algebraic_topology.dold_kan.split_simplicial_object

(last sync)

feat(algebraic_topology/dold_kan): The Dold-Kan equivalence for abelian categories (#17926)

Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

Diff

@@ -18,6 +18,9 @@ import algebraic_topology.dold_kan.functor_n
 In this file we define a functor `nondeg_complex : simplicial_object.split C ⥤ chain_complex C ℕ`
 when `C` is a preadditive category with finite coproducts, and get an isomorphism
 `to_karoubi_nondeg_complex_iso_N₁ : nondeg_complex ⋙ to_karoubi _ ≅ forget C ⋙ dold_kan.N₁`.
+
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 noncomputable theory

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -119,7 +119,7 @@ theorem cofan_inj_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialOb
     {n : ℕ} (A : SimplicialObject.Splitting.IndexSet (op [n])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ PInfty.f n = 0 :=
   by
-  rw [SimplicialObject.Splitting.IndexSet.eqId_iff_mono] at hA 
+  rw [SimplicialObject.Splitting.IndexSet.eqId_iff_mono] at hA
   rw [SimplicialObject.Splitting.cofan_inj_eq, assoc, degeneracy_comp_P_infty X n A.e hA, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero
 -/
@@ -131,12 +131,12 @@ theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
   constructor
   · intro h
     cases n
-    · dsimp at h 
-      rw [comp_id] at h 
+    · dsimp at h
+      rw [comp_id] at h
       rw [h, zero_comp]
     · have h' := f ≫= P_infty_f_add_Q_infty_f (n + 1)
-      dsimp at h' 
-      rw [comp_id, comp_add, h, zero_add] at h' 
+      dsimp at h'
+      rw [comp_id, comp_add, h, zero_add] at h'
       rw [← h', assoc, Q_infty_f, decomposition_Q, preadditive.sum_comp, preadditive.comp_sum,
         Finset.sum_eq_zero]
       intro i hi
@@ -146,7 +146,7 @@ theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
       Fintype.sum_eq_zero]
     intro A
     by_cases hA : A.eq_id
-    · dsimp at hA 
+    · dsimp at hA
       subst hA
       rw [assoc, reassoc_of h, zero_comp]
     · simp only [assoc, s.ι_summand_comp_P_infty_eq_zero A hA, comp_zero]
@@ -192,7 +192,7 @@ def d (i j : ℕ) : s.n i ⟶ s.n j :=
 theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ K[X].d j k ≫ s.πSummand (IndexSet.id (op [k])) = 0 :=
   by
-  rw [A.eq_id_iff_mono] at hA 
+  rw [A.eq_id_iff_mono] at hA
   rw [← assoc, ← s.comp_P_infty_eq_zero_iff, assoc, ← P_infty.comm j k, s.ι_summand_eq, assoc,
     degeneracy_comp_P_infty_assoc X j A.e hA, zero_comp, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero
@@ -212,13 +212,13 @@ def nondegComplex : ChainComplex C ℕ where
     have eq :
       K[X].d i j ≫ 𝟙 (X.obj (op [j])) ≫ K[X].d j k ≫ s.π_summand (index_set.id (op [k])) = 0 := by
       erw [id_comp, HomologicalComplex.d_comp_d_assoc, zero_comp]
-    rw [s.decomposition_id] at eq 
+    rw [s.decomposition_id] at eq
     classical
     rw [Fintype.sum_eq_add_sum_compl (index_set.id (op [j])), add_comp, comp_add, assoc,
-      preadditive.sum_comp, preadditive.comp_sum, Finset.sum_eq_zero, add_zero] at eq 
+      preadditive.sum_comp, preadditive.comp_sum, Finset.sum_eq_zero, add_zero] at eq
     swap
     · intro A hA
-      simp only [Finset.mem_compl, Finset.mem_singleton] at hA 
+      simp only [Finset.mem_compl, Finset.mem_singleton] at hA
       simp only [assoc, ι_summand_comp_d_comp_π_summand_eq_zero _ _ _ _ hA, comp_zero]
     rw [Eq, comp_zero]
 #align simplicial_object.splitting.nondeg_complex SimplicialObject.Splitting.nondegComplex
@@ -288,7 +288,7 @@ def nondegComplexFunctor : Split C ⥤ ChainComplex C ℕ
         dsimp [alternating_face_map_complex]
         erw [ι_summand_naturality_symm_assoc Φ A]
         by_cases A.eq_id
-        · dsimp at h 
+        · dsimp at h
           subst h
           simpa only [splitting.ι_π_summand_eq_id, comp_id, splitting.ι_π_summand_eq_id_assoc]
         · have h' : splitting.index_set.id (op [j]) ≠ A := by symm; exact h

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -214,6 +214,13 @@ def nondegComplex : ChainComplex C ℕ where
       erw [id_comp, HomologicalComplex.d_comp_d_assoc, zero_comp]
     rw [s.decomposition_id] at eq 
     classical
+    rw [Fintype.sum_eq_add_sum_compl (index_set.id (op [j])), add_comp, comp_add, assoc,
+      preadditive.sum_comp, preadditive.comp_sum, Finset.sum_eq_zero, add_zero] at eq 
+    swap
+    · intro A hA
+      simp only [Finset.mem_compl, Finset.mem_singleton] at hA 
+      simp only [assoc, ι_summand_comp_d_comp_π_summand_eq_zero _ _ _ _ hA, comp_zero]
+    rw [Eq, comp_zero]
 #align simplicial_object.splitting.nondeg_complex SimplicialObject.Splitting.nondegComplex
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -214,13 +214,6 @@ def nondegComplex : ChainComplex C ℕ where
       erw [id_comp, HomologicalComplex.d_comp_d_assoc, zero_comp]
     rw [s.decomposition_id] at eq 
     classical
-    rw [Fintype.sum_eq_add_sum_compl (index_set.id (op [j])), add_comp, comp_add, assoc,
-      preadditive.sum_comp, preadditive.comp_sum, Finset.sum_eq_zero, add_zero] at eq 
-    swap
-    · intro A hA
-      simp only [Finset.mem_compl, Finset.mem_singleton] at hA 
-      simp only [assoc, ι_summand_comp_d_comp_π_summand_eq_zero _ _ _ _ hA, comp_zero]
-    rw [Eq, comp_zero]
 #align simplicial_object.splitting.nondeg_complex SimplicialObject.Splitting.nondegComplex
 -/

bump to nightly-2023-12-28-06

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

c30f5587

Diff

@@ -52,9 +52,9 @@ def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ
 #align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummand
 -/
 
-#print SimplicialObject.Splitting.ι_πSummand_eq_id /-
+#print SimplicialObject.Splitting.cofan_inj_πSummand_eq_id /-
 @[simp, reassoc]
-theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
+theorem cofan_inj_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ s.πSummand A = 𝟙 _ :=
   by
   dsimp [ι_summand, π_summand]
@@ -62,12 +62,12 @@ theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A
   erw [colimit.ι_desc, cofan.mk_ι_app]
   dsimp
   simp only [eq_self_iff_true, if_true]
-#align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_id
+#align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.cofan_inj_πSummand_eq_id
 -/
 
-#print SimplicialObject.Splitting.ι_πSummand_eq_zero /-
+#print SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero /-
 @[simp, reassoc]
-theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
+theorem cofan_inj_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
     (h : B ≠ A) : s.ιSummand A ≫ s.πSummand B = 0 :=
   by
   dsimp [ι_summand, π_summand]
@@ -75,7 +75,7 @@ theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (
   erw [colimit.ι_desc, cofan.mk_ι_app]
   apply dif_neg
   exact h.symm
-#align simplicial_object.splitting.ι_π_summand_eq_zero SimplicialObject.Splitting.ι_πSummand_eq_zero
+#align simplicial_object.splitting.ι_π_summand_eq_zero SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero
 -/
 
 variable [Preadditive C]
@@ -111,17 +111,17 @@ theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
 #align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero
 -/
 
-#print SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero /-
+#print SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero /-
 /-- If a simplicial object `X` in an additive category is split,
 then `P_infty` vanishes on all the summands of `X _[n]` which do
 not correspond to the identity of `[n]`. -/
-theorem ιSummand_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialObject.Splitting X)
+theorem cofan_inj_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialObject.Splitting X)
     {n : ℕ} (A : SimplicialObject.Splitting.IndexSet (op [n])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ PInfty.f n = 0 :=
   by
   rw [SimplicialObject.Splitting.IndexSet.eqId_iff_mono] at hA 
-  rw [SimplicialObject.Splitting.ιSummand_eq, assoc, degeneracy_comp_P_infty X n A.e hA, comp_zero]
-#align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero
+  rw [SimplicialObject.Splitting.cofan_inj_eq, assoc, degeneracy_comp_P_infty X n A.e hA, comp_zero]
+#align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero
 -/
 
 #print SimplicialObject.Splitting.comp_PInfty_eq_zero_iff /-
@@ -165,9 +165,9 @@ theorem PInfty_comp_πSummand_id (n : ℕ) :
 #align simplicial_object.splitting.P_infty_comp_π_summand_id SimplicialObject.Splitting.PInfty_comp_πSummand_id
 -/
 
