@ noncomputable section
 
 open CategoryTheory CategoryTheory.Category CategoryTheory.Limits Opposite SimplexCategory
 
-open Simplicial
+open scoped Simplicial
 
 universe u

4f4a1c87

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -210,12 +210,6 @@ def epiComp {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ
 #align simplicial_object.splitting.index_set.epi_comp SimplicialObject.Splitting.IndexSet.epiComp
 -/
 
-/- warning: simplicial_object.splitting.index_set.pull -> SimplicialObject.Splitting.IndexSet.pull is a dubious translation:
-lean 3 declaration is
-  forall {Δ' : Opposite.{1} SimplexCategory} {Δ : Opposite.{1} SimplexCategory}, (SimplicialObject.Splitting.IndexSet Δ) -> (Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ') -> (SimplicialObject.Splitting.IndexSet Δ')
-but is expected to have type
-  forall {Δ' : Opposite.{1} SimplexCategory}, (SimplicialObject.Splitting.IndexSet Δ') -> (forall {A : Opposite.{1} SimplexCategory}, (Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ' A) -> (SimplicialObject.Splitting.IndexSet A))
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.index_set.pull SimplicialObject.Splitting.IndexSet.pullₓ'. -/
 /-- When `A : index_set Δ` and `θ : Δ → Δ'` is a morphism in `simplex_categoryᵒᵖ`,
 an element in `index_set Δ'` can be defined by using the epi-mono factorisation
 of `θ.unop ≫ A.e`. -/
@@ -223,9 +217,6 @@ def pull : IndexSet Δ' :=
   mk (factorThruImage (θ.unop ≫ A.e))
 #align simplicial_object.splitting.index_set.pull SimplicialObject.Splitting.IndexSet.pull
 
-/- warning: simplicial_object.splitting.index_set.fac_pull -> SimplicialObject.Splitting.IndexSet.fac_pull is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.index_set.fac_pull SimplicialObject.Splitting.IndexSet.fac_pullₓ'. -/
 @[reassoc]
 theorem fac_pull : (A.pull θ).e ≫ image.ι (θ.unop ≫ A.e) = θ.unop ≫ A.e :=
   image.fac _
@@ -235,12 +226,6 @@ end IndexSet
 
 variable (N : ℕ → C) (Δ : SimplexCategoryᵒᵖ) (X : SimplicialObject C) (φ : ∀ n, N n ⟶ X _[n])
 
-/- warning: simplicial_object.splitting.summand -> SimplicialObject.Splitting.summand is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u_1}} [_inst_1 : CategoryTheory.Category.{u_2, u_1} C], (Nat -> C) -> (forall (Δ : Opposite.{1} SimplexCategory), (SimplicialObject.Splitting.IndexSet Δ) -> C)
-but is expected to have type
-  forall {C : Type.{u_1}}, (Nat -> C) -> (forall (N : Opposite.{1} SimplexCategory), (SimplicialObject.Splitting.IndexSet N) -> C)
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.summand SimplicialObject.Splitting.summandₓ'. -/
 /-- Given a sequences of objects `N : ℕ → C` in a category `C`, this is
 a family of objects indexed by the elements `A : splitting.index_set Δ`.
 The `Δ`-simplices of a split simplicial objects shall identify to the
@@ -272,12 +257,6 @@ def ιCoprod (A : IndexSet Δ) : N A.1.unop.len ⟶ coprod N Δ :=
 
 variable {N}
 
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-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.map SimplicialObject.Splitting.mapₓ'. -/
 /-- The canonical morphism `coprod N Δ ⟶ X.obj Δ` attached to a sequence
 of objects `N` and a sequence of morphisms `N n ⟶ X _[n]`. -/
 @[simp]
@@ -306,43 +285,22 @@ namespace Splitting
 
 variable {X Y : SimplicialObject C} (s : Splitting X)
 
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-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.map_is_iso SimplicialObject.Splitting.map_isIsoₓ'. -/
 instance map_isIso (Δ : SimplexCategoryᵒᵖ) : IsIso (Splitting.map X s.ι Δ) :=
   s.map_is_iso' Δ
 #align simplicial_object.splitting.map_is_iso SimplicialObject.Splitting.map_isIso
 
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-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.iso SimplicialObject.Splitting.isoₓ'. -/
 /-- The isomorphism on simplices given by the axiom `splitting.map_is_iso'` -/
 @[simps]
 def iso (Δ : SimplexCategoryᵒᵖ) : coprod s.n Δ ≅ X.obj Δ :=
   asIso (Splitting.map X s.ι Δ)
 #align simplicial_object.splitting.iso SimplicialObject.Splitting.iso
 
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-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand SimplicialObject.Splitting.ιSummandₓ'. -/
 /-- Via the isomorphism `s.iso Δ`, this is the inclusion of a summand
 in the direct sum decomposition given by the splitting `s : splitting X`. -/
 def ιSummand {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) : s.n A.1.unop.len ⟶ X.obj Δ :=
   Splitting.ιCoprod s.n A ≫ (s.Iso Δ).Hom
 #align simplicial_object.splitting.ι_summand SimplicialObject.Splitting.ιSummand
 
-/- warning: simplicial_object.splitting.ι_summand_eq -> SimplicialObject.Splitting.ιSummand_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.ιSummand_eqₓ'. -/
 @[reassoc]
 theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A = s.ι A.1.unop.len ≫ X.map A.e.op :=
@@ -351,22 +309,10 @@ theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
   erw [colimit.ι_desc, cofan.mk_ι_app]
 #align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.ιSummand_eq
 
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 theorem ιSummand_id (n : ℕ) : s.ιSummand (IndexSet.id (op [n])) = s.ι n := by
   erw [ι_summand_eq, X.map_id, comp_id]; rfl
 #align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.ιSummand_id
 
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-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.φ SimplicialObject.Splitting.φₓ'. -/
 /-- As it is stated in `splitting.hom_ext`, a morphism `f : X ⟶ Y` from a split
 simplicial object to any simplicial object is determined by its restrictions
 `s.φ f n : s.N n ⟶ Y _[n]` to the distinguished summands in each degree `n`. -/
@@ -375,18 +321,12 @@ def φ (f : X ⟶ Y) (n : ℕ) : s.n n ⟶ Y _[n] :=
   s.ι n ≫ f.app (op [n])
 #align simplicial_object.splitting.φ SimplicialObject.Splitting.φ
 
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-<too large>
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 @[simp, reassoc]
 theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ f.app Δ = s.φ f A.1.unop.len ≫ Y.map A.e.op := by
   simp only [ι_summand_eq_assoc, φ, nat_trans.naturality, assoc]
 #align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_app
 
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-<too large>
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 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
 theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
     (h : ∀ A : IndexSet Δ, s.ιSummand A ≫ f = s.ιSummand A ≫ g) : f = g :=
@@ -398,12 +338,6 @@ theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
   simpa only [ι_summand_eq, iso_hom, colimit.ι_desc_assoc, cofan.mk_ι_app, assoc] using h A
 #align simplicial_object.splitting.hom_ext' SimplicialObject.Splitting.hom_ext'
 
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 theorem hom_ext (f g : X ⟶ Y) (h : ∀ n : ℕ, s.φ f n = s.φ g n) : f = g :=
   by
   ext Δ
@@ -415,12 +349,6 @@ theorem hom_ext (f g : X ⟶ Y) (h : ∀ n : ℕ, s.φ f n = s.φ g n) : f = g :
   simp only [s.ι_summand_comp_app, h]
 #align simplicial_object.splitting.hom_ext SimplicialObject.Splitting.hom_ext
 
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-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.desc SimplicialObject.Splitting.descₓ'. -/
 /-- The map `X.obj Δ ⟶ Z` obtained by providing a family of morphisms on all the
 terms of decomposition given by a splitting `s : splitting X`  -/
 def desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.n A.1.unop.len ⟶ Z) :
@@ -428,12 +356,6 @@ def desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.n A.1.
   (s.Iso Δ).inv ≫ Sigma.desc F
 #align simplicial_object.splitting.desc SimplicialObject.Splitting.desc
 
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-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_desc SimplicialObject.Splitting.ι_descₓ'. -/
 @[simp, reassoc]
 theorem ι_desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.n A.1.unop.len ⟶ Z)
     (A : IndexSet Δ) : s.ιSummand A ≫ s.desc Δ F = F A :=
@@ -455,9 +377,6 @@ def ofIso (e : X ≅ Y) : Splitting Y where
 #align simplicial_object.splitting.of_iso SimplicialObject.Splitting.ofIso
 -/
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_epi_naturality SimplicialObject.Splitting.ιSummand_epi_naturalityₓ'. -/
 @[reassoc]
 theorem ιSummand_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ₁ ⟶ Δ₂)
     [Epi p.unop] : s.ιSummand A ≫ X.map p = s.ιSummand (A.epi_comp p) :=
@@ -507,12 +426,6 @@ structure Hom (S₁ S₂ : Split C) where
 #align simplicial_object.split.hom SimplicialObject.Split.Hom
 -/
 
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-Case conversion may be inaccurate. Consider using '#align simplicial_object.split.hom.ext SimplicialObject.Split.Hom.extₓ'. -/
 @[ext]
 theorem Hom.ext {S₁ S₂ : Split C} (Φ₁ Φ₂ : Hom S₁ S₂) (h : ∀ n : ℕ, Φ₁.f n = Φ₂.f n) : Φ₁ = Φ₂ :=
   by
@@ -548,74 +461,35 @@ variable {C}
 
 namespace Split
 
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 theorem congr_F {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ = Φ₂) : Φ₁.f = Φ₂.f := by rw [h]
 #align simplicial_object.split.congr_F SimplicialObject.Split.congr_F
 
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 theorem congr_f {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ = Φ₂) (n : ℕ) : Φ₁.f n = Φ₂.f n := by
   rw [h]
 #align simplicial_object.split.congr_f SimplicialObject.Split.congr_f
 
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 @[simp]
 theorem id_F (S : Split C) : (𝟙 S : S ⟶ S).f = 𝟙 S.pt :=
   rfl
 #align simplicial_object.split.id_F SimplicialObject.Split.id_F
 
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 @[simp]
 theorem id_f (S : Split C) (n : ℕ) : (𝟙 S : S ⟶ S).f n = 𝟙 (S.s.n n) :=
   rfl
 #align simplicial_object.split.id_f SimplicialObject.Split.id_f
 
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 @[simp]
 theorem comp_F {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ : S₂ ⟶ S₃) :
     (Φ₁₂ ≫ Φ₂₃).f = Φ₁₂.f ≫ Φ₂₃.f :=
   rfl
 #align simplicial_object.split.comp_F SimplicialObject.Split.comp_F
 
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 @[simp]
 theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ : S₂ ⟶ S₃) (n : ℕ) :
     (Φ₁₂ ≫ Φ₂₃).f n = Φ₁₂.f n ≫ Φ₂₃.f n :=
   rfl
 #align simplicial_object.split.comp_f SimplicialObject.Split.comp_f
 
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 @[simp, reassoc]
 theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}
     (A : Splitting.IndexSet Δ) : S₁.s.ιSummand A ≫ Φ.f.app Δ = Φ.f A.1.unop.len ≫ S₂.s.ιSummand A :=
@@ -624,12 +498,6 @@ theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ
 
 variable (C)
 
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 /-- The functor `simplicial_object.split C ⥤ simplicial_object C` which forgets
 the splitting. -/
 @[simps]
@@ -639,12 +507,6 @@ def forget : Split C ⥤ SimplicialObject C
   map S₁ S₂ Φ := Φ.f
 #align simplicial_object.split.forget SimplicialObject.Split.forget
 
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 /-- The functor `simplicial_object.split C ⥤ C` which sends a simplicial object equipped
 with a splitting to its nondegenerate `n`-simplices. -/
 @[simps]
@@ -653,12 +515,6 @@ def evalN (n : ℕ) : Split C ⥤ C where
   map S₁ S₂ Φ := Φ.f n
 #align simplicial_object.split.eval_N SimplicialObject.Split.evalN
 