-#print SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty /-
+#print SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty /-
 @[simp, reassoc]
-theorem πSummand_comp_ιSummand_comp_PInfty_eq_PInfty (n : ℕ) :
+theorem πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty (n : ℕ) :
     s.πSummand (IndexSet.id (op [n])) ≫ s.ιSummand (IndexSet.id (op [n])) ≫ PInfty.f n =
       PInfty.f n :=
   by
@@ -176,7 +176,7 @@ theorem πSummand_comp_ιSummand_comp_PInfty_eq_PInfty (n : ℕ) :
   rw [Fintype.sum_eq_single (index_set.id (op [n])), assoc]
   rintro A (hA : ¬A.eq_id)
   rw [assoc, s.ι_summand_comp_P_infty_eq_zero A hA, comp_zero]
-#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty
+#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty
 -/
 
 #print SimplicialObject.Splitting.d /-

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ 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.SplitSimplicialObject
-import Mathbin.AlgebraicTopology.DoldKan.Degeneracies
-import Mathbin.AlgebraicTopology.DoldKan.FunctorN
+import AlgebraicTopology.SplitSimplicialObject
+import AlgebraicTopology.DoldKan.Degeneracies
+import AlgebraicTopology.DoldKan.FunctorN
 
 #align_import algebraic_topology.dold_kan.split_simplicial_object from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"

bump to nightly-2023-08-06-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

b0e28731

Diff

@@ -7,7 +7,7 @@ import Mathbin.AlgebraicTopology.SplitSimplicialObject
 import Mathbin.AlgebraicTopology.DoldKan.Degeneracies
 import Mathbin.AlgebraicTopology.DoldKan.FunctorN
 
-#align_import algebraic_topology.dold_kan.split_simplicial_object from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+#align_import algebraic_topology.dold_kan.split_simplicial_object from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 
@@ -19,6 +19,9 @@ import Mathbin.AlgebraicTopology.DoldKan.FunctorN
 In this file we define a functor `nondeg_complex : simplicial_object.split C ⥤ chain_complex C ℕ`
 when `C` is a preadditive category with finite coproducts, and get an isomorphism
 `to_karoubi_nondeg_complex_iso_N₁ : nondeg_complex ⋙ to_karoubi _ ≅ forget C ⋙ dold_kan.N₁`.
+
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 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.dold_kan.split_simplicial_object
-! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.SplitSimplicialObject
 import Mathbin.AlgebraicTopology.DoldKan.Degeneracies
 import Mathbin.AlgebraicTopology.DoldKan.FunctorN
 
+#align_import algebraic_topology.dold_kan.split_simplicial_object from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+
 /-!
 
 # Split simplicial objects in preadditive categories

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -39,6 +39,7 @@ namespace Splitting
 variable {C : Type _} [Category C] [HasFiniteCoproducts C] {X : SimplicialObject C}
   (s : Splitting X)
 
+#print SimplicialObject.Splitting.πSummand /-
 /-- The projection on a summand of the coproduct decomposition given
 by a splitting of a simplicial object. -/
 def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
@@ -49,7 +50,9 @@ def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ
   · exact eq_to_hom (by subst h; rfl)
   · exact 0
 #align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummand
+-/
 
+#print SimplicialObject.Splitting.ι_πSummand_eq_id /-
 @[simp, reassoc]
 theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ s.πSummand A = 𝟙 _ :=
@@ -60,7 +63,9 @@ theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A
   dsimp
   simp only [eq_self_iff_true, if_true]
 #align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_id
+-/
 
+#print SimplicialObject.Splitting.ι_πSummand_eq_zero /-
 @[simp, reassoc]
 theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
     (h : B ≠ A) : s.ιSummand A ≫ s.πSummand B = 0 :=
@@ -71,9 +76,11 @@ theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (
   apply dif_neg
   exact h.symm
 #align simplicial_object.splitting.ι_π_summand_eq_zero SimplicialObject.Splitting.ι_πSummand_eq_zero
+-/
 
 variable [Preadditive C]
 
+#print SimplicialObject.Splitting.decomposition_id /-
 theorem decomposition_id (Δ : SimplexCategoryᵒᵖ) :
     𝟙 (X.obj Δ) = ∑ A : IndexSet Δ, s.πSummand A ≫ s.ιSummand A :=
   by
@@ -84,7 +91,9 @@ theorem decomposition_id (Δ : SimplexCategoryᵒᵖ) :
     rw [s.ι_π_summand_eq_zero_assoc _ _ h₂, zero_comp]
   · simp only [Finset.mem_univ, not_true, IsEmpty.forall_iff]
 #align simplicial_object.splitting.decomposition_id SimplicialObject.Splitting.decomposition_id
+-/
 
+#print SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero /-
 @[simp, reassoc]
 theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ s.πSummand (IndexSet.id (op [n + 1])) = 0 :=
@@ -100,7 +109,9 @@ theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
   dsimp at h ⊢
   linarith
 #align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero
+-/
 
+#print SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero /-
 /-- If a simplicial object `X` in an additive category is split,
 then `P_infty` vanishes on all the summands of `X _[n]` which do
 not correspond to the identity of `[n]`. -/
@@ -111,7 +122,9 @@ theorem ιSummand_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialOb
   rw [SimplicialObject.Splitting.IndexSet.eqId_iff_mono] at hA 
   rw [SimplicialObject.Splitting.ιSummand_eq, assoc, degeneracy_comp_P_infty X n A.e hA, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero
+-/
 
+#print SimplicialObject.Splitting.comp_PInfty_eq_zero_iff /-
 theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
     f ≫ PInfty.f n = 0 ↔ f ≫ s.πSummand (IndexSet.id (op [n])) = 0 :=
   by
@@ -138,6 +151,7 @@ theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
       rw [assoc, reassoc_of h, zero_comp]
     · simp only [assoc, s.ι_summand_comp_P_infty_eq_zero A hA, comp_zero]
 #align simplicial_object.splitting.comp_P_infty_eq_zero_iff SimplicialObject.Splitting.comp_PInfty_eq_zero_iff
+-/
 
 #print SimplicialObject.Splitting.PInfty_comp_πSummand_id /-
 @[simp, reassoc]
@@ -151,6 +165,7 @@ theorem PInfty_comp_πSummand_id (n : ℕ) :
 #align simplicial_object.splitting.P_infty_comp_π_summand_id SimplicialObject.Splitting.PInfty_comp_πSummand_id
 -/
 
+#print SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty /-
 @[simp, reassoc]
 theorem πSummand_comp_ιSummand_comp_PInfty_eq_PInfty (n : ℕ) :
     s.πSummand (IndexSet.id (op [n])) ≫ s.ιSummand (IndexSet.id (op [n])) ≫ PInfty.f n =
@@ -162,6 +177,7 @@ theorem πSummand_comp_ιSummand_comp_PInfty_eq_PInfty (n : ℕ) :
   rintro A (hA : ¬A.eq_id)
   rw [assoc, s.ι_summand_comp_P_infty_eq_zero A hA, comp_zero]
 #align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty
+-/
 
 #print SimplicialObject.Splitting.d /-
 /-- The differentials `s.d i j : s.N i ⟶ s.N j` on nondegenerate simplices of a split
@@ -172,6 +188,7 @@ def d (i j : ℕ) : s.n i ⟶ s.n j :=
 #align simplicial_object.splitting.d SimplicialObject.Splitting.d
 -/
 
+#print SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero /-
 theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ K[X].d j k ≫ s.πSummand (IndexSet.id (op [k])) = 0 :=
   by
@@ -179,6 +196,7 @@ theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j
   rw [← assoc, ← s.comp_P_infty_eq_zero_iff, assoc, ← P_infty.comm j k, s.ι_summand_eq, assoc,
     degeneracy_comp_P_infty_assoc X j A.e hA, zero_comp, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero
+-/
 
 #print SimplicialObject.Splitting.nondegComplex /-
 /-- If `s` is a splitting of a simplicial object `X` in a preadditive category,
@@ -206,6 +224,7 @@ def nondegComplex : ChainComplex C ℕ where
 #align simplicial_object.splitting.nondeg_complex SimplicialObject.Splitting.nondegComplex
 -/
 
+#print SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ /-
 /-- The chain complex `s.nondeg_complex` attached to a splitting of a simplicial object `X`
 becomes isomorphic to the normalized Moore complex `N₁.obj X` defined as a formal direct
 factor in the category `karoubi (chain_complex C ℕ)`. -/
@@ -241,6 +260,7 @@ def toKaroubiNondegComplexIsoN₁ : (toKaroubi _).obj s.nondegComplex ≅ N₁.o
     simp only [π_summand_comp_ι_summand_comp_P_infty_eq_P_infty, karoubi.comp_f,
       HomologicalComplex.comp_f, N₁_obj_p, karoubi.id_eq]
 #align simplicial_object.splitting.to_karoubi_nondeg_complex_iso_N₁ SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁
+-/
 
 end Splitting
 
@@ -248,6 +268,7 @@ namespace Split
 
 variable {C : Type _} [Category C] [Preadditive C] [HasFiniteCoproducts C]
 
+#print SimplicialObject.Split.nondegComplexFunctor /-
 /-- The functor which sends a split simplicial object in a preadditive category to
 the chain complex which consists of nondegenerate simplices. -/
 @[simps]
@@ -274,7 +295,9 @@ def nondegComplexFunctor : Split C ⥤ ChainComplex C ℕ
           rw [S₁.s.ι_π_summand_eq_zero_assoc _ _ h', S₂.s.ι_π_summand_eq_zero _ _ h', zero_comp,
             comp_zero] }
 #align simplicial_object.split.nondeg_complex_functor SimplicialObject.Split.nondegComplexFunctor
+-/
 
+#print SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁ /-
 /-- The natural isomorphism (in `karoubi (chain_complex C ℕ)`) between the chain complex
 of nondegenerate simplices of a split simplicial object and the normalized Moore complex
 defined as a formal direct factor of the alternating face map complex. -/
@@ -291,6 +314,7 @@ def toKaroubiNondegComplexFunctorIsoN₁ :
     erw [← split.ι_summand_naturality_symm_assoc Φ (splitting.index_set.id (op [n]))]
     rw [P_infty_f_naturality]
 #align simplicial_object.split.to_karoubi_nondeg_complex_functor_iso_N₁ SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁
+-/
 
 end Split

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -196,13 +196,13 @@ def nondegComplex : ChainComplex C ℕ where
       erw [id_comp, HomologicalComplex.d_comp_d_assoc, zero_comp]
     rw [s.decomposition_id] at eq 
     classical
-      rw [Fintype.sum_eq_add_sum_compl (index_set.id (op [j])), add_comp, comp_add, assoc,
-        preadditive.sum_comp, preadditive.comp_sum, Finset.sum_eq_zero, add_zero] at eq 
-      swap
-      · intro A hA
-        simp only [Finset.mem_compl, Finset.mem_singleton] at hA 
-        simp only [assoc, ι_summand_comp_d_comp_π_summand_eq_zero _ _ _ _ hA, comp_zero]
-      rw [Eq, comp_zero]
+    rw [Fintype.sum_eq_add_sum_compl (index_set.id (op [j])), add_comp, comp_add, assoc,
+      preadditive.sum_comp, preadditive.comp_sum, Finset.sum_eq_zero, add_zero] at eq 
+    swap
+    · intro A hA
+      simp only [Finset.mem_compl, Finset.mem_singleton] at hA 
+      simp only [assoc, ι_summand_comp_d_comp_π_summand_eq_zero _ _ _ _ hA, comp_zero]
+    rw [Eq, comp_zero]
 #align simplicial_object.splitting.nondeg_complex SimplicialObject.Splitting.nondegComplex
 -/

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -27,8 +27,8 @@ when `C` is a preadditive category with finite coproducts, and get an isomorphis
 
 noncomputable section
 
-open
-  CategoryTheory CategoryTheory.Limits CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Idempotents Opposite AlgebraicTopology AlgebraicTopology.DoldKan
+open CategoryTheory CategoryTheory.Limits CategoryTheory.Category CategoryTheory.Preadditive
+  CategoryTheory.Idempotents Opposite AlgebraicTopology AlgebraicTopology.DoldKan
 
 open scoped BigOperators Simplicial DoldKan
 
@@ -97,7 +97,7 @@ theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
   change ¬(A.epi_comp (SimplexCategory.σ i).op).EqId
   rw [index_set.eq_id_iff_len_eq]
   have h := SimplexCategory.len_le_of_epi (inferInstance : epi A.e)
-  dsimp at h⊢
+  dsimp at h ⊢
   linarith
 #align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero
 
@@ -108,7 +108,7 @@ theorem ιSummand_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialOb
     {n : ℕ} (A : SimplicialObject.Splitting.IndexSet (op [n])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ PInfty.f n = 0 :=
   by
-  rw [SimplicialObject.Splitting.IndexSet.eqId_iff_mono] at hA
+  rw [SimplicialObject.Splitting.IndexSet.eqId_iff_mono] at hA 
   rw [SimplicialObject.Splitting.ιSummand_eq, assoc, degeneracy_comp_P_infty X n A.e hA, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero
 
@@ -118,12 +118,12 @@ theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
   constructor
   · intro h
     cases n
-    · dsimp at h
-      rw [comp_id] at h
+    · dsimp at h 
+      rw [comp_id] at h 
       rw [h, zero_comp]
     · have h' := f ≫= P_infty_f_add_Q_infty_f (n + 1)
-      dsimp at h'
-      rw [comp_id, comp_add, h, zero_add] at h'
+      dsimp at h' 
+      rw [comp_id, comp_add, h, zero_add] at h' 
       rw [← h', assoc, Q_infty_f, decomposition_Q, preadditive.sum_comp, preadditive.comp_sum,
         Finset.sum_eq_zero]
       intro i hi
@@ -133,7 +133,7 @@ theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
       Fintype.sum_eq_zero]
     intro A
     by_cases hA : A.eq_id
-    · dsimp at hA
+    · dsimp at hA 
       subst hA
       rw [assoc, reassoc_of h, zero_comp]
     · simp only [assoc, s.ι_summand_comp_P_infty_eq_zero A hA, comp_zero]
@@ -175,7 +175,7 @@ def d (i j : ℕ) : s.n i ⟶ s.n j :=
 theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ K[X].d j k ≫ s.πSummand (IndexSet.id (op [k])) = 0 :=
   by
-  rw [A.eq_id_iff_mono] at hA
+  rw [A.eq_id_iff_mono] at hA 
   rw [← assoc, ← s.comp_P_infty_eq_zero_iff, assoc, ← P_infty.comm j k, s.ι_summand_eq, assoc,
     degeneracy_comp_P_infty_assoc X j A.e hA, zero_comp, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero
@@ -194,13 +194,13 @@ def nondegComplex : ChainComplex C ℕ where
     have eq :
       K[X].d i j ≫ 𝟙 (X.obj (op [j])) ≫ K[X].d j k ≫ s.π_summand (index_set.id (op [k])) = 0 := by
       erw [id_comp, HomologicalComplex.d_comp_d_assoc, zero_comp]
-    rw [s.decomposition_id] at eq
+    rw [s.decomposition_id] at eq 
     classical
       rw [Fintype.sum_eq_add_sum_compl (index_set.id (op [j])), add_comp, comp_add, assoc,
-        preadditive.sum_comp, preadditive.comp_sum, Finset.sum_eq_zero, add_zero] at eq
+        preadditive.sum_comp, preadditive.comp_sum, Finset.sum_eq_zero, add_zero] at eq 
       swap
       · intro A hA
-        simp only [Finset.mem_compl, Finset.mem_singleton] at hA
+        simp only [Finset.mem_compl, Finset.mem_singleton] at hA 
         simp only [assoc, ι_summand_comp_d_comp_π_summand_eq_zero _ _ _ _ hA, comp_zero]
       rw [Eq, comp_zero]
 #align simplicial_object.splitting.nondeg_complex SimplicialObject.Splitting.nondegComplex
@@ -267,7 +267,7 @@ def nondegComplexFunctor : Split C ⥤ ChainComplex C ℕ
         dsimp [alternating_face_map_complex]
         erw [ι_summand_naturality_symm_assoc Φ A]
         by_cases A.eq_id
-        · dsimp at h
+        · dsimp at h 
           subst h
           simpa only [splitting.ι_π_summand_eq_id, comp_id, splitting.ι_π_summand_eq_id_assoc]
         · have h' : splitting.index_set.id (op [j]) ≠ A := by symm; exact h

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -30,7 +30,7 @@ noncomputable section
 open
   CategoryTheory CategoryTheory.Limits CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Idempotents Opposite AlgebraicTopology AlgebraicTopology.DoldKan
 
-open BigOperators Simplicial DoldKan
+open scoped BigOperators Simplicial DoldKan
 
 namespace SimplicialObject

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -39,12 +39,6 @@ namespace Splitting
 variable {C : Type _} [Category C] [HasFiniteCoproducts C] {X : SimplicialObject C}
   (s : Splitting X)
 
-/- warning: simplicial_object.splitting.π_summand -> SimplicialObject.Splitting.πSummand 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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {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)) (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.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))))
-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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {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)) (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.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))))
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummandₓ'. -/
 /-- The projection on a summand of the coproduct decomposition given
 by a splitting of a simplicial object. -/
 def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
@@ -56,9 +50,6 @@ def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ
   · exact 0
 #align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummand
 
-/- warning: simplicial_object.splitting.ι_π_summand_eq_id -> SimplicialObject.Splitting.ι_πSummand_eq_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_idₓ'. -/
 @[simp, reassoc]
 theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ s.πSummand A = 𝟙 _ :=
@@ -70,9 +61,6 @@ theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A
   simp only [eq_self_iff_true, if_true]
 #align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_id
 
-/- warning: simplicial_object.splitting.ι_π_summand_eq_zero -> SimplicialObject.Splitting.ι_πSummand_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_π_summand_eq_zero SimplicialObject.Splitting.ι_πSummand_eq_zeroₓ'. -/
 @[simp, reassoc]
 theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
     (h : B ≠ A) : s.ιSummand A ≫ s.πSummand B = 0 :=
@@ -86,9 +74,6 @@ theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (
 
 variable [Preadditive C]
 