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-  forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{max (succ u1) (succ u2), max u1 u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u1 u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u1 u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) C _inst_1) (CategoryTheory.Functor.category.{u2, u2, max u1 u2, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) C _inst_1))) (SimplicialObject.Split.evalN.{u1, u2} C _inst_1 _inst_2 (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (CategoryTheory.Functor.comp.{u2, u2, u2, max u1 u2, max u1 u2, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) C _inst_1 (SimplicialObject.Split.forget.{u1, u2} C _inst_1 _inst_2) (Prefunctor.obj.{1, max (succ u1) (succ u2), 0, max u1 u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) (CategoryTheory.Functor.{u2, u2, max u1 u2, u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (CategoryTheory.Functor.category.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u1 u2} (CategoryTheory.Functor.{u2, u2, max u1 u2, u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (CategoryTheory.Functor.category.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u1 u2} (CategoryTheory.Functor.{u2, u2, max u1 u2, u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (CategoryTheory.Functor.category.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1) (CategoryTheory.Functor.category.{u2, u2, max u1 u2, u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (CategoryTheory.Functor.category.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{0, max u1 u2, 0, max u1 u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) (CategoryTheory.Functor.{u2, u2, max u1 u2, u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (CategoryTheory.Functor.category.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1) (CategoryTheory.Functor.category.{u2, u2, max u1 u2, u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (CategoryTheory.Functor.category.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1) (CategoryTheory.evaluation.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1)) Δ))
-Case conversion may be inaccurate. Consider using '#align simplicial_object.split.nat_trans_ι_summand SimplicialObject.Split.natTransιSummandₓ'. -/
 /-- The inclusion of each summand in the coproduct decomposition of simplices
 in split simplicial objects is a natural transformation of functors
 `simplicial_object.split C ⥤ C` -/

4f4a1c87

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -111,9 +111,7 @@ instance : Fintype (IndexSet Δ) :=
       induction Δ₁ using Opposite.rec'
       induction Δ₂ using Opposite.rec'
       simp only at h₁
-      have h₂ : Δ₁ = Δ₂ := by
-        ext1
-        simpa only [Fin.mk_eq_mk] using h₁.1
+      have h₂ : Δ₁ = Δ₂ := by ext1; simpa only [Fin.mk_eq_mk] using h₁.1
       subst h₂
       refine' ext _ _ rfl _
       ext : 2
@@ -359,10 +357,8 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (SimplicialObject.Splitting.ι.{u1, u2} C _inst_1 _inst_2 X s n)
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.ιSummand_idₓ'. -/
-theorem ιSummand_id (n : ℕ) : s.ιSummand (IndexSet.id (op [n])) = s.ι n :=
-  by
-  erw [ι_summand_eq, X.map_id, comp_id]
-  rfl
+theorem ιSummand_id (n : ℕ) : s.ιSummand (IndexSet.id (op [n])) = s.ι n := by
+  erw [ι_summand_eq, X.map_id, comp_id]; rfl
 #align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.ιSummand_id
 
 /- warning: simplicial_object.splitting.φ -> SimplicialObject.Splitting.φ is a dubious translation:
@@ -522,9 +518,7 @@ theorem Hom.ext {S₁ S₂ : Split C} (Φ₁ Φ₂ : Hom S₁ S₂) (h : ∀ n :
   by
   rcases Φ₁ with ⟨F₁, f₁, c₁⟩
   rcases Φ₂ with ⟨F₂, f₂, c₂⟩
-  have h' : f₁ = f₂ := by
-    ext
-    apply h
+  have h' : f₁ = f₂ := by ext; apply h
   subst h'
   simp only [eq_self_iff_true, and_true_iff]
   apply S₁.s.hom_ext

4f4a1c87

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -226,10 +226,7 @@ def pull : IndexSet Δ' :=
 #align simplicial_object.splitting.index_set.pull SimplicialObject.Splitting.IndexSet.pull
 
 /- warning: simplicial_object.splitting.index_set.fac_pull -> SimplicialObject.Splitting.IndexSet.fac_pull is a dubious translation:
-lean 3 declaration is
-  forall {Δ' : Opposite.{1} SimplexCategory} {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ'), Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) (SimplicialObject.Splitting.IndexSet.pull Δ' Δ A θ))) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (SimplicialObject.Splitting.IndexSet.e Δ' (SimplicialObject.Splitting.IndexSet.pull Δ' Δ A θ)) (CategoryTheory.Limits.image.ι.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (SimplicialObject.Splitting.IndexSet.pull._proof_1 Δ' Δ A θ))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A))
-but is expected to have type
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(CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' A θ) (SimplicialObject.Splitting.IndexSet.e Δ' Δ)) (CategoryTheory.Limits.HasImages.has_image.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.instHasStrongEpiMonoFactorisationsSimplexCategorySmallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' A θ) (SimplicialObject.Splitting.IndexSet.e Δ' Δ))))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.index_set.fac_pull SimplicialObject.Splitting.IndexSet.fac_pullₓ'. -/
 @[reassoc]
 theorem fac_pull : (A.pull θ).e ≫ image.ι (θ.unop ≫ A.e) = θ.unop ≫ A.e :=
@@ -346,10 +343,7 @@ def ιSummand {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) : s.n A.1.unop.len
 #align simplicial_object.splitting.ι_summand SimplicialObject.Splitting.ιSummand
 
 /- warning: simplicial_object.splitting.ι_summand_eq -> SimplicialObject.Splitting.ιSummand_eq is a dubious translation:
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(Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} 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(CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ))) (SimplicialObject.Splitting.ι.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))))) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ)) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (SimplicialObject.Splitting.IndexSet.e Δ A))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.ιSummand_eqₓ'. -/
 @[reassoc]
 theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
@@ -386,10 +380,7 @@ def φ (f : X ⟶ Y) (n : ℕ) : s.n n ⟶ Y _[n] :=
 #align simplicial_object.splitting.φ SimplicialObject.Splitting.φ
 
 /- warning: simplicial_object.splitting.ι_summand_comp_app -> SimplicialObject.Splitting.ιSummand_comp_app is a dubious translation:
-lean 3 declaration is
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(Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (SimplicialObject.Splitting.IndexSet.e Δ A))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_appₓ'. -/
 @[simp, reassoc]
 theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
@@ -398,10 +389,7 @@ theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : Index
 #align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_app
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.hom_ext' SimplicialObject.Splitting.hom_ext'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
 theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
@@ -472,10 +460,7 @@ def ofIso (e : X ≅ Y) : Splitting Y where
 -/
 
 /- warning: simplicial_object.splitting.ι_summand_epi_naturality -> SimplicialObject.Splitting.ιSummand_epi_naturality is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_epi_naturality SimplicialObject.Splitting.ιSummand_epi_naturalityₓ'. -/
 @[reassoc]
 theorem ιSummand_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ₁ ⟶ Δ₂)
@@ -635,10 +620,7 @@ theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ :
 #align simplicial_object.split.comp_f SimplicialObject.Split.comp_f
 
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-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] {S₁ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} (Φ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂)) Δ)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁)) Δ) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂)) Δ) (SimplicialObject.Splitting.ιSummand.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) Δ A) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.Hom.F.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ) Δ)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₂) (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂)) Δ) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (SimplicialObject.Splitting.ιSummand.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₂) Δ A))
+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.split.ι_summand_naturality_symm SimplicialObject.Split.ιSummand_naturality_symmₓ'. -/
 @[simp, reassoc]
 theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}

4f4a1c87

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -231,7 +231,7 @@ lean 3 declaration is
 but is expected to have type
   forall {Δ' : Opposite.{1} SimplexCategory} (Δ : SimplicialObject.Splitting.IndexSet Δ') {A : Opposite.{1} SimplexCategory} (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ' A), Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.pull Δ' Δ A θ))) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (SimplicialObject.Splitting.IndexSet.e A (SimplicialObject.Splitting.IndexSet.pull Δ' Δ A θ)) (CategoryTheory.Limits.image.ι.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' A θ) (SimplicialObject.Splitting.IndexSet.e Δ' Δ)) (CategoryTheory.Limits.HasImages.has_image.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.instHasStrongEpiMonoFactorisationsSimplexCategorySmallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' A θ) (SimplicialObject.Splitting.IndexSet.e Δ' Δ))))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' A θ) (SimplicialObject.Splitting.IndexSet.e Δ' Δ))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.index_set.fac_pull SimplicialObject.Splitting.IndexSet.fac_pullₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem fac_pull : (A.pull θ).e ≫ image.ι (θ.unop ≫ A.e) = θ.unop ≫ A.e :=
   image.fac _
 #align simplicial_object.splitting.index_set.fac_pull SimplicialObject.Splitting.IndexSet.fac_pull
@@ -351,7 +351,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ)) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ))) (SimplicialObject.Splitting.ι.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))))) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ)) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (SimplicialObject.Splitting.IndexSet.e Δ A))))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.ιSummand_eqₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A = s.ι A.1.unop.len ≫ X.map A.e.op :=
   by
@@ -391,7 +391,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {Y : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (f : Quiver.Hom.{succ u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))) X Y) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y) Δ)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y) Δ) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (CategoryTheory.NatTrans.app.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Y f Δ)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ))) (SimplicialObject.Splitting.φ.{u1, u2} C _inst_1 _inst_2 X Y s f (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))))) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ)) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (SimplicialObject.Splitting.IndexSet.e Δ A))))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_appₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ f.app Δ = s.φ f A.1.unop.len ≫ Y.map A.e.op := by
   simp only [ι_summand_eq_assoc, φ, nat_trans.naturality, assoc]
@@ -450,7 +450,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Z : C} (Δ : Opposite.{1} SimplexCategory) (F : forall (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) Z) (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) Z) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ) Z (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.desc.{u1, u2} C _inst_1 _inst_2 X s Z Δ F)) (F A)
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_desc SimplicialObject.Splitting.ι_descₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ι_desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.n A.1.unop.len ⟶ Z)
     (A : IndexSet Δ) : s.ιSummand A ≫ s.desc Δ F = F A :=
   by
@@ -477,7 +477,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Δ₁ : Opposite.{1} SimplexCategory} {Δ₂ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ₁) (p : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ₁ Δ₂) [_inst_3 : CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ₂) (Opposite.unop.{1} SimplexCategory Δ₁) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ₁ Δ₂ p)], Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ₂)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ₁) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ₂) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ₁ A) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ₁ Δ₂ p)) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ₂ (SimplicialObject.Splitting.IndexSet.epiComp Δ₁ Δ₂ A p _inst_3))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_epi_naturality SimplicialObject.Splitting.ιSummand_epi_naturalityₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem ιSummand_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ₁ ⟶ Δ₂)
     [Epi p.unop] : s.ιSummand A ≫ X.map p = s.ιSummand (A.epi_comp p) :=
   by
@@ -550,7 +550,7 @@ theorem Hom.ext {S₁ S₂ : Split C} (Φ₁ Φ₂ : Hom S₁ S₂) (h : ∀ n :
 
 restate_axiom hom.comm'
 
-attribute [simp, reassoc.1] hom.comm
+attribute [simp, reassoc] hom.comm
 
 end Split
 
@@ -640,7 +640,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] {S₁ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} (Φ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂)) Δ)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁)) Δ) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂)) Δ) (SimplicialObject.Splitting.ιSummand.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) Δ A) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.Hom.F.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ) Δ)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₂) (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂)) Δ) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (SimplicialObject.Splitting.ιSummand.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₂) Δ A))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.split.ι_summand_naturality_symm SimplicialObject.Split.ιSummand_naturality_symmₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}
     (A : Splitting.IndexSet Δ) : S₁.s.ιSummand A ≫ Φ.f.app Δ = Φ.f A.1.unop.len ≫ S₂.s.ιSummand A :=
   by rw [S₁.s.ι_summand_eq, S₂.s.ι_summand_eq, assoc, Φ.F.naturality, ← Φ.comm_assoc]

4f4a1c87

bump to nightly-2023-04-18-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

c37d1701

Diff

@@ -108,8 +108,8 @@ instance : Fintype (IndexSet Δ) :=
       IndexSet Δ → Sigma fun k : Fin (Δ.unop.len + 1) => Fin (Δ.unop.len + 1) → Fin (k + 1))
     (by
       rintro ⟨Δ₁, α₁⟩ ⟨Δ₂, α₂⟩ h₁
-      induction Δ₁ using Opposite.rec
-      induction Δ₂ using Opposite.rec
+      induction Δ₁ using Opposite.rec'
+      induction Δ₂ using Opposite.rec'
       simp only at h₁
       have h₂ : Δ₁ = Δ₂ := by
         ext1
@@ -425,7 +425,7 @@ theorem hom_ext (f g : X ⟶ Y) (h : ∀ n : ℕ, s.φ f n = s.φ g n) : f = g :
   ext Δ
   apply s.hom_ext'
   intro A
-  induction Δ using Opposite.rec
+  induction Δ using Opposite.rec'
   induction' Δ using SimplexCategory.rec with n
   dsimp
   simp only [s.ι_summand_comp_app, h]