-/- warning: simplicial_object.splitting.decomposition_id -> SimplicialObject.Splitting.decomposition_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.decomposition_id SimplicialObject.Splitting.decomposition_idₓ'. -/
 theorem decomposition_id (Δ : SimplexCategoryᵒᵖ) :
     𝟙 (X.obj Δ) = ∑ A : IndexSet Δ, s.πSummand A ≫ s.ιSummand A :=
   by
@@ -100,9 +85,6 @@ theorem decomposition_id (Δ : SimplexCategoryᵒᵖ) :
   · simp only [Finset.mem_univ, not_true, IsEmpty.forall_iff]
 #align simplicial_object.splitting.decomposition_id SimplicialObject.Splitting.decomposition_id
 
-/- warning: simplicial_object.splitting.σ_comp_π_summand_id_eq_zero -> SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zeroₓ'. -/
 @[simp, reassoc]
 theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ s.πSummand (IndexSet.id (op [n + 1])) = 0 :=
@@ -119,9 +101,6 @@ theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
   linarith
 #align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero
 
-/- warning: simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero -> SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zeroₓ'. -/
 /-- If a simplicial object `X` in an additive category is split,
 then `P_infty` vanishes on all the summands of `X _[n]` which do
 not correspond to the identity of `[n]`. -/
@@ -133,9 +112,6 @@ theorem ιSummand_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialOb
   rw [SimplicialObject.Splitting.ιSummand_eq, assoc, degeneracy_comp_P_infty X n A.e hA, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero
 
-/- warning: simplicial_object.splitting.comp_P_infty_eq_zero_iff -> SimplicialObject.Splitting.comp_PInfty_eq_zero_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.comp_P_infty_eq_zero_iff SimplicialObject.Splitting.comp_PInfty_eq_zero_iffₓ'. -/
 theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
     f ≫ PInfty.f n = 0 ↔ f ≫ s.πSummand (IndexSet.id (op [n])) = 0 :=
   by
@@ -175,9 +151,6 @@ theorem PInfty_comp_πSummand_id (n : ℕ) :
 #align simplicial_object.splitting.P_infty_comp_π_summand_id SimplicialObject.Splitting.PInfty_comp_πSummand_id
 -/
 
-/- warning: simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty -> SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInftyₓ'. -/
 @[simp, reassoc]
 theorem πSummand_comp_ιSummand_comp_PInfty_eq_PInfty (n : ℕ) :
     s.πSummand (IndexSet.id (op [n])) ≫ s.ιSummand (IndexSet.id (op [n])) ≫ PInfty.f n =
@@ -199,9 +172,6 @@ def d (i j : ℕ) : s.n i ⟶ s.n j :=
 #align simplicial_object.splitting.d SimplicialObject.Splitting.d
 -/
 
-/- warning: simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero -> SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zeroₓ'. -/
 theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ K[X].d j k ≫ s.πSummand (IndexSet.id (op [k])) = 0 :=
   by
@@ -236,9 +206,6 @@ def nondegComplex : ChainComplex C ℕ where
 #align simplicial_object.splitting.nondeg_complex SimplicialObject.Splitting.nondegComplex
 -/
 
-/- warning: simplicial_object.splitting.to_karoubi_nondeg_complex_iso_N₁ -> SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.to_karoubi_nondeg_complex_iso_N₁ SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ₓ'. -/
 /-- The chain complex `s.nondeg_complex` attached to a splitting of a simplicial object `X`
 becomes isomorphic to the normalized Moore complex `N₁.obj X` defined as a formal direct
 factor in the category `karoubi (chain_complex C ℕ)`. -/
@@ -281,12 +248,6 @@ namespace Split
 
 variable {C : Type _} [Category C] [Preadditive C] [HasFiniteCoproducts C]
 
-/- warning: simplicial_object.split.nondeg_complex_functor -> SimplicialObject.Split.nondegComplexFunctor is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align simplicial_object.split.nondeg_complex_functor SimplicialObject.Split.nondegComplexFunctorₓ'. -/
 /-- The functor which sends a split simplicial object in a preadditive category to
 the chain complex which consists of nondegenerate simplices. -/
 @[simps]
@@ -314,9 +275,6 @@ def nondegComplexFunctor : Split C ⥤ ChainComplex C ℕ
             comp_zero] }
 #align simplicial_object.split.nondeg_complex_functor SimplicialObject.Split.nondegComplexFunctor
 
-/- warning: simplicial_object.split.to_karoubi_nondeg_complex_functor_iso_N₁ -> SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplicial_object.split.to_karoubi_nondeg_complex_functor_iso_N₁ SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁ₓ'. -/
 /-- The natural isomorphism (in `karoubi (chain_complex C ℕ)`) between the chain complex
 of nondegenerate simplices of a split simplicial object and the normalized Moore complex
 defined as a formal direct factor of the alternating face map complex. -/

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -52,12 +52,7 @@ def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ
   by
   refine' (s.iso Δ).inv ≫ sigma.desc fun B => _
   by_cases B = A
-  ·
-    exact
-      eq_to_hom
-        (by
-          subst h
-          rfl)
+  · exact eq_to_hom (by subst h; rfl)
   · exact 0
 #align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummand
 
@@ -257,10 +252,7 @@ def toKaroubiNondegComplexIsoN₁ : (toKaroubi _).obj s.nondegComplex ≅ N₁.o
             dsimp
             rw [assoc, assoc, assoc, π_summand_comp_ι_summand_comp_P_infty_eq_P_infty,
               HomologicalComplex.Hom.comm] }
-      comm := by
-        ext n
-        dsimp
-        rw [id_comp, assoc, P_infty_f_idem] }
+      comm := by ext n; dsimp; rw [id_comp, assoc, P_infty_f_idem] }
   inv :=
     { f :=
         { f := fun n => s.πSummand (IndexSet.id (op [n]))
@@ -272,10 +264,7 @@ def toKaroubiNondegComplexIsoN₁ : (toKaroubi _).obj s.nondegComplex ≅ N₁.o
             · intro A h hA
               simp only [assoc, s.ι_summand_comp_d_comp_π_summand_eq_zero _ _ _ hA, comp_zero]
             · simp only [Finset.mem_univ, not_true, IsEmpty.forall_iff] }
-      comm := by
-        ext n
-        dsimp
-        simp only [comp_id, P_infty_comp_π_summand_id] }
+      comm := by ext n; dsimp; simp only [comp_id, P_infty_comp_π_summand_id] }
   hom_inv_id' := by
     ext n
     simpa only [assoc, P_infty_comp_π_summand_id, karoubi.comp_f, HomologicalComplex.comp_f,
@@ -320,10 +309,7 @@ def nondegComplexFunctor : Split C ⥤ ChainComplex C ℕ
         · dsimp at h
           subst h
           simpa only [splitting.ι_π_summand_eq_id, comp_id, splitting.ι_π_summand_eq_id_assoc]
-        · have h' : splitting.index_set.id (op [j]) ≠ A :=
-            by
-            symm
-            exact h
+        · have h' : splitting.index_set.id (op [j]) ≠ A := by symm; exact h
           rw [S₁.s.ι_π_summand_eq_zero_assoc _ _ h', S₂.s.ι_π_summand_eq_zero _ _ h', zero_comp,
             comp_zero] }
 #align simplicial_object.split.nondeg_complex_functor SimplicialObject.Split.nondegComplexFunctor

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -62,10 +62,7 @@ def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ
 #align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummand
 
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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)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_idₓ'. -/
 @[simp, reassoc]
 theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
@@ -79,10 +76,7 @@ theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A
 #align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_id
 
 /- warning: simplicial_object.splitting.ι_π_summand_eq_zero -> SimplicialObject.Splitting.ι_πSummand_eq_zero is a dubious translation:
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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)) B)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s _inst_3 Δ B)) (OfNat.ofNat.{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)))) (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)) B))))) 0 (OfNat.mk.{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)))) (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)) B))))) 0 (Zero.zero.{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)))) (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)) B))))) (CategoryTheory.Limits.HasZeroMorphisms.hasZero.{u2, u1} C _inst_1 _inst_3 (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)))) (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)) B)))))))))
-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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (B : SimplicialObject.Splitting.IndexSet Δ), (Ne.{1} (SimplicialObject.Splitting.IndexSet Δ) B A) -> (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)))) (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} 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(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.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)) B)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s _inst_3 Δ B)) (OfNat.ofNat.{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} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_π_summand_eq_zero SimplicialObject.Splitting.ι_πSummand_eq_zeroₓ'. -/
 @[simp, reassoc]
 theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
@@ -98,10 +92,7 @@ theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (
 variable [Preadditive C]
 
 /- warning: simplicial_object.splitting.decomposition_id -> SimplicialObject.Splitting.decomposition_id is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.decomposition_id SimplicialObject.Splitting.decomposition_idₓ'. -/
 theorem decomposition_id (Δ : SimplexCategoryᵒᵖ) :
     𝟙 (X.obj Δ) = ∑ A : IndexSet Δ, s.πSummand A ≫ s.ιSummand A :=
@@ -115,10 +106,7 @@ theorem decomposition_id (Δ : SimplexCategoryᵒᵖ) :
 #align simplicial_object.splitting.decomposition_id SimplicialObject.Splitting.decomposition_id
 
 /- warning: simplicial_object.splitting.σ_comp_π_summand_id_eq_zero -> SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zeroₓ'. -/
 @[simp, reassoc]
 theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
@@ -137,10 +125,7 @@ theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
 #align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero
 
 /- warning: simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero -> SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zeroₓ'. -/
 /-- If a simplicial object `X` in an additive category is split,
 then `P_infty` vanishes on all the summands of `X _[n]` which do
@@ -154,10 +139,7 @@ theorem ιSummand_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialOb
 #align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero
 
 /- warning: simplicial_object.splitting.comp_P_infty_eq_zero_iff -> SimplicialObject.Splitting.comp_PInfty_eq_zero_iff is a dubious translation:
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(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)))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.comp_P_infty_eq_zero_iff SimplicialObject.Splitting.comp_PInfty_eq_zero_iffₓ'. -/
 theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
     f ≫ PInfty.f n = 0 ↔ f ≫ s.πSummand (IndexSet.id (op [n])) = 0 :=
@@ -199,10 +181,7 @@ theorem PInfty_comp_πSummand_id (n : ℕ) :
 -/
 
 /- warning: simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty -> SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInftyₓ'. -/
 @[simp, reassoc]
 theorem πSummand_comp_ιSummand_comp_PInfty_eq_PInfty (n : ℕ) :
@@ -226,10 +205,7 @@ def d (i j : ℕ) : s.n i ⟶ s.n j :=
 -/
 
 /- warning: simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero -> SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(Opposite.op.{1} SimplexCategory (SimplexCategory.mk k)))))))) (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 (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (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 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(SimplexCategory.mk k))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))))))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j)) A) (CategoryTheory.CategoryStruct.comp.{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 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (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 j))) (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 j))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (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 k))) (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 k))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k)))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zeroₓ'. -/
 theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ K[X].d j k ≫ s.πSummand (IndexSet.id (op [k])) = 0 :=
@@ -266,10 +242,7 @@ def nondegComplex : ChainComplex C ℕ where
 -/
 
 /- warning: simplicial_object.splitting.to_karoubi_nondeg_complex_iso_N₁ -> SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ is a dubious translation:
-lean 3 declaration is
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_inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.Idempotents.toKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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(HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.to_karoubi_nondeg_complex_iso_N₁ SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ₓ'. -/
 /-- The chain complex `s.nondeg_complex` attached to a splitting of a simplicial object `X`
 becomes isomorphic to the normalized Moore complex `N₁.obj X` defined as a formal direct
@@ -356,10 +329,7 @@ def nondegComplexFunctor : Split C ⥤ ChainComplex C ℕ
 #align simplicial_object.split.nondeg_complex_functor SimplicialObject.Split.nondegComplexFunctor
 
 /- warning: simplicial_object.split.to_karoubi_nondeg_complex_functor_iso_N₁ -> SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁ is a dubious translation:
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-but is expected to have type
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(HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.category.{u2, u2, max u1 u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_3) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.comp.{u2, u2, u2, max u2 u1, max u2 u1, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_3) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_3) (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (SimplicialObject.Split.nondegComplexFunctor.{u1, u2} C _inst_1 _inst_2 _inst_3) (CategoryTheory.Idempotents.toKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.comp.{u2, u2, u2, max u1 u2, max u1 u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_3) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (SimplicialObject.Split.forget.{u1, u2} C _inst_1 _inst_3) (AlgebraicTopology.DoldKan.N₁.{u1, u2} C _inst_1 _inst_2))
+<too large>
 Case conversion may be inaccurate. Consider using '#align simplicial_object.split.to_karoubi_nondeg_complex_functor_iso_N₁ SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁ₓ'. -/
 /-- The natural isomorphism (in `karoubi (chain_complex C ℕ)`) between the chain complex
 of nondegenerate simplices of a split simplicial object and the normalized Moore complex

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -67,7 +67,7 @@ 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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {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)))) (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.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) (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)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s _inst_3 Δ A)) (CategoryTheory.CategoryStruct.id.{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)))))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_idₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ s.πSummand A = 𝟙 _ :=
   by
@@ -84,7 +84,7 @@ 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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (B : SimplicialObject.Splitting.IndexSet Δ), (Ne.{1} (SimplicialObject.Splitting.IndexSet Δ) B A) -> (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)))) (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)) B))))) (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) (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)) B)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s _inst_3 Δ B)) (OfNat.ofNat.{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)))) (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)) B))))) 0 (Zero.toOfNat0.{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)))) (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)) B))))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 _inst_3 (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)))) (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)) B))))))))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_π_summand_eq_zero SimplicialObject.Splitting.ι_πSummand_eq_zeroₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
     (h : B ≠ A) : s.ιSummand A ≫ s.πSummand B = 0 :=
   by
@@ -120,7 +120,7 @@ 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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u2} (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) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))))) (CategoryTheory.CategoryStruct.comp.{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) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))))) (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X n i) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))) (OfNat.ofNat.{u2} (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) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))))) 0 (Zero.toOfNat0.{u2} (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) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (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.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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))))))))
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zeroₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ s.πSummand (IndexSet.id (op [n + 1])) = 0 :=
   by
@@ -187,7 +187,7 @@ theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
 #align simplicial_object.splitting.comp_P_infty_eq_zero_iff SimplicialObject.Splitting.comp_PInfty_eq_zero_iff
 
 #print SimplicialObject.Splitting.PInfty_comp_πSummand_id /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem PInfty_comp_πSummand_id (n : ℕ) :
     PInfty.f n ≫ s.πSummand (IndexSet.id (op [n])) = s.πSummand (IndexSet.id (op [n])) :=
   by
@@ -204,7 +204,7 @@ 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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (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)) (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))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) n)) (CategoryTheory.CategoryStruct.comp.{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) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) n) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk 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 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))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) 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)))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_3 X) n))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_3 X) n)
 Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInftyₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem πSummand_comp_ιSummand_comp_PInfty_eq_PInfty (n : ℕ) :
     s.πSummand (IndexSet.id (op [n])) ≫ s.ιSummand (IndexSet.id (op [n])) ≫ PInfty.f n =
       PInfty.f n :=

bump to nightly-2023-04-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e281deff072232a3c5b3e90034bd65dde396312

8c574543

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.dold_kan.split_simplicial_object
-! leanprover-community/mathlib commit 31019c2504b17f85af7e0577585fad996935a317
+! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.AlgebraicTopology.DoldKan.FunctorN
 
 # Split simplicial objects in preadditive categories
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define a functor `nondeg_complex : simplicial_object.split C ⥤ chain_complex C ℕ`
 when `C` is a preadditive category with finite coproducts, and get an isomorphism
 `to_karoubi_nondeg_complex_iso_N₁ : nondeg_complex ⋙ to_karoubi _ ≅ forget C ⋙ dold_kan.N₁`.

bump to nightly-2023-04-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/246f6f7989ff86bd07e1b014846f11304f33cf9e

301bd2a9

Diff

@@ -36,6 +36,12 @@ namespace Splitting
 variable {C : Type _} [Category C] [HasFiniteCoproducts C] {X : SimplicialObject C}
   (s : Splitting X)
 
+/- warning: simplicial_object.splitting.π_summand -> SimplicialObject.Splitting.πSummand 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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {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)) (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.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))))
+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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {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)) (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.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))))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummandₓ'. -/
 /-- The projection on a summand of the coproduct decomposition given
 by a splitting of a simplicial object. -/
 def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
@@ -52,6 +58,12 @@ def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ
   · exact 0
 #align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummand
 
+/- warning: simplicial_object.splitting.ι_π_summand_eq_id -> SimplicialObject.Splitting.ι_πSummand_eq_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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {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)))) (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.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) (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)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s _inst_3 Δ A)) (CategoryTheory.CategoryStruct.id.{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)))))
+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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {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)))) (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.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) (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)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s _inst_3 Δ A)) (CategoryTheory.CategoryStruct.id.{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)))))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_idₓ'. -/
 @[simp, reassoc.1]
 theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ s.πSummand A = 𝟙 _ :=
@@ -63,6 +75,12 @@ theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A
   simp only [eq_self_iff_true, if_true]
 #align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_id
 
+/- warning: simplicial_object.splitting.ι_π_summand_eq_zero -> SimplicialObject.Splitting.ι_πSummand_eq_zero 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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (B : SimplicialObject.Splitting.IndexSet Δ), (Ne.{1} (SimplicialObject.Splitting.IndexSet Δ) B A) -> (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 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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)) B))))) (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) (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)) B)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s _inst_3 Δ B)) (OfNat.ofNat.{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)))) (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)) B))))) 0 (OfNat.mk.{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)))) (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)) B))))) 0 (Zero.zero.{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)))) (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)) B))))) (CategoryTheory.Limits.HasZeroMorphisms.hasZero.{u2, u1} C _inst_1 _inst_3 (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)))) (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)) B)))))))))
+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) [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (B : SimplicialObject.Splitting.IndexSet Δ), (Ne.{1} (SimplicialObject.Splitting.IndexSet Δ) B A) -> (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)))) (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)) B))))) (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) (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)) B)))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s _inst_3 Δ B)) (OfNat.ofNat.{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)))) (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)) B))))) 0 (Zero.toOfNat0.{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)))) (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)) B))))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 _inst_3 (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)))) (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)) B))))))))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_π_summand_eq_zero SimplicialObject.Splitting.ι_πSummand_eq_zeroₓ'. -/
 @[simp, reassoc.1]
 theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
     (h : B ≠ A) : s.ιSummand A ≫ s.πSummand B = 0 :=
@@ -76,6 +94,12 @@ theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (
 
 variable [Preadditive C]
 