4f4a1c87

bump to nightly-2023-04-16-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b

63127953

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 
 ! This file was ported from Lean 3 source module algebraic_topology.split_simplicial_object
-! leanprover-community/mathlib commit dd1f8496baa505636a82748e6b652165ea888733
+! leanprover-community/mathlib commit 4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Limits.Shapes.FiniteProducts
 
 # Split simplicial objects
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we introduce the notion of split simplicial object.
 If `C` is a category that has finite coproducts, a splitting
 `s : splitting X` of a simplical object `X` in `C` consists

dd1f8496

bump to nightly-2023-04-14-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4

60fdc414

Diff

@@ -51,32 +51,41 @@ namespace SimplicialObject
 
 namespace Splitting
 
+#print SimplicialObject.Splitting.IndexSet /-
 /-- The index set which appears in the definition of split simplicial objects. -/
 def IndexSet (Δ : SimplexCategoryᵒᵖ) :=
   ΣΔ' : SimplexCategoryᵒᵖ, { α : Δ.unop ⟶ Δ'.unop // Epi α }
 #align simplicial_object.splitting.index_set SimplicialObject.Splitting.IndexSet
+-/
 
 namespace IndexSet
 
+#print SimplicialObject.Splitting.IndexSet.mk /-
 /-- The element in `splitting.index_set Δ` attached to an epimorphism `f : Δ ⟶ Δ'`. -/
 @[simps]
 def mk {Δ Δ' : SimplexCategory} (f : Δ ⟶ Δ') [Epi f] : IndexSet (op Δ) :=
   ⟨op Δ', f, inferInstance⟩
 #align simplicial_object.splitting.index_set.mk SimplicialObject.Splitting.IndexSet.mk
+-/
 
 variable {Δ' Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) (θ : Δ ⟶ Δ')
 
+#print SimplicialObject.Splitting.IndexSet.e /-
 /-- The epimorphism in `simplex_category` associated to `A : splitting.index_set Δ` -/
 def e :=
   A.2.1
 #align simplicial_object.splitting.index_set.e SimplicialObject.Splitting.IndexSet.e
+-/
 
 instance : Epi A.e :=
   A.2.2
 
+#print SimplicialObject.Splitting.IndexSet.ext' /-
 theorem ext' : A = ⟨A.1, ⟨A.e, A.2.2⟩⟩ := by tidy
 #align simplicial_object.splitting.index_set.ext' SimplicialObject.Splitting.IndexSet.ext'
+-/
 
+#print SimplicialObject.Splitting.IndexSet.ext /-
 theorem ext (A₁ A₂ : IndexSet Δ) (h₁ : A₁.1 = A₂.1) (h₂ : A₁.e ≫ eqToHom (by rw [h₁]) = A₂.e) :
     A₁ = A₂ := by
   rcases A₁ with ⟨Δ₁, ⟨α₁, hα₁⟩⟩
@@ -86,6 +95,7 @@ theorem ext (A₁ A₂ : IndexSet Δ) (h₁ : A₁.1 = A₂.1) (h₂ : A₁.e 
   simp only [eq_to_hom_refl, comp_id, index_set.e] at h₂
   simp only [h₂]
 #align simplicial_object.splitting.index_set.ext SimplicialObject.Splitting.IndexSet.ext
+-/
 
 instance : Fintype (IndexSet Δ) :=
   Fintype.ofInjective
@@ -108,24 +118,29 @@ instance : Fintype (IndexSet Δ) :=
 
 variable (Δ)
 
+#print SimplicialObject.Splitting.IndexSet.id /-
 /-- The distinguished element in `splitting.index_set Δ` which corresponds to the
 identity of `Δ`. -/
 def id : IndexSet Δ :=
   ⟨Δ, ⟨𝟙 _, by infer_instance⟩⟩
 #align simplicial_object.splitting.index_set.id SimplicialObject.Splitting.IndexSet.id
+-/
 
 instance : Inhabited (IndexSet Δ) :=
   ⟨id Δ⟩
 
 variable {Δ}
 
+#print SimplicialObject.Splitting.IndexSet.EqId /-
 /-- The condition that an element `splitting.index_set Δ` is the distinguished
 element `splitting.index_set.id Δ`. -/
 @[simp]
 def EqId : Prop :=
   A = id _
 #align simplicial_object.splitting.index_set.eq_id SimplicialObject.Splitting.IndexSet.EqId
+-/
 
+#print SimplicialObject.Splitting.IndexSet.eqId_iff_eq /-
 theorem eqId_iff_eq : A.EqId ↔ A.1 = Δ := by
   constructor
   · intro h
@@ -141,7 +156,9 @@ theorem eqId_iff_eq : A.EqId ↔ A.1 = Δ := by
       simp only [eq_to_hom_refl, comp_id]
       exact eq_id_of_epi f
 #align simplicial_object.splitting.index_set.eq_id_iff_eq SimplicialObject.Splitting.IndexSet.eqId_iff_eq
+-/
 
+#print SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq /-
 theorem eqId_iff_len_eq : A.EqId ↔ A.1.unop.len = Δ.unop.len :=
   by
   rw [eq_id_iff_eq]
@@ -153,7 +170,9 @@ theorem eqId_iff_len_eq : A.EqId ↔ A.1.unop.len = Δ.unop.len :=
     ext
     exact h
 #align simplicial_object.splitting.index_set.eq_id_iff_len_eq SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq
+-/
 
+#print SimplicialObject.Splitting.IndexSet.eqId_iff_len_le /-
 theorem eqId_iff_len_le : A.EqId ↔ Δ.unop.len ≤ A.1.unop.len :=
   by
   rw [eq_id_iff_len_eq]
@@ -162,7 +181,9 @@ theorem eqId_iff_len_le : A.EqId ↔ Δ.unop.len ≤ A.1.unop.len :=
     rw [h]
   · exact le_antisymm (len_le_of_epi (inferInstance : epi A.e))
 #align simplicial_object.splitting.index_set.eq_id_iff_len_le SimplicialObject.Splitting.IndexSet.eqId_iff_len_le
+-/
 
+#print SimplicialObject.Splitting.IndexSet.eqId_iff_mono /-
 theorem eqId_iff_mono : A.EqId ↔ Mono A.e :=
   by
   constructor
@@ -175,7 +196,9 @@ theorem eqId_iff_mono : A.EqId ↔ Mono A.e :=
     rw [eq_id_iff_len_le]
     exact len_le_of_mono h
 #align simplicial_object.splitting.index_set.eq_id_iff_mono SimplicialObject.Splitting.IndexSet.eqId_iff_mono
+-/
 
+#print SimplicialObject.Splitting.IndexSet.epiComp /-
 /-- Given `A : index_set Δ₁`, if `p.unop : unop Δ₂ ⟶ unop Δ₁` is an epi, this
 is the obvious element in `A : index_set Δ₂` associated to the composition
 of epimorphisms `p.unop ≫ A.e`. -/
@@ -184,7 +207,14 @@ def epiComp {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ
     IndexSet Δ₂ :=
   ⟨A.1, ⟨p.unop ≫ A.e, epi_comp _ _⟩⟩
 #align simplicial_object.splitting.index_set.epi_comp SimplicialObject.Splitting.IndexSet.epiComp
+-/
 
+/- warning: simplicial_object.splitting.index_set.pull -> SimplicialObject.Splitting.IndexSet.pull is a dubious translation:
+lean 3 declaration is
+  forall {Δ' : Opposite.{1} SimplexCategory} {Δ : Opposite.{1} SimplexCategory}, (SimplicialObject.Splitting.IndexSet Δ) -> (Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ') -> (SimplicialObject.Splitting.IndexSet Δ')
+but is expected to have type
+  forall {Δ' : Opposite.{1} SimplexCategory}, (SimplicialObject.Splitting.IndexSet Δ') -> (forall {A : Opposite.{1} SimplexCategory}, (Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ' A) -> (SimplicialObject.Splitting.IndexSet A))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.index_set.pull SimplicialObject.Splitting.IndexSet.pullₓ'. -/
 /-- When `A : index_set Δ` and `θ : Δ → Δ'` is a morphism in `simplex_categoryᵒᵖ`,
 an element in `index_set Δ'` can be defined by using the epi-mono factorisation
 of `θ.unop ≫ A.e`. -/
@@ -192,6 +222,12 @@ def pull : IndexSet Δ' :=
   mk (factorThruImage (θ.unop ≫ A.e))
 #align simplicial_object.splitting.index_set.pull SimplicialObject.Splitting.IndexSet.pull
 
+/- warning: simplicial_object.splitting.index_set.fac_pull -> SimplicialObject.Splitting.IndexSet.fac_pull is a dubious translation:
+lean 3 declaration is
+  forall {Δ' : Opposite.{1} SimplexCategory} {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ'), Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory 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SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory 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(CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A))
+but is expected to have type
+  forall {Δ' : Opposite.{1} SimplexCategory} (Δ : SimplicialObject.Splitting.IndexSet Δ') {A : Opposite.{1} SimplexCategory} (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ' A), Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory 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SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (SimplicialObject.Splitting.IndexSet.e A (SimplicialObject.Splitting.IndexSet.pull Δ' Δ A θ)) (CategoryTheory.Limits.image.ι.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' A θ) (SimplicialObject.Splitting.IndexSet.e Δ' Δ)) (CategoryTheory.Limits.HasImages.has_image.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.instHasStrongEpiMonoFactorisationsSimplexCategorySmallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' A θ) (SimplicialObject.Splitting.IndexSet.e Δ' Δ))))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory A) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ'_1 : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1)) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ'_1) α)) Δ)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' A θ) (SimplicialObject.Splitting.IndexSet.e Δ' Δ))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.index_set.fac_pull SimplicialObject.Splitting.IndexSet.fac_pullₓ'. -/
 @[reassoc.1]
 theorem fac_pull : (A.pull θ).e ≫ image.ι (θ.unop ≫ A.e) = θ.unop ≫ A.e :=
   image.fac _
@@ -201,6 +237,12 @@ end IndexSet
 
 variable (N : ℕ → C) (Δ : SimplexCategoryᵒᵖ) (X : SimplicialObject C) (φ : ∀ n, N n ⟶ X _[n])
 
+/- warning: simplicial_object.splitting.summand -> SimplicialObject.Splitting.summand is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u_1}} [_inst_1 : CategoryTheory.Category.{u_2, u_1} C], (Nat -> C) -> (forall (Δ : Opposite.{1} SimplexCategory), (SimplicialObject.Splitting.IndexSet Δ) -> C)
+but is expected to have type
+  forall {C : Type.{u_1}}, (Nat -> C) -> (forall (N : Opposite.{1} SimplexCategory), (SimplicialObject.Splitting.IndexSet N) -> C)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.summand SimplicialObject.Splitting.summandₓ'. -/
 /-- Given a sequences of objects `N : ℕ → C` in a category `C`, this is
 a family of objects indexed by the elements `A : splitting.index_set Δ`.
 The `Δ`-simplices of a split simplicial objects shall identify to the
@@ -212,22 +254,32 @@ def summand (A : IndexSet Δ) : C :=
 
 variable [HasFiniteCoproducts C]
 
+#print SimplicialObject.Splitting.coprod /-
 /-- The coproduct of the family `summand N Δ` -/
 @[simp]
 def coprod :=
   ∐ summand N Δ
 #align simplicial_object.splitting.coprod SimplicialObject.Splitting.coprod
+-/
 
 variable {Δ}
 
+#print SimplicialObject.Splitting.ιCoprod /-
 /-- The inclusion of a summand in the coproduct. -/
 @[simp]
 def ιCoprod (A : IndexSet Δ) : N A.1.unop.len ⟶ coprod N Δ :=
   Sigma.ι _ A
 #align simplicial_object.splitting.ι_coprod SimplicialObject.Splitting.ιCoprod
+-/
 
 variable {N}
 
+/- warning: simplicial_object.splitting.map -> SimplicialObject.Splitting.map is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] {N : Nat -> C} (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1), (forall (n : Nat), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (N n) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) -> (forall [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] (Δ : Opposite.{1} SimplexCategory), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 N Δ _inst_2) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] {N : Nat -> C} (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1), (forall (n : Nat), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (N n) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) -> (forall [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] (Δ : Opposite.{1} SimplexCategory), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 N Δ _inst_2) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.map SimplicialObject.Splitting.mapₓ'. -/
 /-- The canonical morphism `coprod N Δ ⟶ X.obj Δ` attached to a sequence
 of objects `N` and a sequence of morphisms `N n ⟶ X _[n]`. -/
 @[simp]
@@ -239,6 +291,7 @@ end Splitting
 
 variable [HasFiniteCoproducts C]
 