+/- warning: simplicial_object.splitting.decomposition_id -> SimplicialObject.Splitting.decomposition_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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (Δ : Opposite.{1} SimplexCategory), Eq.{succ u2} (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) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ)) (CategoryTheory.CategoryStruct.id.{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)) (Finset.sum.{u2, 0} (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) (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.IndexSet Δ) (AddCommGroup.toAddCommMonoid.{u2} (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) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ)) (CategoryTheory.Preadditive.homGroup.{u2, u1} C _inst_1 _inst_3 (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Δ))) (Finset.univ.{0} (SimplicialObject.Splitting.IndexSet Δ) (SimplicialObject.Splitting.IndexSet.fintype Δ)) (fun (A : SimplicialObject.Splitting.IndexSet Δ) => CategoryTheory.CategoryStruct.comp.{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) (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.πSummand.{u1, u2} C _inst_1 _inst_2 X s (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Δ A) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A)))
+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 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 X) Δ)) (SimplicialObject.Splitting.IndexSet Δ) (AddCommGroup.toAddCommMonoid.{u2} 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_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) (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} 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(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.πSummand.{u1, u2} C _inst_1 _inst_2 X s (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Δ A) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s Δ A)))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.decomposition_id SimplicialObject.Splitting.decomposition_idₓ'. -/
 theorem decomposition_id (Δ : SimplexCategoryᵒᵖ) :
     𝟙 (X.obj Δ) = ∑ A : IndexSet Δ, s.πSummand A ≫ s.ιSummand A :=
   by
@@ -87,6 +111,12 @@ theorem decomposition_id (Δ : SimplexCategoryᵒᵖ) :
   · simp only [Finset.mem_univ, not_true, IsEmpty.forall_iff]
 #align simplicial_object.splitting.decomposition_id SimplicialObject.Splitting.decomposition_id
 
+/- warning: simplicial_object.splitting.σ_comp_π_summand_id_eq_zero -> SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))))) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory 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(CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))))) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory 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(CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)))))))))))))
+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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u2} (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) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} 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(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) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 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 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(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.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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (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 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))))))))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zeroₓ'. -/
 @[simp, reassoc.1]
 theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ s.πSummand (IndexSet.id (op [n + 1])) = 0 :=
@@ -103,18 +133,30 @@ theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
   linarith
 #align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero
 
+/- warning: simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero -> SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zeroₓ'. -/
 /-- If a simplicial object `X` in an additive category is split,
 then `P_infty` vanishes on all the summands of `X _[n]` which do
 not correspond to the identity of `[n]`. -/
-theorem ιSummand_comp_pInfty_eq_zero {X : SimplicialObject C} (s : SimplicialObject.Splitting X)
+theorem ιSummand_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialObject.Splitting X)
     {n : ℕ} (A : SimplicialObject.Splitting.IndexSet (op [n])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ PInfty.f n = 0 :=
   by
   rw [SimplicialObject.Splitting.IndexSet.eqId_iff_mono] at hA
   rw [SimplicialObject.Splitting.ιSummand_eq, assoc, degeneracy_comp_P_infty X n A.e hA, comp_zero]
-#align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_pInfty_eq_zero
-
-theorem comp_pInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
+#align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero
+
+/- warning: simplicial_object.splitting.comp_P_infty_eq_zero_iff -> SimplicialObject.Splitting.comp_PInfty_eq_zero_iff is a dubious translation:
+lean 3 declaration is
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+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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {Z : C} {n : Nat} (f : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Z (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} 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_inst_3 X) n)) 0 (Zero.toOfNat0.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Z (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) n)) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Z (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) n))))) (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Z (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} 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u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) Z (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.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 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_inst_2 X s (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))) (OfNat.ofNat.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Z (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} 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+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.comp_P_infty_eq_zero_iff SimplicialObject.Splitting.comp_PInfty_eq_zero_iffₓ'. -/
+theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
     f ≫ PInfty.f n = 0 ↔ f ≫ s.πSummand (IndexSet.id (op [n])) = 0 :=
   by
   constructor
@@ -139,20 +181,28 @@ theorem comp_pInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
       subst hA
       rw [assoc, reassoc_of h, zero_comp]
     · simp only [assoc, s.ι_summand_comp_P_infty_eq_zero A hA, comp_zero]
-#align simplicial_object.splitting.comp_P_infty_eq_zero_iff SimplicialObject.Splitting.comp_pInfty_eq_zero_iff
+#align simplicial_object.splitting.comp_P_infty_eq_zero_iff SimplicialObject.Splitting.comp_PInfty_eq_zero_iff
 
+#print SimplicialObject.Splitting.PInfty_comp_πSummand_id /-
 @[simp, reassoc.1]
-theorem pInfty_comp_πSummand_id (n : ℕ) :
+theorem PInfty_comp_πSummand_id (n : ℕ) :
     PInfty.f n ≫ s.πSummand (IndexSet.id (op [n])) = s.πSummand (IndexSet.id (op [n])) :=
   by
   conv_rhs => rw [← id_comp (s.π_summand _)]
   symm
   rw [← sub_eq_zero, ← sub_comp, ← comp_P_infty_eq_zero_iff, sub_comp, id_comp, P_infty_f_idem,
     sub_self]
-#align simplicial_object.splitting.P_infty_comp_π_summand_id SimplicialObject.Splitting.pInfty_comp_πSummand_id
+#align simplicial_object.splitting.P_infty_comp_π_summand_id SimplicialObject.Splitting.PInfty_comp_πSummand_id
+-/
 
+/- warning: simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty -> SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty 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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (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)) (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))) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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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))) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) 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 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+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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (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)) (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} 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(AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) n) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk 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 X s (SimplexCategory.len (Opposite.unop.{1} SimplexCategory 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Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_3 X) n))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_3 X) n)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInftyₓ'. -/
 @[simp, reassoc.1]
-theorem πSummand_comp_ιSummand_comp_pInfty_eq_pInfty (n : ℕ) :
+theorem πSummand_comp_ιSummand_comp_PInfty_eq_PInfty (n : ℕ) :
     s.πSummand (IndexSet.id (op [n])) ≫ s.ιSummand (IndexSet.id (op [n])) ≫ PInfty.f n =
       PInfty.f n :=
   by
@@ -161,15 +211,23 @@ theorem πSummand_comp_ιSummand_comp_pInfty_eq_pInfty (n : ℕ) :
   rw [Fintype.sum_eq_single (index_set.id (op [n])), assoc]
   rintro A (hA : ¬A.eq_id)
   rw [assoc, s.ι_summand_comp_P_infty_eq_zero A hA, comp_zero]
-#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_pInfty_eq_pInfty
+#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty
 
+#print SimplicialObject.Splitting.d /-
 /-- The differentials `s.d i j : s.N i ⟶ s.N j` on nondegenerate simplices of a split
 simplicial object are induced by the differentials on the alternating face map complex. -/
 @[simp]
 def d (i j : ℕ) : s.n i ⟶ s.n j :=
   s.ιSummand (IndexSet.id (op [i])) ≫ K[X].d i j ≫ s.πSummand (IndexSet.id (op [j]))
 #align simplicial_object.splitting.d SimplicialObject.Splitting.d
+-/
 
+/- warning: simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero -> SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero 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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (j : Nat) (k : Nat) (A : SimplicialObject.Splitting.IndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))), (Not (SimplicialObject.Splitting.IndexSet.EqId (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j)) A)) -> (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 j))) (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 j))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (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 k))) (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 k))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k)))))))) (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 (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (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 j))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (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 (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (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 k))) (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 k))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))))))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_2 X s (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j)) A) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (CategoryTheory.Functor.obj.{0, u2, 0, u1} 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_3 X) j k) (SimplicialObject.Splitting.πSummand.{u1, u2} C _inst_1 _inst_2 X s (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k)))))) (OfNat.ofNat.{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 j))) (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 j))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (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 k))) (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 k))) (Opposite.unop.{1} SimplexCategory Δ')) => 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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 j))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (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)) 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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 j))) (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 j))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (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 k))) (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 k))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k)))))))) (CategoryTheory.Limits.HasZeroMorphisms.hasZero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (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 j))) (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 j))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (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 k))) (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 k))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))))))))))))
+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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (j : Nat) (k : Nat) (A : SimplicialObject.Splitting.IndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))), (Not (SimplicialObject.Splitting.IndexSet.EqId (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j)) A)) -> (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 j))) (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 j))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (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 k))) (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 k))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k)))))))) (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 (Opposite.op.{1} SimplexCategory (SimplexCategory.mk j))) (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 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SimplexCategory (SimplexCategory.mk k))) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk k)))))))))))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zeroₓ'. -/
 theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j])) (hA : ¬A.EqId) :
     s.ιSummand A ≫ K[X].d j k ≫ s.πSummand (IndexSet.id (op [k])) = 0 :=
   by
@@ -178,6 +236,7 @@ theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j
     degeneracy_comp_P_infty_assoc X j A.e hA, zero_comp, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero
 
+#print SimplicialObject.Splitting.nondegComplex /-
 /-- If `s` is a splitting of a simplicial object `X` in a preadditive category,
 `s.nondeg_complex` is a chain complex which is given in degree `n` by
 the nondegenerate `n`-simplices of `X`. -/
@@ -201,7 +260,14 @@ def nondegComplex : ChainComplex C ℕ where
         simp only [assoc, ι_summand_comp_d_comp_π_summand_eq_zero _ _ _ _ hA, comp_zero]
       rw [Eq, comp_zero]
 #align simplicial_object.splitting.nondeg_complex SimplicialObject.Splitting.nondegComplex
+-/
 
+/- warning: simplicial_object.splitting.to_karoubi_nondeg_complex_iso_N₁ -> SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ is a dubious translation:
+lean 3 declaration is
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(ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.Idempotents.toKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (SimplicialObject.Splitting.nondegComplex.{u1, u2} C _inst_1 _inst_2 X s _inst_3)) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (AlgebraicTopology.DoldKan.N₁.{u1, u2} C _inst_1 _inst_3) X)
+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) [_inst_3 : CategoryTheory.Preadditive.{u2, u1} C _inst_1], CategoryTheory.Iso.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (Prefunctor.obj.{succ u2, succ u2, max u1 u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u1 u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.toKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (SimplicialObject.Splitting.nondegComplex.{u1, u2} C _inst_1 _inst_2 X s _inst_3)) (Prefunctor.obj.{succ u2, succ u2, max u2 u1, 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.instCategorySimplicialObject.{u2, u1} C _inst_1))) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (AlgebraicTopology.DoldKan.N₁.{u1, u2} C _inst_1 _inst_3)) X)
+Case conversion may be inaccurate. Consider using '#align simplicial_object.splitting.to_karoubi_nondeg_complex_iso_N₁ SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ₓ'. -/
 /-- The chain complex `s.nondeg_complex` attached to a splitting of a simplicial object `X`
 becomes isomorphic to the normalized Moore complex `N₁.obj X` defined as a formal direct
 factor in the category `karoubi (chain_complex C ℕ)`. -/
@@ -250,6 +316,12 @@ namespace Split
 
 variable {C : Type _} [Category C] [Preadditive C] [HasFiniteCoproducts C]
 
+/- warning: simplicial_object.split.nondeg_complex_functor -> SimplicialObject.Split.nondegComplexFunctor is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], CategoryTheory.Functor.{u2, u2, max u1 u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_3) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_3) (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.nondeg_complex_functor SimplicialObject.Split.nondegComplexFunctorₓ'. -/
 /-- The functor which sends a split simplicial object in a preadditive category to
 the chain complex which consists of nondegenerate simplices. -/
 @[simps]
@@ -280,6 +352,12 @@ def nondegComplexFunctor : Split C ⥤ ChainComplex C ℕ
             comp_zero] }
 #align simplicial_object.split.nondeg_complex_functor SimplicialObject.Split.nondegComplexFunctor
 
+/- warning: simplicial_object.split.to_karoubi_nondeg_complex_functor_iso_N₁ -> SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁ is a dubious translation:
+lean 3 declaration is
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(ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (SimplicialObject.Split.forget.{u1, u2} C _inst_1 _inst_3) (AlgebraicTopology.DoldKan.N₁.{u1, u2} C _inst_1 _inst_2))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], CategoryTheory.Iso.{max u1 u2, max (max (max u1 u2) u2 u1) u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_3) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.comp.{u2, u2, u2, max u2 u1, max u2 u1, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_3) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_3) (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (SimplicialObject.Split.nondegComplexFunctor.{u1, u2} C _inst_1 _inst_2 _inst_3) (CategoryTheory.Idempotents.toKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.comp.{u2, u2, u2, max u1 u2, max u1 u2, max u1 u2} (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_3) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (SimplicialObject.Split.forget.{u1, u2} C _inst_1 _inst_3) (AlgebraicTopology.DoldKan.N₁.{u1, u2} C _inst_1 _inst_2))
+Case conversion may be inaccurate. Consider using '#align simplicial_object.split.to_karoubi_nondeg_complex_functor_iso_N₁ SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁ₓ'. -/
 /-- The natural isomorphism (in `karoubi (chain_complex C ℕ)`) between the chain complex
 of nondegenerate simplices of a split simplicial object and the normalized Moore complex
 defined as a formal direct factor of the alternating face map complex. -/

bump to nightly-2023-04-20-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

e863e061

Diff

@@ -108,14 +108,14 @@ then `P_infty` vanishes on all the summands of `X _[n]` which do
 not correspond to the identity of `[n]`. -/
 theorem ιSummand_comp_pInfty_eq_zero {X : SimplicialObject C} (s : SimplicialObject.Splitting X)
     {n : ℕ} (A : SimplicialObject.Splitting.IndexSet (op [n])) (hA : ¬A.EqId) :
-    s.ιSummand A ≫ pInfty.f n = 0 :=
+    s.ιSummand A ≫ PInfty.f n = 0 :=
   by
   rw [SimplicialObject.Splitting.IndexSet.eqId_iff_mono] at hA
   rw [SimplicialObject.Splitting.ιSummand_eq, assoc, degeneracy_comp_P_infty X n A.e hA, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_pInfty_eq_zero
 
 theorem comp_pInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
-    f ≫ pInfty.f n = 0 ↔ f ≫ s.πSummand (IndexSet.id (op [n])) = 0 :=
+    f ≫ PInfty.f n = 0 ↔ f ≫ s.πSummand (IndexSet.id (op [n])) = 0 :=
   by
   constructor
   · intro h
@@ -143,7 +143,7 @@ theorem comp_pInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
 
 @[simp, reassoc.1]
 theorem pInfty_comp_πSummand_id (n : ℕ) :
-    pInfty.f n ≫ s.πSummand (IndexSet.id (op [n])) = s.πSummand (IndexSet.id (op [n])) :=
+    PInfty.f n ≫ s.πSummand (IndexSet.id (op [n])) = s.πSummand (IndexSet.id (op [n])) :=
   by
   conv_rhs => rw [← id_comp (s.π_summand _)]
   symm
@@ -153,8 +153,8 @@ theorem pInfty_comp_πSummand_id (n : ℕ) :
 
 @[simp, reassoc.1]
 theorem πSummand_comp_ιSummand_comp_pInfty_eq_pInfty (n : ℕ) :
-    s.πSummand (IndexSet.id (op [n])) ≫ s.ιSummand (IndexSet.id (op [n])) ≫ pInfty.f n =
-      pInfty.f n :=
+    s.πSummand (IndexSet.id (op [n])) ≫ s.ιSummand (IndexSet.id (op [n])) ≫ PInfty.f n =
+      PInfty.f n :=
   by
   conv_rhs => rw [← id_comp (P_infty.f n)]
   erw [s.decomposition_id, preadditive.sum_comp]
@@ -206,11 +206,11 @@ def nondegComplex : ChainComplex C ℕ where
 becomes isomorphic to the normalized Moore complex `N₁.obj X` defined as a formal direct
 factor in the category `karoubi (chain_complex C ℕ)`. -/
 @[simps]
-def toKaroubiNondegComplexIsoN₁ : (toKaroubi _).obj s.nondegComplex ≅ n₁.obj X
+def toKaroubiNondegComplexIsoN₁ : (toKaroubi _).obj s.nondegComplex ≅ N₁.obj X
     where
   Hom :=
     { f :=
-        { f := fun n => s.ιSummand (IndexSet.id (op [n])) ≫ pInfty.f n
+        { f := fun n => s.ιSummand (IndexSet.id (op [n])) ≫ PInfty.f n
           comm' := fun i j hij => by
             dsimp
             rw [assoc, assoc, assoc, π_summand_comp_ι_summand_comp_P_infty_eq_P_infty,
@@ -285,7 +285,7 @@ of nondegenerate simplices of a split simplicial object and the normalized Moore
 defined as a formal direct factor of the alternating face map complex. -/
 @[simps]
 def toKaroubiNondegComplexFunctorIsoN₁ :
-    nondegComplexFunctor ⋙ toKaroubi (ChainComplex C ℕ) ≅ forget C ⋙ DoldKan.n₁ :=
+    nondegComplexFunctor ⋙ toKaroubi (ChainComplex C ℕ) ≅ forget C ⋙ DoldKan.N₁ :=
   NatIso.ofComponents (fun S => S.s.toKaroubiNondegComplexIsoN₁) fun S₁ S₂ Φ =>
     by
     ext n

bump to nightly-2023-02-28-22

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

1fb1623f

Diff

@@ -183,7 +183,7 @@ theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j
 the nondegenerate `n`-simplices of `X`. -/
 @[simps]
 def nondegComplex : ChainComplex C ℕ where
-  x := s.n
+  pt := s.n
   d := s.d
   shape' i j hij := by simp only [d, K[X].shape i j hij, zero_comp, comp_zero]
   d_comp_d' i j k hij hjk := by