+#print SimplicialObject.Splitting /-
 /-- A splitting of a simplicial object `X` consists of the datum of a sequence
 of objects `N`, a sequence of morphisms `ι : N n ⟶ X _[n]` such that
 for all `Δ : simplex_categoryhᵒᵖ`, the canonical map `splitting.map X ι Δ`
@@ -249,27 +302,52 @@ structure Splitting (X : SimplicialObject C) where
   ι : ∀ n, N n ⟶ X _[n]
   map_is_iso' : ∀ Δ : SimplexCategoryᵒᵖ, IsIso (Splitting.map X ι Δ)
 #align simplicial_object.splitting SimplicialObject.Splitting
+-/
 
 namespace Splitting
 
 variable {X Y : SimplicialObject C} (s : Splitting X)
 
+/- warning: simplicial_object.splitting.map_is_iso -> SimplicialObject.Splitting.map_isIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (Δ : Opposite.{1} SimplexCategory), CategoryTheory.IsIso.{u2, u1} C _inst_1 (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (fun (n : Nat) => SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s n) Δ _inst_2) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ) (SimplicialObject.Splitting.map.{u1, u2} C _inst_1 (fun (n : Nat) => SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s n) X (SimplicialObject.Splitting.ι.{u1, u2} C _inst_1 _inst_2 X s) _inst_2 Δ)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (Δ : Opposite.{1} SimplexCategory), CategoryTheory.IsIso.{u2, u1} C _inst_1 (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (fun (n : Nat) => SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s n) Δ _inst_2) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ) (SimplicialObject.Splitting.map.{u1, u2} C _inst_1 (fun (n : Nat) => SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s n) X (SimplicialObject.Splitting.ι.{u1, u2} C _inst_1 _inst_2 X s) _inst_2 Δ)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.map_is_iso SimplicialObject.Splitting.map_isIsoₓ'. -/
 instance map_isIso (Δ : SimplexCategoryᵒᵖ) : IsIso (Splitting.map X s.ι Δ) :=
   s.map_is_iso' Δ
 #align simplicial_object.splitting.map_is_iso SimplicialObject.Splitting.map_isIso
 
+/- warning: simplicial_object.splitting.iso -> SimplicialObject.Splitting.iso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (Δ : Opposite.{1} SimplexCategory), CategoryTheory.Iso.{u2, u1} C _inst_1 (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s) Δ _inst_2) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (Δ : Opposite.{1} SimplexCategory), CategoryTheory.Iso.{u2, u1} C _inst_1 (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s) Δ _inst_2) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.iso SimplicialObject.Splitting.isoₓ'. -/
 /-- The isomorphism on simplices given by the axiom `splitting.map_is_iso'` -/
 @[simps]
 def iso (Δ : SimplexCategoryᵒᵖ) : coprod s.n Δ ≅ X.obj Δ :=
   asIso (Splitting.map X s.ι Δ)
 #align simplicial_object.splitting.iso SimplicialObject.Splitting.iso
 
+/- warning: simplicial_object.splitting.ι_summand -> SimplicialObject.Splitting.ιSummand is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand SimplicialObject.Splitting.ιSummandₓ'. -/
 /-- Via the isomorphism `s.iso Δ`, this is the inclusion of a summand
 in the direct sum decomposition given by the splitting `s : splitting X`. -/
 def ιSummand {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) : s.n A.1.unop.len ⟶ X.obj Δ :=
   Splitting.ιCoprod s.n A ≫ (s.Iso Δ).Hom
 #align simplicial_object.splitting.ι_summand SimplicialObject.Splitting.ιSummand
 
+/- warning: simplicial_object.splitting.ι_summand_eq -> SimplicialObject.Splitting.ιSummand_eq is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ)) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} 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(CategoryTheory.Functor.map.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))))) Δ (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (SimplicialObject.Splitting.IndexSet.e Δ A))))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ)) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ))) (SimplicialObject.Splitting.ι.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))))) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ)) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (SimplicialObject.Splitting.IndexSet.e Δ A))))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.ιSummand_eqₓ'. -/
 @[reassoc.1]
 theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A = s.ι A.1.unop.len ≫ X.map A.e.op :=
@@ -278,12 +356,24 @@ theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
   erw [colimit.ι_desc, cofan.mk_ι_app]
 #align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.ιSummand_eq
 
+/- warning: simplicial_object.splitting.ι_summand_id -> SimplicialObject.Splitting.ιSummand_id is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (SimplicialObject.Splitting.ι.{u1, u2} C _inst_1 _inst_2 X s n)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (SimplicialObject.Splitting.ι.{u1, u2} C _inst_1 _inst_2 X s n)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.ιSummand_idₓ'. -/
 theorem ιSummand_id (n : ℕ) : s.ιSummand (IndexSet.id (op [n])) = s.ι n :=
   by
   erw [ι_summand_eq, X.map_id, comp_id]
   rfl
 #align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.ιSummand_id
 
+/- warning: simplicial_object.splitting.φ -> SimplicialObject.Splitting.φ is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {Y : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X), (Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) X Y) -> (forall (n : Nat), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s n) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {Y : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X), (Quiver.Hom.{succ u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))) X Y) -> (forall (n : Nat), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s n) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.φ SimplicialObject.Splitting.φₓ'. -/
 /-- As it is stated in `splitting.hom_ext`, a morphism `f : X ⟶ Y` from a split
 simplicial object to any simplicial object is determined by its restrictions
 `s.φ f n : s.N n ⟶ Y _[n]` to the distinguished summands in each degree `n`. -/
@@ -292,12 +382,24 @@ def φ (f : X ⟶ Y) (n : ℕ) : s.n n ⟶ Y _[n] :=
   s.ι n ≫ f.app (op [n])
 #align simplicial_object.splitting.φ SimplicialObject.Splitting.φ
 
+/- warning: simplicial_object.splitting.ι_summand_comp_app -> SimplicialObject.Splitting.ιSummand_comp_app is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ))) (SimplicialObject.Splitting.φ.{u1, u2} C _inst_1 _inst_2 X Y s f (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory 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(Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (SimplicialObject.Splitting.IndexSet.e Δ A))))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_appₓ'. -/
 @[simp, reassoc.1]
 theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ f.app Δ = s.φ f A.1.unop.len ≫ Y.map A.e.op := by
   simp only [ι_summand_eq_assoc, φ, nat_trans.naturality, assoc]
 #align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_app
 
+/- warning: simplicial_object.splitting.hom_ext' -> SimplicialObject.Splitting.hom_ext' is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ) Z) f g)
+but is expected to have type
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(CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ) Z) f g)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.hom_ext' SimplicialObject.Splitting.hom_ext'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
 theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
     (h : ∀ A : IndexSet Δ, s.ιSummand A ≫ f = s.ιSummand A ≫ g) : f = g :=
@@ -309,6 +411,12 @@ theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
   simpa only [ι_summand_eq, iso_hom, colimit.ι_desc_assoc, cofan.mk_ι_app, assoc] using h A
 #align simplicial_object.splitting.hom_ext' SimplicialObject.Splitting.hom_ext'
 
+/- warning: simplicial_object.splitting.hom_ext -> SimplicialObject.Splitting.hom_ext is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {Y : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (f : Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) X Y) (g : Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) X Y), (forall (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s n) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (SimplicialObject.Splitting.φ.{u1, u2} C _inst_1 _inst_2 X Y s f n) (SimplicialObject.Splitting.φ.{u1, u2} C _inst_1 _inst_2 X Y s g n)) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) X Y) f g)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {Y : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) (f : Quiver.Hom.{succ u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))) X Y) (g : Quiver.Hom.{succ u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))) X Y), (forall (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s n) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 Y) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (SimplicialObject.Splitting.φ.{u1, u2} C _inst_1 _inst_2 X Y s f n) (SimplicialObject.Splitting.φ.{u1, u2} C _inst_1 _inst_2 X Y s g n)) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))) X Y) f g)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.hom_ext SimplicialObject.Splitting.hom_extₓ'. -/
 theorem hom_ext (f g : X ⟶ Y) (h : ∀ n : ℕ, s.φ f n = s.φ g n) : f = g :=
   by
   ext Δ
@@ -320,6 +428,12 @@ theorem hom_ext (f g : X ⟶ Y) (h : ∀ n : ℕ, s.φ f n = s.φ g n) : f = g :
   simp only [s.ι_summand_comp_app, h]
 #align simplicial_object.splitting.hom_ext SimplicialObject.Splitting.hom_ext
 
+/- warning: simplicial_object.splitting.desc -> SimplicialObject.Splitting.desc is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Z : C} (Δ : Opposite.{1} SimplexCategory), (forall (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) Z) -> (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ) Z)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Z : C} (Δ : Opposite.{1} SimplexCategory), (forall (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) Z) -> (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ) Z)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.desc SimplicialObject.Splitting.descₓ'. -/
 /-- The map `X.obj Δ ⟶ Z` obtained by providing a family of morphisms on all the
 terms of decomposition given by a splitting `s : splitting X`  -/
 def desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.n A.1.unop.len ⟶ Z) :
@@ -327,6 +441,12 @@ def desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.n A.1.
   (s.Iso Δ).inv ≫ Sigma.desc F
 #align simplicial_object.splitting.desc SimplicialObject.Splitting.desc
 
+/- warning: simplicial_object.splitting.ι_desc -> SimplicialObject.Splitting.ι_desc is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Z : C} (Δ : Opposite.{1} SimplexCategory) (F : forall (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) Z) (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) Z) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ) Z (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.desc.{u1, u2} C _inst_1 _inst_2 X s Z Δ F)) (F A)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Z : C} (Δ : Opposite.{1} SimplexCategory) (F : forall (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) Z) (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) Z) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ) Z (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.desc.{u1, u2} C _inst_1 _inst_2 X s Z Δ F)) (F A)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_desc SimplicialObject.Splitting.ι_descₓ'. -/
 @[simp, reassoc.1]
 theorem ι_desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.n A.1.unop.len ⟶ Z)
     (A : IndexSet Δ) : s.ιSummand A ≫ s.desc Δ F = F A :=
@@ -336,6 +456,7 @@ theorem ι_desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s
   erw [colimit.ι_desc, cofan.mk_ι_app]
 #align simplicial_object.splitting.ι_desc SimplicialObject.Splitting.ι_desc
 
+#print SimplicialObject.Splitting.ofIso /-
 /-- A simplicial object that is isomorphic to a split simplicial object is split. -/
 @[simps]
 def ofIso (e : X ≅ Y) : Splitting Y where
@@ -345,7 +466,14 @@ def ofIso (e : X ≅ Y) : Splitting Y where
     convert(inferInstance : is_iso ((s.iso Δ).Hom ≫ e.hom.app Δ))
     tidy
 #align simplicial_object.splitting.of_iso SimplicialObject.Splitting.ofIso
+-/
 
+/- warning: simplicial_object.splitting.ι_summand_epi_naturality -> SimplicialObject.Splitting.ιSummand_epi_naturality is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Δ₁ : Opposite.{1} SimplexCategory} {Δ₂ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ₁) (p : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ₁ Δ₂) [_inst_3 : CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ₂) (Opposite.unop.{1} SimplexCategory Δ₁) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ₁ Δ₂ p)], Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ₂)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ₁) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ₂) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ₁ A) (CategoryTheory.Functor.map.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ₁ Δ₂ p)) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ₂ (SimplicialObject.Splitting.IndexSet.epiComp Δ₁ Δ₂ A p _inst_3))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (s : SimplicialObject.Splitting.{u1, u2} C _inst_1 _inst_2 X) {Δ₁ : Opposite.{1} SimplexCategory} {Δ₂ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ₁) (p : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ₁ Δ₂) [_inst_3 : CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ₂) (Opposite.unop.{1} SimplexCategory Δ₁) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory 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CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ₁) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) Δ₂)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_2 X s (SimplexCategory.len (Opposite.unop.{1} 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+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_epi_naturality SimplicialObject.Splitting.ιSummand_epi_naturalityₓ'. -/
 @[reassoc.1]
 theorem ιSummand_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ₁ ⟶ Δ₂)
     [Epi p.unop] : s.ιSummand A ≫ X.map p = s.ιSummand (A.epi_comp p) :=
@@ -360,6 +488,7 @@ end Splitting
 
 variable (C)
 
+#print SimplicialObject.Split /-
 /-- The category `simplicial_object.split C` is the category of simplicial objects
 in `C` equipped with a splitting, and morphisms are morphisms of simplicial objects
 which are compatible with the splittings. -/
@@ -368,18 +497,22 @@ structure Split where
   pt : SimplicialObject C
   s : Splitting X
 #align simplicial_object.split SimplicialObject.Split
+-/
 
 namespace Split
 
 variable {C}
 
+#print SimplicialObject.Split.mk' /-
 /-- The object in `simplicial_object.split C` attached to a splitting `s : splitting X`
 of a simplicial object `X`. -/
 @[simps]
 def mk' {X : SimplicialObject C} (s : Splitting X) : Split C :=
   ⟨X, s⟩
 #align simplicial_object.split.mk' SimplicialObject.Split.mk'
+-/
 
+#print SimplicialObject.Split.Hom /-
 /-- Morphisms in `simplicial_object.split C` are morphisms of simplicial objects that
 are compatible with the splittings. -/
 @[nolint has_nonempty_instance]
@@ -388,7 +521,14 @@ structure Hom (S₁ S₂ : Split C) where
   f : ∀ n : ℕ, S₁.s.n n ⟶ S₂.s.n n
   comm' : ∀ n : ℕ, S₁.s.ι n ≫ F.app (op [n]) = f n ≫ S₂.s.ι n
 #align simplicial_object.split.hom SimplicialObject.Split.Hom
+-/
 
+/- warning: simplicial_object.split.hom.ext -> SimplicialObject.Split.Hom.ext is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {S₁ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} (Φ₁ : SimplicialObject.Split.Hom.{u1, u2} C _inst_1 _inst_2 S₁ S₂) (Φ₂ : SimplicialObject.Split.Hom.{u1, u2} C _inst_1 _inst_2 S₁ S₂), (forall (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₂) n)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₁ n) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₂ n)) -> (Eq.{succ u2} (SimplicialObject.Split.Hom.{u1, u2} C _inst_1 _inst_2 S₁ S₂) Φ₁ Φ₂)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] {S₁ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} (Φ₁ : SimplicialObject.Split.Hom.{u2, u1} C _inst_1 _inst_2 S₁ S₂) (Φ₂ : SimplicialObject.Split.Hom.{u2, u1} C _inst_1 _inst_2 S₁ S₂), (forall (n : Nat), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₂) n)) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ₁ n) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ₂ n)) -> (Eq.{succ u1} (SimplicialObject.Split.Hom.{u2, u1} C _inst_1 _inst_2 S₁ S₂) Φ₁ Φ₂)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.hom.ext SimplicialObject.Split.Hom.extₓ'. -/
 @[ext]
 theorem Hom.ext {S₁ S₂ : Split C} (Φ₁ Φ₂ : Hom S₁ S₂) (h : ∀ n : ℕ, Φ₁.f n = Φ₂.f n) : Φ₁ = Φ₂ :=
   by
@@ -426,49 +566,64 @@ variable {C}
 
 namespace Split
 
-theorem congr_f {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ = Φ₂) : Φ₁.f = Φ₂.f := by rw [h]
-#align simplicial_object.split.congr_F SimplicialObject.Split.congr_f
+/- warning: simplicial_object.split.congr_F -> SimplicialObject.Split.congr_F is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {S₁ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {Φ₁ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂} {Φ₂ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂}, (Eq.{succ u2} (Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂) Φ₁ Φ₂) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₂)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₁) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₂))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] {S₁ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {Φ₁ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂} {Φ₂ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂}, (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂) Φ₁ Φ₂) -> (Eq.{succ u1} (forall (n : Nat), Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₂) n)) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ₁) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ₂))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.congr_F SimplicialObject.Split.congr_Fₓ'. -/
+theorem congr_F {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ = Φ₂) : Φ₁.f = Φ₂.f := by rw [h]
+#align simplicial_object.split.congr_F SimplicialObject.Split.congr_F
 
-/- warning: simplicial_object.split.congr_f clashes with simplicial_object.split.congr_F -> SimplicialObject.Split.congr_f
-warning: simplicial_object.split.congr_f -> SimplicialObject.Split.congr_f is a dubious translation:
+/- warning: simplicial_object.split.congr_f -> SimplicialObject.Split.congr_f is a dubious translation:
 lean 3 declaration is
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {S₁ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {Φ₁ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂} {Φ₂ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂}, (Eq.{succ u2} (Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂) Φ₁ Φ₂) -> (forall (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₂) n)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₁ n) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₂ n))
 but is expected to have type
-  PUnit.{0}
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] {S₁ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {Φ₁ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂} {Φ₂ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂}, (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂) Φ₁ Φ₂) -> (forall (n : Nat), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₂) n)) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ₁ n) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ₂ n))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.split.congr_f SimplicialObject.Split.congr_fₓ'. -/
 theorem congr_f {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ = Φ₂) (n : ℕ) : Φ₁.f n = Φ₂.f n := by
   rw [h]
 #align simplicial_object.split.congr_f SimplicialObject.Split.congr_f
 
+/- warning: simplicial_object.split.id_F -> SimplicialObject.Split.id_F is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] (S : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2), Eq.{succ u2} (Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S S (CategoryTheory.CategoryStruct.id.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2)) S)) (CategoryTheory.CategoryStruct.id.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1)) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] (S : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S)) (SimplicialObject.Split.Hom.F.{u2, u1} C _inst_1 _inst_2 S S (CategoryTheory.CategoryStruct.id.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2)) S)) (CategoryTheory.CategoryStruct.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.id_F SimplicialObject.Split.id_Fₓ'. -/
 @[simp]
-theorem id_f (S : Split C) : (𝟙 S : S ⟶ S).f = 𝟙 S.pt :=
+theorem id_F (S : Split C) : (𝟙 S : S ⟶ S).f = 𝟙 S.pt :=
   rfl
-#align simplicial_object.split.id_F SimplicialObject.Split.id_f
+#align simplicial_object.split.id_F SimplicialObject.Split.id_F
 
-/- warning: simplicial_object.split.id_f clashes with simplicial_object.split.id_F -> SimplicialObject.Split.id_f
-warning: simplicial_object.split.id_f -> SimplicialObject.Split.id_f is a dubious translation:
+/- warning: simplicial_object.split.id_f -> SimplicialObject.Split.id_f is a dubious translation:
 lean 3 declaration is
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] (S : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S) n)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S S (CategoryTheory.CategoryStruct.id.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2)) S) n) (CategoryTheory.CategoryStruct.id.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S) n))
 but is expected to have type
-  PUnit.{0}
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] (S : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (n : Nat), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S) n) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S) n)) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S S (CategoryTheory.CategoryStruct.id.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2)) S) n) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S) n))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.split.id_f SimplicialObject.Split.id_fₓ'. -/
 @[simp]
 theorem id_f (S : Split C) (n : ℕ) : (𝟙 S : S ⟶ S).f n = 𝟙 (S.s.n n) :=
   rfl
 #align simplicial_object.split.id_f SimplicialObject.Split.id_f
 
+/- warning: simplicial_object.split.comp_F -> SimplicialObject.Split.comp_F is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {S₁ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₃ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} (Φ₁₂ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂) (Φ₂₃ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₂ S₃), Eq.{succ u2} (Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₃)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₃ (CategoryTheory.CategoryStruct.comp.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2)) S₁ S₂ S₃ Φ₁₂ Φ₂₃)) (CategoryTheory.CategoryStruct.comp.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1)) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₃) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₁₂) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₂ S₃ Φ₂₃))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] {S₁ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₃ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} (Φ₁₂ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂) (Φ₂₃ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₂ S₃), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₃)) (SimplicialObject.Split.Hom.F.{u2, u1} C _inst_1 _inst_2 S₁ S₃ (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2)) S₁ S₂ S₃ Φ₁₂ Φ₂₃)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₃) (SimplicialObject.Split.Hom.F.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ₁₂) (SimplicialObject.Split.Hom.F.{u2, u1} C _inst_1 _inst_2 S₂ S₃ Φ₂₃))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.comp_F SimplicialObject.Split.comp_Fₓ'. -/
 @[simp]
-theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ : S₂ ⟶ S₃) :
+theorem comp_F {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ : S₂ ⟶ S₃) :
     (Φ₁₂ ≫ Φ₂₃).f = Φ₁₂.f ≫ Φ₂₃.f :=
   rfl
-#align simplicial_object.split.comp_F SimplicialObject.Split.comp_f
+#align simplicial_object.split.comp_F SimplicialObject.Split.comp_F
 
-/- warning: simplicial_object.split.comp_f clashes with simplicial_object.split.comp_F -> SimplicialObject.Split.comp_f
-warning: simplicial_object.split.comp_f -> SimplicialObject.Split.comp_f is a dubious translation:
+/- warning: simplicial_object.split.comp_f -> SimplicialObject.Split.comp_f is a dubious translation:
 lean 3 declaration is
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {S₁ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₃ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} (Φ₁₂ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂) (Φ₂₃ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₂ S₃) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₃) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₃) n)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₃ (CategoryTheory.CategoryStruct.comp.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2)) S₁ S₂ S₃ Φ₁₂ Φ₂₃) n) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₂) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₃) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₃) n) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₁₂ n) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₂ S₃ Φ₂₃ n))
 but is expected to have type
-  PUnit.{0}
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] {S₁ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₃ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} (Φ₁₂ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂) (Φ₂₃ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₂ S₃) (n : Nat), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₃) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₃) n)) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₃ (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2)) S₁ S₂ S₃ Φ₁₂ Φ₂₃) n) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₂) n) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₃) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₃) n) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ₁₂ n) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₂ S₃ Φ₂₃ n))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.split.comp_f SimplicialObject.Split.comp_fₓ'. -/
 @[simp]
 theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ : S₂ ⟶ S₃) (n : ℕ) :
@@ -476,6 +631,12 @@ theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ :
   rfl
 #align simplicial_object.split.comp_f SimplicialObject.Split.comp_f
 
+/- warning: simplicial_object.split.ι_summand_naturality_symm -> SimplicialObject.Split.ιSummand_naturality_symm is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {S₁ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} (Φ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) 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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u1, u2} C _inst_1] {S₁ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2} (Φ : Quiver.Hom.{succ u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (SimplicialObject.Split.{u2, u1} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u2, u1} C _inst_1 _inst_2))) S₁ S₂) {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (SimplicialObject.Splitting.N.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₁) 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SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂)) Δ) (SimplicialObject.Split.Hom.f.{u2, u1} C _inst_1 _inst_2 S₁ S₂ Φ (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (SimplicialObject.Splitting.ιSummand.{u2, u1} C _inst_1 _inst_2 (SimplicialObject.Split.X.{u2, u1} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u2, u1} C _inst_1 _inst_2 S₂) Δ A))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.ι_summand_naturality_symm SimplicialObject.Split.ιSummand_naturality_symmₓ'. -/
 @[simp, reassoc.1]
 theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}
     (A : Splitting.IndexSet Δ) : S₁.s.ιSummand A ≫ Φ.f.app Δ = Φ.f A.1.unop.len ≫ S₂.s.ιSummand A :=
@@ -484,6 +645,12 @@ theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ
 
 variable (C)
 
+/- warning: simplicial_object.split.forget -> SimplicialObject.Split.forget is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], CategoryTheory.Functor.{u2, u2, max u1 u2, max u2 u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1)
+but is expected to have type
+  forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], CategoryTheory.Functor.{u2, u2, max u2 u1, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.forget SimplicialObject.Split.forgetₓ'. -/
 /-- The functor `simplicial_object.split C ⥤ simplicial_object C` which forgets
 the splitting. -/
 @[simps]
@@ -493,6 +660,12 @@ def forget : Split C ⥤ SimplicialObject C
   map S₁ S₂ Φ := Φ.f
 #align simplicial_object.split.forget SimplicialObject.Split.forget
 
+/- warning: simplicial_object.split.eval_N -> SimplicialObject.Split.evalN is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], Nat -> (CategoryTheory.Functor.{u2, u2, max u1 u2, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2) C _inst_1)
+but is expected to have type
+  forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], Nat -> (CategoryTheory.Functor.{u2, u2, max u2 u1, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) C _inst_1)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.eval_N SimplicialObject.Split.evalNₓ'. -/
 /-- The functor `simplicial_object.split C ⥤ C` which sends a simplicial object equipped
 with a splitting to its nondegenerate `n`-simplices. -/
 @[simps]
@@ -501,6 +674,12 @@ def evalN (n : ℕ) : Split C ⥤ C where
   map S₁ S₂ Φ := Φ.f n
 #align simplicial_object.split.eval_N SimplicialObject.Split.evalN
 
+/- warning: simplicial_object.split.nat_trans_ι_summand -> SimplicialObject.Split.natTransιSummand is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{succ (max u1 u2), max u1 u2} (CategoryTheory.Functor.{u2, u2, max u1 u2, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2) C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u1 u2} (CategoryTheory.Functor.{u2, u2, max u1 u2, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u1 u2} (CategoryTheory.Functor.{u2, u2, max u1 u2, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2) C _inst_1) (CategoryTheory.Functor.category.{u2, u2, max u1 u2, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2) C _inst_1))) (SimplicialObject.Split.evalN.{u1, u2} C _inst_1 _inst_2 (SimplexCategory.len (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (CategoryTheory.Functor.comp.{u2, u2, u2, max u1 u2, max u2 u1, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) C _inst_1 (SimplicialObject.Split.forget.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{0, max u2 u1, 0, max u2 u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) (CategoryTheory.Functor.{u2, u2, max u2 u1, u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (CategoryTheory.Functor.category.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1) (CategoryTheory.Functor.category.{u2, u2, max u2 u1, u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (CategoryTheory.Functor.category.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1) (CategoryTheory.evaluation.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) Δ))
+but is expected to have type
+  forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ), Quiver.Hom.{max (succ u1) (succ u2), max u1 u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u1 u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u1 u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, u1} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_2) C _inst_1) (CategoryTheory.Functor.category.{u2, u2, max u1 u2, u1} 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0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1) (CategoryTheory.Functor.category.{u2, u2, max u1 u2, u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (CategoryTheory.Functor.category.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) C _inst_1) (CategoryTheory.evaluation.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1)) Δ))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.nat_trans_ι_summand SimplicialObject.Split.natTransιSummandₓ'. -/
 /-- The inclusion of each summand in the coproduct decomposition of simplices
 in split simplicial objects is a natural transformation of functors
 `simplicial_object.split C ⥤ C` -/

dd1f8496

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -342,7 +342,7 @@ def ofIso (e : X ≅ Y) : Splitting Y where
   n := s.n
   ι n := s.ι n ≫ e.Hom.app (op [n])
   map_is_iso' Δ := by
-    convert (inferInstance : is_iso ((s.iso Δ).Hom ≫ e.hom.app Δ))
+    convert(inferInstance : is_iso ((s.iso Δ).Hom ≫ e.hom.app Δ))
     tidy
 #align simplicial_object.splitting.of_iso SimplicialObject.Splitting.ofIso

dd1f8496

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -298,14 +298,14 @@ theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : Index
   simp only [ι_summand_eq_assoc, φ, nat_trans.naturality, assoc]
 #align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_app
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `discrete_cases #[] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
 theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
     (h : ∀ A : IndexSet Δ, s.ιSummand A ≫ f = s.ιSummand A ≫ g) : f = g :=
   by
   rw [← cancel_epi (s.iso Δ).Hom]
   ext A
   trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `discrete_cases #[]"
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[]"
   simpa only [ι_summand_eq, iso_hom, colimit.ι_desc_assoc, cofan.mk_ι_app, assoc] using h A
 #align simplicial_object.splitting.hom_ext' SimplicialObject.Splitting.hom_ext'

dd1f8496

bump to nightly-2023-02-28-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

1fb1623f

Diff

@@ -365,7 +365,7 @@ in `C` equipped with a splitting, and morphisms are morphisms of simplicial obje
 which are compatible with the splittings. -/
 @[ext, nolint has_nonempty_instance]
 structure Split where
-  x : SimplicialObject C
+  pt : SimplicialObject C
   s : Splitting X
 #align simplicial_object.split SimplicialObject.Split
 
@@ -384,7 +384,7 @@ def mk' {X : SimplicialObject C} (s : Splitting X) : Split C :=
 are compatible with the splittings. -/
 @[nolint has_nonempty_instance]
 structure Hom (S₁ S₂ : Split C) where
-  f : S₁.x ⟶ S₂.x
+  f : S₁.pt ⟶ S₂.pt
   f : ∀ n : ℕ, S₁.s.n n ⟶ S₂.s.n n
   comm' : ∀ n : ℕ, S₁.s.ι n ≫ F.app (op [n]) = f n ≫ S₂.s.ι n
 #align simplicial_object.split.hom SimplicialObject.Split.Hom
@@ -441,7 +441,7 @@ theorem congr_f {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ =
 #align simplicial_object.split.congr_f SimplicialObject.Split.congr_f
 
 @[simp]
-theorem id_f (S : Split C) : (𝟙 S : S ⟶ S).f = 𝟙 S.x :=
+theorem id_f (S : Split C) : (𝟙 S : S ⟶ S).f = 𝟙 S.pt :=
   rfl
 #align simplicial_object.split.id_F SimplicialObject.Split.id_f
 
@@ -489,7 +489,7 @@ the splitting. -/
 @[simps]
 def forget : Split C ⥤ SimplicialObject C
     where
-  obj S := S.x
+  obj S := S.pt
   map S₁ S₂ Φ := Φ.f
 #align simplicial_object.split.forget SimplicialObject.Split.forget

dd1f8496

bump to nightly-2023-02-27-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

91d8c210

Diff

@@ -430,12 +430,15 @@ theorem congr_f {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ =
 #align simplicial_object.split.congr_F SimplicialObject.Split.congr_f
 
 /- warning: simplicial_object.split.congr_f clashes with simplicial_object.split.congr_F -> SimplicialObject.Split.congr_f
+warning: simplicial_object.split.congr_f -> SimplicialObject.Split.congr_f is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {S₁ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {Φ₁ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂} {Φ₂ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂}, (Eq.{succ u2} (Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂) Φ₁ Φ₂) -> (forall (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₂) n)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₁ n) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₂ n))
+but is expected to have type
+  PUnit.{0}
 Case conversion may be inaccurate. Consider using '#align simplicial_object.split.congr_f SimplicialObject.Split.congr_fₓ'. -/
-#print SimplicialObject.Split.congr_f /-
 theorem congr_f {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ = Φ₂) (n : ℕ) : Φ₁.f n = Φ₂.f n := by
   rw [h]
 #align simplicial_object.split.congr_f SimplicialObject.Split.congr_f
--/
 
 @[simp]
 theorem id_f (S : Split C) : (𝟙 S : S ⟶ S).f = 𝟙 S.x :=
@@ -443,13 +446,16 @@ theorem id_f (S : Split C) : (𝟙 S : S ⟶ S).f = 𝟙 S.x :=
 #align simplicial_object.split.id_F SimplicialObject.Split.id_f
 
 /- warning: simplicial_object.split.id_f clashes with simplicial_object.split.id_F -> SimplicialObject.Split.id_f
+warning: simplicial_object.split.id_f -> SimplicialObject.Split.id_f is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] (S : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S) n)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S S (CategoryTheory.CategoryStruct.id.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2)) S) n) (CategoryTheory.CategoryStruct.id.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S) n))
+but is expected to have type
+  PUnit.{0}
 Case conversion may be inaccurate. Consider using '#align simplicial_object.split.id_f SimplicialObject.Split.id_fₓ'. -/
-#print SimplicialObject.Split.id_f /-
 @[simp]
 theorem id_f (S : Split C) (n : ℕ) : (𝟙 S : S ⟶ S).f n = 𝟙 (S.s.n n) :=
   rfl
 #align simplicial_object.split.id_f SimplicialObject.Split.id_f
--/
 
 @[simp]
 theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ : S₂ ⟶ S₃) :
@@ -458,14 +464,17 @@ theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ :
 #align simplicial_object.split.comp_F SimplicialObject.Split.comp_f
 
 /- warning: simplicial_object.split.comp_f clashes with simplicial_object.split.comp_F -> SimplicialObject.Split.comp_f
+warning: simplicial_object.split.comp_f -> SimplicialObject.Split.comp_f is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {S₁ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₂ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} {S₃ : SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2} (Φ₁₂ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₁ S₂) (Φ₂₃ : Quiver.Hom.{succ u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2))) S₂ S₃) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₃) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₃) n)) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₃ (CategoryTheory.CategoryStruct.comp.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_2) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_2)) S₁ S₂ S₃ Φ₁₂ Φ₂₃) n) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₁) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₁) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₂) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₂) n) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_2 (SimplicialObject.Split.x.{u1, u2} C _inst_1 _inst_2 S₃) (SimplicialObject.Split.s.{u1, u2} C _inst_1 _inst_2 S₃) n) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₁ S₂ Φ₁₂ n) (SimplicialObject.Split.Hom.f.{u1, u2} C _inst_1 _inst_2 S₂ S₃ Φ₂₃ n))
+but is expected to have type
+  PUnit.{0}
 Case conversion may be inaccurate. Consider using '#align simplicial_object.split.comp_f SimplicialObject.Split.comp_fₓ'. -/
-#print SimplicialObject.Split.comp_f /-
 @[simp]
 theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ : S₂ ⟶ S₃) (n : ℕ) :
     (Φ₁₂ ≫ Φ₂₃).f n = Φ₁₂.f n ≫ Φ₂₃.f n :=
   rfl
 #align simplicial_object.split.comp_f SimplicialObject.Split.comp_f
--/
 
 @[simp, reassoc.1]
 theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}

dd1f8496

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

dd1f8496

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -214,7 +214,7 @@ def cofan' (Δ : SimplexCategoryᵒᵖ) : Cofan (summand N Δ) :=
 
 end Splitting
 
---porting note (#10927): removed @[nolint has_nonempty_instance]
+--porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- A splitting of a simplicial object `X` consists of the datum of a sequence
 of objects `N`, a sequence of morphisms `ι : N n ⟶ X _[n]` such that
 for all `Δ : SimplexCategoryᵒᵖ`, the canonical map `Splitting.map X ι Δ`
@@ -314,7 +314,7 @@ end Splitting
 
 variable (C)
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- The category `SimplicialObject.Split C` is the category of simplicial objects
 in `C` equipped with a splitting, and morphisms are morphisms of simplicial objects
 which are compatible with the splittings. -/
@@ -337,7 +337,7 @@ def mk' {X : SimplicialObject C} (s : Splitting X) : Split C :=
   ⟨X, s⟩
 #align simplicial_object.split.mk' SimplicialObject.Split.mk'
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- Morphisms in `SimplicialObject.Split C` are morphisms of simplicial objects that
 are compatible with the splittings. -/
 structure Hom (S₁ S₂ : Split C) where

dd1f8496

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -383,7 +383,7 @@ variable {C}
 
 namespace Split
 
--- porting note: added as `Hom.ext` is not triggered automatically
+-- Porting note: added as `Hom.ext` is not triggered automatically
 @[ext]
 theorem hom_ext {S₁ S₂ : Split C} (Φ₁ Φ₂ : S₁ ⟶ S₂) (h : ∀ n : ℕ, Φ₁.f n = Φ₂.f n) : Φ₁ = Φ₂ :=
   Hom.ext _ _ h

dd1f8496

chore: classify removed @[nolint has_nonempty_instance] porting notes (#10929)

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

2599c3bb

Diff

@@ -214,7 +214,7 @@ def cofan' (Δ : SimplexCategoryᵒᵖ) : Cofan (summand N Δ) :=
 
 end Splitting
 
---porting note: removed @[nolint has_nonempty_instance]
+--porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- A splitting of a simplicial object `X` consists of the datum of a sequence
 of objects `N`, a sequence of morphisms `ι : N n ⟶ X _[n]` such that
 for all `Δ : SimplexCategoryᵒᵖ`, the canonical map `Splitting.map X ι Δ`
@@ -314,7 +314,7 @@ end Splitting
 
 variable (C)
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- The category `SimplicialObject.Split C` is the category of simplicial objects
 in `C` equipped with a splitting, and morphisms are morphisms of simplicial objects
 which are compatible with the splittings. -/
@@ -337,7 +337,7 @@ def mk' {X : SimplicialObject C} (s : Splitting X) : Split C :=
   ⟨X, s⟩
 #align simplicial_object.split.mk' SimplicialObject.Split.mk'
 
--- Porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- Morphisms in `SimplicialObject.Split C` are morphisms of simplicial objects that
 are compatible with the splittings. -/
 structure Hom (S₁ S₂ : Split C) where

dd1f8496

style: reduce spacing variation in "porting note" comments (#10886)

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

86b84c52

Diff

@@ -337,7 +337,7 @@ def mk' {X : SimplicialObject C} (s : Splitting X) : Split C :=
   ⟨X, s⟩
 #align simplicial_object.split.mk' SimplicialObject.Split.mk'
 
--- porting note : removed @[nolint has_nonempty_instance]
+-- Porting note: removed @[nolint has_nonempty_instance]
 /-- Morphisms in `SimplicialObject.Split C` are morphisms of simplicial objects that
 are compatible with the splittings. -/
 structure Hom (S₁ S₂ : Split C) where

Diff

@@ -14,7 +14,7 @@ import Mathlib.CategoryTheory.Limits.Shapes.Products
 
 In this file, we introduce the notion of split simplicial object.
 If `C` is a category that has finite coproducts, a splitting
-`s : Splitting X` of a simplical object `X` in `C` consists
+`s : Splitting X` of a simplicial object `X` in `C` consists
 of the datum of a sequence of objects `s.N : ℕ → C` (which
 we shall refer to as "nondegenerate simplices") and a
 sequence of morphisms `s.ι n : s.N n → X _[n]` that have
@@ -341,7 +341,7 @@ def mk' {X : SimplicialObject C} (s : Splitting X) : Split C :=
 /-- Morphisms in `SimplicialObject.Split C` are morphisms of simplicial objects that
 are compatible with the splittings. -/
 structure Hom (S₁ S₂ : Split C) where
-  /-- the morphism between the underlying simplical objects -/
+  /-- the morphism between the underlying simplicial objects -/
   F : S₁.X ⟶ S₂.X
   /-- the morphism between the "nondegenerate" `n`-simplices for all `n : ℕ` -/
   f : ∀ n : ℕ, S₁.s.N n ⟶ S₂.s.N n

dd1f8496

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
 import Mathlib.AlgebraicTopology.SimplicialObject
-import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
+import Mathlib.CategoryTheory.Limits.Shapes.Products
 
 #align_import algebraic_topology.split_simplicial_object from "leanprover-community/mathlib"@"dd1f8496baa505636a82748e6b652165ea888733"

dd1f8496

refactor(AlgebraicTopology): using the cofan API for SplitSimplicialObject (#8531)

This PR changes the definition of a splitting of simplicial objects. The new definition makes a better use of the cofan API. As a result, it is no longer necessary to assume that the category has finite coproducts.

f9e2c2ca

Diff

@@ -208,84 +208,47 @@ def summand (A : IndexSet Δ) : C :=
   N A.1.unop.len
 #align simplicial_object.splitting.summand SimplicialObject.Splitting.summand
 
-variable [HasFiniteCoproducts C]
-
-/-- The coproduct of the family `summand N Δ` -/
-abbrev coprod := ∐ summand N Δ
-#align simplicial_object.splitting.coprod SimplicialObject.Splitting.coprod
-
-variable {Δ}
-
-/-- The inclusion of a summand in the coproduct. -/
-@[simp]
-def ιCoprod (A : IndexSet Δ) : N A.1.unop.len ⟶ coprod N Δ :=
-  Sigma.ι (summand N Δ) A
-#align simplicial_object.splitting.ι_coprod SimplicialObject.Splitting.ιCoprod
-
-variable {N}
-
-/-- The canonical morphism `coprod N Δ ⟶ X.obj Δ` attached to a sequence
-of objects `N` and a sequence of morphisms `N n ⟶ X _[n]`. -/
-@[simp]
-def map (Δ : SimplexCategoryᵒᵖ) : coprod N Δ ⟶ X.obj Δ :=
-  Sigma.desc fun A => φ A.1.unop.len ≫ X.map A.e.op
-#align simplicial_object.splitting.map SimplicialObject.Splitting.map
+/-- The cofan for `summand N Δ` induced by morphisms `N n ⟶ X_ [n]` for all `n : ℕ`. -/
+def cofan' (Δ : SimplexCategoryᵒᵖ) : Cofan (summand N Δ) :=
+  Cofan.mk (X.obj Δ) (fun A => φ A.1.unop.len ≫ X.map A.e.op)
 
 end Splitting
 
-variable [HasFiniteCoproducts C]
-
 --porting note: removed @[nolint has_nonempty_instance]
 /-- A splitting of a simplicial object `X` consists of the datum of a sequence
 of objects `N`, a sequence of morphisms `ι : N n ⟶ X _[n]` such that
 for all `Δ : SimplexCategoryᵒᵖ`, the canonical map `Splitting.map X ι Δ`
 is an isomorphism. -/
 structure Splitting (X : SimplicialObject C) where
+  /-- The "nondegenerate simplices" `N n` for all `n : ℕ`. -/
   N : ℕ → C
+  /-- The "inclusion" `N n ⟶ X _[n]` for all `n : ℕ`. -/
   ι : ∀ n, N n ⟶ X _[n]
-  map_isIso : ∀ Δ : SimplexCategoryᵒᵖ, IsIso (Splitting.map X ι Δ)
+  /-- For each `Δ`, `X.obj Δ` identifies to the coproduct of the objects `N A.1.unop.len`
+  for all `A : IndexSet Δ`.  -/
+  isColimit' : ∀ Δ : SimplexCategoryᵒᵖ, IsColimit (Splitting.cofan' N X ι Δ)
 #align simplicial_object.splitting SimplicialObject.Splitting
 
 namespace Splitting
 
 variable {X Y : SimplicialObject C} (s : Splitting X)
 
-attribute [instance] Splitting.map_isIso
-#align simplicial_object.splitting.map_is_iso SimplicialObject.Splitting.map_isIso
+/-- The cofan for `summand s.N Δ` induced by a splitting of a simplicial object.  -/
+def cofan (Δ : SimplexCategoryᵒᵖ) : Cofan (summand s.N Δ) :=
+  Cofan.mk (X.obj Δ) (fun A => s.ι A.1.unop.len ≫ X.map A.e.op)
 
--- Porting note:
--- This used to be `@[simps]`, but now `Splitting.map` is unfolded in the generated lemmas. Why?
--- Instead we write these lemmas by hand.
-/-- The isomorphism on simplices given by the axiom `Splitting.map_isIso` -/
-def iso (Δ : SimplexCategoryᵒᵖ) : coprod s.N Δ ≅ X.obj Δ :=
-  asIso (Splitting.map X s.ι Δ)
-#align simplicial_object.splitting.iso SimplicialObject.Splitting.iso
-
-@[simp]
-theorem iso_hom (Δ : SimplexCategoryᵒᵖ) : (iso s Δ).hom = Splitting.map X s.ι Δ :=
-  rfl
-
-@[simp]
-theorem iso_inv (Δ : SimplexCategoryᵒᵖ) : (iso s Δ).inv = inv (Splitting.map X s.ι Δ) :=
-  rfl
-
-/-- Via the isomorphism `s.iso Δ`, this is the inclusion of a summand
-in the direct sum decomposition given by the splitting `s : Splitting X`. -/
-def ιSummand {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) : s.N A.1.unop.len ⟶ X.obj Δ :=
-  Splitting.ιCoprod s.N A ≫ (s.iso Δ).hom
-#align simplicial_object.splitting.ι_summand SimplicialObject.Splitting.ιSummand
+/-- The cofan `s.cofan Δ` is colimit. -/
+def isColimit (Δ : SimplexCategoryᵒᵖ) : IsColimit (s.cofan Δ) := s.isColimit' Δ
 
 @[reassoc]
-theorem ιSummand_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
-    s.ιSummand A = s.ι A.1.unop.len ≫ X.map A.e.op := by
-  dsimp only [ιSummand, Iso.hom]
-  erw [colimit.ι_desc, Cofan.mk_ι_app]
-#align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.ιSummand_eq
-
-theorem ιSummand_id (n : ℕ) : s.ιSummand (IndexSet.id (op [n])) = s.ι n := by
-  erw [ιSummand_eq, X.map_id, comp_id]
+theorem cofan_inj_eq {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
+    (s.cofan Δ).inj  A = s.ι A.1.unop.len ≫ X.map A.e.op := rfl
+#align simplicial_object.splitting.ι_summand_eq SimplicialObject.Splitting.cofan_inj_eq
+
+theorem cofan_inj_id (n : ℕ) : (s.cofan _).inj (IndexSet.id (op [n])) = s.ι n := by
+  erw [cofan_inj_eq, X.map_id, comp_id]
   rfl
-#align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.ιSummand_id
+#align simplicial_object.splitting.ι_summand_id SimplicialObject.Splitting.cofan_inj_id
 
 /-- As it is stated in `Splitting.hom_ext`, a morphism `f : X ⟶ Y` from a split
 simplicial object to any simplicial object is determined by its restrictions
@@ -296,17 +259,15 @@ def φ (f : X ⟶ Y) (n : ℕ) : s.N n ⟶ Y _[n] :=
 #align simplicial_object.splitting.φ SimplicialObject.Splitting.φ
 
 @[reassoc (attr := simp)]
-theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
-    s.ιSummand A ≫ f.app Δ = s.φ f A.1.unop.len ≫ Y.map A.e.op := by
-  simp only [ιSummand_eq_assoc, φ, assoc]
+theorem cofan_inj_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
+    (s.cofan Δ).inj A ≫ f.app Δ = s.φ f A.1.unop.len ≫ Y.map A.e.op := by
+  simp only [cofan_inj_eq_assoc, φ, assoc]
   erw [NatTrans.naturality]
-#align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.ιSummand_comp_app
+#align simplicial_object.splitting.ι_summand_comp_app SimplicialObject.Splitting.cofan_inj_comp_app
 
 theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
-    (h : ∀ A : IndexSet Δ, s.ιSummand A ≫ f = s.ιSummand A ≫ g) : f = g := by
-  rw [← cancel_epi (s.iso Δ).hom]
-  ext A
-  simpa only [ιSummand_eq, iso_hom, map, colimit.ι_desc_assoc, Cofan.mk_ι_app] using h A
+    (h : ∀ A : IndexSet Δ, (s.cofan Δ).inj A ≫ f = (s.cofan Δ).inj A ≫ g) : f = g :=
+  Cofan.IsColimit.hom_ext (s.isColimit Δ) _ _ h
 #align simplicial_object.splitting.hom_ext' SimplicialObject.Splitting.hom_ext'
 
 theorem hom_ext (f g : X ⟶ Y) (h : ∀ n : ℕ, s.φ f n = s.φ g n) : f = g := by
@@ -316,22 +277,20 @@ theorem hom_ext (f g : X ⟶ Y) (h : ∀ n : ℕ, s.φ f n = s.φ g n) : f = g :
   induction' Δ using Opposite.rec with Δ
   induction' Δ using SimplexCategory.rec with n
   dsimp
-  simp only [s.ιSummand_comp_app, h]
+  simp only [s.cofan_inj_comp_app, h]
 #align simplicial_object.splitting.hom_ext SimplicialObject.Splitting.hom_ext
 
 /-- The map `X.obj Δ ⟶ Z` obtained by providing a family of morphisms on all the
 terms of decomposition given by a splitting `s : Splitting X`  -/
 def desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.N A.1.unop.len ⟶ Z) :
     X.obj Δ ⟶ Z :=
-  (s.iso Δ).inv ≫ Sigma.desc F
+  Cofan.IsColimit.desc (s.isColimit Δ) F
 #align simplicial_object.splitting.desc SimplicialObject.Splitting.desc
 
 @[reassoc (attr := simp)]
 theorem ι_desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.N A.1.unop.len ⟶ Z)
-    (A : IndexSet Δ) : s.ιSummand A ≫ s.desc Δ F = F A := by
-  dsimp only [ιSummand, desc]
-  simp only [assoc, Iso.hom_inv_id_assoc, ιCoprod]
-  erw [colimit.ι_desc, Cofan.mk_ι_app]
+    (A : IndexSet Δ) : (s.cofan Δ).inj A ≫ s.desc Δ F = F A := by
+  apply Cofan.IsColimit.fac
 #align simplicial_object.splitting.ι_desc SimplicialObject.Splitting.ι_desc
 
 /-- A simplicial object that is isomorphic to a split simplicial object is split. -/
@@ -339,20 +298,17 @@ theorem ι_desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s
 def ofIso (e : X ≅ Y) : Splitting Y where
   N := s.N
   ι n := s.ι n ≫ e.hom.app (op [n])
-  map_isIso Δ := by
-    convert (inferInstance : IsIso ((s.iso Δ).hom ≫ e.hom.app Δ))
-    ext
-    simp [map]
+  isColimit' Δ := IsColimit.ofIsoColimit (s.isColimit Δ ) (Cofan.ext (e.app Δ)
+    (fun A => by simp [cofan, cofan']))
 #align simplicial_object.splitting.of_iso SimplicialObject.Splitting.ofIso
 
 @[reassoc]
-theorem ιSummand_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ₁ ⟶ Δ₂)
-    [Epi p.unop] : s.ιSummand A ≫ X.map p = s.ιSummand (A.epiComp p) := by
-  dsimp [ιSummand]
-  erw [colimit.ι_desc, colimit.ι_desc, Cofan.mk_ι_app, Cofan.mk_ι_app]
-  dsimp only [IndexSet.epiComp, IndexSet.e]
-  rw [op_comp, X.map_comp, assoc, Quiver.Hom.op_unop]
-#align simplicial_object.splitting.ι_summand_epi_naturality SimplicialObject.Splitting.ιSummand_epi_naturality
+theorem cofan_inj_epi_naturality {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ₁ ⟶ Δ₂)
+    [Epi p.unop] : (s.cofan Δ₁).inj A ≫ X.map p = (s.cofan Δ₂).inj (A.epiComp p) := by
+  dsimp [cofan]
+  rw [assoc, ← X.map_comp]
+  rfl
+#align simplicial_object.splitting.ι_summand_epi_naturality SimplicialObject.Splitting.cofan_inj_epi_naturality
 
 end Splitting
 
@@ -364,7 +320,9 @@ in `C` equipped with a splitting, and morphisms are morphisms of simplicial obje
 which are compatible with the splittings. -/
 @[ext]
 structure Split where
+  /-- the underlying simplicial object -/
   X : SimplicialObject C
+  /-- a splitting of the simplicial object -/
   s : Splitting X
 #align simplicial_object.split SimplicialObject.Split
 
@@ -383,7 +341,9 @@ def mk' {X : SimplicialObject C} (s : Splitting X) : Split C :=
 /-- Morphisms in `SimplicialObject.Split C` are morphisms of simplicial objects that
 are compatible with the splittings. -/
 structure Hom (S₁ S₂ : Split C) where
+  /-- the morphism between the underlying simplical objects -/
   F : S₁.X ⟶ S₂.X
+  /-- the morphism between the "nondegenerate" `n`-simplices for all `n : ℕ` -/
   f : ∀ n : ℕ, S₁.s.N n ⟶ S₂.s.N n
   comm : ∀ n : ℕ, S₁.s.ι n ≫ F.app (op [n]) = f n ≫ S₂.s.ι n := by aesop_cat
 #align simplicial_object.split.hom SimplicialObject.Split.Hom
@@ -461,11 +421,11 @@ theorem comp_f {S₁ S₂ S₃ : Split C} (Φ₁₂ : S₁ ⟶ S₂) (Φ₂₃ :
 #align simplicial_object.split.comp_f SimplicialObject.Split.comp_f
 
 @[reassoc (attr := simp 1100)]
-theorem ιSummand_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}
+theorem cofan_inj_naturality_symm {S₁ S₂ : Split C} (Φ : S₁ ⟶ S₂) {Δ : SimplexCategoryᵒᵖ}
     (A : Splitting.IndexSet Δ) :
-    S₁.s.ιSummand A ≫ Φ.F.app Δ = Φ.f A.1.unop.len ≫ S₂.s.ιSummand A := by
-  erw [S₁.s.ιSummand_eq, S₂.s.ιSummand_eq, assoc, Φ.F.naturality, ← Φ.comm_assoc ]
-#align simplicial_object.split.ι_summand_naturality_symm SimplicialObject.Split.ιSummand_naturality_symm
+    (S₁.s.cofan Δ).inj A ≫ Φ.F.app Δ = Φ.f A.1.unop.len ≫ (S₂.s.cofan Δ).inj A := by
+  erw [S₁.s.cofan_inj_eq, S₂.s.cofan_inj_eq, assoc, Φ.F.naturality, ← Φ.comm_assoc]
+#align simplicial_object.split.ι_summand_naturality_symm SimplicialObject.Split.cofan_inj_naturality_symm
 
 variable (C)
 
@@ -490,11 +450,11 @@ set_option linter.uppercaseLean3 false in
 in split simplicial objects is a natural transformation of functors
 `SimplicialObject.Split C ⥤ C` -/
 @[simps]
-def natTransιSummand {Δ : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) :
+def natTransCofanInj {Δ : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) :
     evalN C A.1.unop.len ⟶ forget C ⋙ (evaluation SimplexCategoryᵒᵖ C).obj Δ where
-  app S := S.s.ιSummand A
-  naturality _ _ Φ := (ιSummand_naturality_symm Φ A).symm
-#align simplicial_object.split.nat_trans_ι_summand SimplicialObject.Split.natTransιSummand
+  app S := (S.s.cofan Δ).inj A
+  naturality _ _ Φ := (cofan_inj_naturality_symm Φ A).symm
+#align simplicial_object.split.nat_trans_ι_summand SimplicialObject.Split.natTransCofanInj
 
 end Split

dd1f8496

chore: remove unused simps (#6632)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

916c75c1

Diff

@@ -97,7 +97,6 @@ instance : Fintype (IndexSet Δ) :=
       simp only [unop_op, Sigma.mk.inj_iff, Fin.mk.injEq] at h₁
       have h₂ : Δ₁ = Δ₂ := by
         ext1
-        simp at h₁
         simpa only [Fin.mk_eq_mk] using h₁.1
       subst h₂
       refine' ext _ _ rfl _

dd1f8496

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -42,7 +42,7 @@ open Simplicial
 
 universe u
 
-variable {C : Type _} [Category C]
+variable {C : Type*} [Category C]
 
 namespace SimplicialObject

dd1f8496

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.split_simplicial_object
-! leanprover-community/mathlib commit dd1f8496baa505636a82748e6b652165ea888733
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.SimplicialObject
 import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
 
+#align_import algebraic_topology.split_simplicial_object from "leanprover-community/mathlib"@"dd1f8496baa505636a82748e6b652165ea888733"
+
 /-!
 
 # Split simplicial objects

dd1f8496

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -257,12 +257,22 @@ variable {X Y : SimplicialObject C} (s : Splitting X)
 attribute [instance] Splitting.map_isIso
 #align simplicial_object.splitting.map_is_iso SimplicialObject.Splitting.map_isIso
 
+-- Porting note:
+-- This used to be `@[simps]`, but now `Splitting.map` is unfolded in the generated lemmas. Why?
+-- Instead we write these lemmas by hand.
 /-- The isomorphism on simplices given by the axiom `Splitting.map_isIso` -/
-@[simps!]
 def iso (Δ : SimplexCategoryᵒᵖ) : coprod s.N Δ ≅ X.obj Δ :=
   asIso (Splitting.map X s.ι Δ)
 #align simplicial_object.splitting.iso SimplicialObject.Splitting.iso
 
+@[simp]
+theorem iso_hom (Δ : SimplexCategoryᵒᵖ) : (iso s Δ).hom = Splitting.map X s.ι Δ :=
+  rfl
+
+@[simp]
+theorem iso_inv (Δ : SimplexCategoryᵒᵖ) : (iso s Δ).inv = inv (Splitting.map X s.ι Δ) :=
+  rfl
+
 /-- Via the isomorphism `s.iso Δ`, this is the inclusion of a summand
 in the direct sum decomposition given by the splitting `s : Splitting X`. -/
 def ιSummand {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) : s.N A.1.unop.len ⟶ X.obj Δ :=

dd1f8496

feat: more consistent use of ext, and updating porting notes. (#5242)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

dbae2f17

Diff

@@ -215,9 +215,7 @@ def summand (A : IndexSet Δ) : C :=
 variable [HasFiniteCoproducts C]
 
 /-- The coproduct of the family `summand N Δ` -/
-@[simp]
-def coprod :=
-  ∐ summand N Δ
+abbrev coprod := ∐ summand N Δ
 #align simplicial_object.splitting.coprod SimplicialObject.Splitting.coprod
 
 variable {Δ}
@@ -301,8 +299,7 @@ theorem ιSummand_comp_app (f : X ⟶ Y) {Δ : SimplexCategoryᵒᵖ} (A : Index
 theorem hom_ext' {Z : C} {Δ : SimplexCategoryᵒᵖ} (f g : X.obj Δ ⟶ Z)
     (h : ∀ A : IndexSet Δ, s.ιSummand A ≫ f = s.ιSummand A ≫ g) : f = g := by
   rw [← cancel_epi (s.iso Δ).hom]
-  apply colimit.hom_ext
-  rintro ⟨A⟩
+  ext A
   simpa only [ιSummand_eq, iso_hom, map, colimit.ι_desc_assoc, Cofan.mk_ι_app] using h A
 #align simplicial_object.splitting.hom_ext' SimplicialObject.Splitting.hom_ext'
 
@@ -338,7 +335,7 @@ def ofIso (e : X ≅ Y) : Splitting Y where
   ι n := s.ι n ≫ e.hom.app (op [n])
   map_isIso Δ := by
     convert (inferInstance : IsIso ((s.iso Δ).hom ≫ e.hom.app Δ))
-    apply colimit.hom_ext
+    ext
     simp [map]
 #align simplicial_object.splitting.of_iso SimplicialObject.Splitting.ofIso

dd1f8496

chore: fix many typos (#4983)

These are all doc fixes

54b72114

Diff

@@ -187,8 +187,8 @@ def epiComp {Δ₁ Δ₂ : SimplexCategoryᵒᵖ} (A : IndexSet Δ₁) (p : Δ
 
 variable {Δ' : SimplexCategoryᵒᵖ} (θ : Δ ⟶ Δ')
 
-/-- When `A : index_set Δ` and `θ : Δ → Δ'` is a morphism in `simplex_categoryᵒᵖ`,
-an element in `index_set Δ'` can be defined by using the epi-mono factorisation
+/-- When `A : IndexSet Δ` and `θ : Δ → Δ'` is a morphism in `SimplexCategoryᵒᵖ`,
+an element in `IndexSet Δ'` can be defined by using the epi-mono factorisation
 of `θ.unop ≫ A.e`. -/
 def pull : IndexSet Δ' :=
   mk (factorThruImage (θ.unop ≫ A.e))
@@ -244,7 +244,7 @@ variable [HasFiniteCoproducts C]
 --porting note: removed @[nolint has_nonempty_instance]
 /-- A splitting of a simplicial object `X` consists of the datum of a sequence
 of objects `N`, a sequence of morphisms `ι : N n ⟶ X _[n]` such that
-for all `Δ : SimplexCategoryhᵒᵖ`, the canonical map `Splitting.map X ι Δ`
+for all `Δ : SimplexCategoryᵒᵖ`, the canonical map `Splitting.map X ι Δ`
 is an isomorphism. -/
 structure Splitting (X : SimplicialObject C) where
   N : ℕ → C

dd1f8496

feat: port AlgebraicTopology.DoldKan.GammaCompN (#3568)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

0b676a27

Diff

@@ -111,6 +111,7 @@ variable (Δ)
 
 /-- The distinguished element in `Splitting.IndexSet Δ` which corresponds to the
 identity of `Δ`. -/
+@[simps]
 def id : IndexSet Δ :=
   ⟨Δ, ⟨𝟙 _, by infer_instance⟩⟩
 #align simplicial_object.splitting.index_set.id SimplicialObject.Splitting.IndexSet.id

dd1f8496

feat: port AlgebraicTopology.DoldKan.FunctorGamma (#3566)

b53dd023

Diff

@@ -419,6 +419,11 @@ variable {C}
 
 namespace Split
 
+-- porting note: added as `Hom.ext` is not triggered automatically
+@[ext]
+theorem hom_ext {S₁ S₂ : Split C} (Φ₁ Φ₂ : S₁ ⟶ S₂) (h : ∀ n : ℕ, Φ₁.f n = Φ₂.f n) : Φ₁ = Φ₂ :=
+  Hom.ext _ _ h
+
 theorem congr_F {S₁ S₂ : Split C} {Φ₁ Φ₂ : S₁ ⟶ S₂} (h : Φ₁ = Φ₂) : Φ₁.f = Φ₂.f := by rw [h]
 set_option linter.uppercaseLean3 false in
 #align simplicial_object.split.congr_F SimplicialObject.Split.congr_F

dd1f8496

feat: port AlgebraicTopology.SplitSimplicialObject (#3432)

6a4ba7f1

`algebraic_topology.split_simplicial_object` ⟷ `Mathlib.AlgebraicTopology.SplitSimplicialObject`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 6 + 307

algebraic_topology.split_simplicial_object ⟷ Mathlib.AlgebraicTopology.SplitSimplicialObject

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 6 + 307

`algebraic_topology.split_simplicial_object` ⟷ `Mathlib.AlgebraicTopology.SplitSimplicialObject`