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

refactor: optimize proofs with omega (#11093)

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

37bc4aba

Diff

@@ -82,7 +82,7 @@ theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
   rw [IndexSet.eqId_iff_len_eq]
   have h := SimplexCategory.len_le_of_epi (inferInstance : Epi A.e)
   dsimp at h ⊢
-  linarith
+  omega
 #align simplicial_object.splitting.σ_comp_π_summand_id_eq_zero SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero
 
 /-- If a simplicial object `X` in an additive category is split,

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

@@ -30,48 +30,43 @@ namespace SimplicialObject
 
 namespace Splitting
 
-variable {C : Type*} [Category C] [HasFiniteCoproducts C] {X : SimplicialObject C}
+variable {C : Type*} [Category C] {X : SimplicialObject C}
   (s : Splitting X)
 
 /-- The projection on a summand of the coproduct decomposition given
 by a splitting of a simplicial object. -/
 noncomputable def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
-    X.obj Δ ⟶ s.N A.1.unop.len := by
-  refine' (s.iso Δ).inv ≫ Sigma.desc fun B => _
-  by_cases h : B = A
-  · exact eqToHom (by subst h; rfl)
-  · exact 0
+    X.obj Δ ⟶ s.N A.1.unop.len :=
+  s.desc Δ (fun B => by
+    by_cases h : B = A
+    · exact eqToHom (by subst h; rfl)
+    · exact 0)
 #align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummand
 
 @[reassoc (attr := simp)]
-theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
-    s.ιSummand A ≫ s.πSummand A = 𝟙 _ := by
-  dsimp only [ιSummand, iso_hom, πSummand, iso_inv, summand]
-  simp only [summand, assoc, IsIso.hom_inv_id_assoc]
-  erw [colimit.ι_desc, Cofan.mk_ι_app]
-  dsimp
-  simp only [dite_eq_ite, ite_true]
-#align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.ι_πSummand_eq_id
+theorem cofan_inj_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
+    (s.cofan Δ).inj A ≫ s.πSummand A = 𝟙 _ := by
+  simp [πSummand]
+#align simplicial_object.splitting.ι_π_summand_eq_id SimplicialObject.Splitting.cofan_inj_πSummand_eq_id
 
 @[reassoc (attr := simp)]
-theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
-    (h : B ≠ A) : s.ιSummand A ≫ s.πSummand B = 0 := by
-  dsimp only [ιSummand, iso_hom, πSummand, iso_inv, summand]
-  simp only [summand, assoc, IsIso.hom_inv_id_assoc]
-  erw [colimit.ι_desc, Cofan.mk_ι_app]
-  exact dif_neg h.symm
-#align simplicial_object.splitting.ι_π_summand_eq_zero SimplicialObject.Splitting.ι_πSummand_eq_zero
+theorem cofan_inj_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
+    (h : B ≠ A) : (s.cofan Δ).inj A ≫ s.πSummand B = 0 := by
+  dsimp [πSummand]
+  rw [ι_desc, dif_neg h.symm]
+#align simplicial_object.splitting.ι_π_summand_eq_zero SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero
 
 variable [Preadditive C]
 
 theorem decomposition_id (Δ : SimplexCategoryᵒᵖ) :
-    𝟙 (X.obj Δ) = ∑ A : IndexSet Δ, s.πSummand A ≫ s.ιSummand A := by
+    𝟙 (X.obj Δ) = ∑ A : IndexSet Δ, s.πSummand A ≫ (s.cofan Δ).inj A := by
   apply s.hom_ext'
   intro A
-  rw [comp_id, comp_sum, Finset.sum_eq_single A, ι_πSummand_eq_id_assoc]
+  dsimp
+  erw [comp_id, comp_sum, Finset.sum_eq_single A, cofan_inj_πSummand_eq_id_assoc]
   · intro B _ h₂
-    rw [s.ι_πSummand_eq_zero_assoc _ _ h₂, zero_comp]
-  · simp only [Finset.mem_univ, not_true, IsEmpty.forall_iff]
+    rw [s.cofan_inj_πSummand_eq_zero_assoc _ _ h₂, zero_comp]
+  · simp
 #align simplicial_object.splitting.decomposition_id SimplicialObject.Splitting.decomposition_id
 
 @[reassoc (attr := simp)]
@@ -80,7 +75,8 @@ theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
   apply s.hom_ext'
   intro A
   dsimp only [SimplicialObject.σ]
-  rw [comp_zero, s.ιSummand_epi_naturality_assoc A (SimplexCategory.σ i).op, ι_πSummand_eq_zero]
+  rw [comp_zero, s.cofan_inj_epi_naturality_assoc A (SimplexCategory.σ i).op,
+    cofan_inj_πSummand_eq_zero]
   rw [ne_comm]
   change ¬(A.epiComp (SimplexCategory.σ i).op).EqId
   rw [IndexSet.eqId_iff_len_eq]
@@ -92,13 +88,13 @@ theorem σ_comp_πSummand_id_eq_zero {n : ℕ} (i : Fin (n + 1)) :
 /-- If a simplicial object `X` in an additive category is split,
 then `PInfty` vanishes on all the summands of `X _[n]` which do
 not correspond to the identity of `[n]`. -/
-theorem ιSummand_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialObject.Splitting X)
+theorem cofan_inj_comp_PInfty_eq_zero {X : SimplicialObject C} (s : SimplicialObject.Splitting X)
     {n : ℕ} (A : SimplicialObject.Splitting.IndexSet (op [n])) (hA : ¬A.EqId) :
-    s.ιSummand A ≫ PInfty.f n = 0 := by
+    (s.cofan _).inj A ≫ PInfty.f n = 0 := by
   rw [SimplicialObject.Splitting.IndexSet.eqId_iff_mono] at hA
-  rw [SimplicialObject.Splitting.ιSummand_eq, assoc, degeneracy_comp_PInfty X n A.e hA, comp_zero]
+  rw [SimplicialObject.Splitting.cofan_inj_eq, assoc, degeneracy_comp_PInfty X n A.e hA, comp_zero]
 set_option linter.uppercaseLean3 false in
-#align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero
+#align simplicial_object.splitting.ι_summand_comp_P_infty_eq_zero SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero
 
 theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
     f ≫ PInfty.f n = 0 ↔ f ≫ s.πSummand (IndexSet.id (op [n])) = 0 := by
@@ -123,7 +119,7 @@ theorem comp_PInfty_eq_zero_iff {Z : C} {n : ℕ} (f : Z ⟶ X _[n]) :
     · dsimp at hA
       subst hA
       rw [assoc, reassoc_of% h, zero_comp]
-    · simp only [assoc, s.ιSummand_comp_PInfty_eq_zero A hA, comp_zero]
+    · simp only [assoc, s.cofan_inj_comp_PInfty_eq_zero A hA, comp_zero]
 set_option linter.uppercaseLean3 false in
 #align simplicial_object.splitting.comp_P_infty_eq_zero_iff SimplicialObject.Splitting.comp_PInfty_eq_zero_iff
 
@@ -138,28 +134,28 @@ set_option linter.uppercaseLean3 false in
 #align simplicial_object.splitting.P_infty_comp_π_summand_id SimplicialObject.Splitting.PInfty_comp_πSummand_id
 
 @[reassoc (attr := simp)]
-theorem πSummand_comp_ιSummand_comp_PInfty_eq_PInfty (n : ℕ) :
-    s.πSummand (IndexSet.id (op [n])) ≫ s.ιSummand (IndexSet.id (op [n])) ≫ PInfty.f n =
+theorem πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty (n : ℕ) :
+    s.πSummand (IndexSet.id (op [n])) ≫ (s.cofan _).inj (IndexSet.id (op [n])) ≫ PInfty.f n =
       PInfty.f n := by
   conv_rhs => rw [← id_comp (PInfty.f n)]
   erw [s.decomposition_id, Preadditive.sum_comp]
   rw [Fintype.sum_eq_single (IndexSet.id (op [n])), assoc]
   rintro A (hA : ¬A.EqId)
-  rw [assoc, s.ιSummand_comp_PInfty_eq_zero A hA, comp_zero]
+  rw [assoc, s.cofan_inj_comp_PInfty_eq_zero A hA, comp_zero]
 set_option linter.uppercaseLean3 false in
-#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_ιSummand_comp_PInfty_eq_PInfty
+#align simplicial_object.splitting.π_summand_comp_ι_summand_comp_P_infty_eq_P_infty SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty
 
 /-- The differentials `s.d i j : s.N i ⟶ s.N j` on nondegenerate simplices of a split
 simplicial object are induced by the differentials on the alternating face map complex. -/
 @[simp]
 noncomputable def d (i j : ℕ) : s.N i ⟶ s.N j :=
-  s.ιSummand (IndexSet.id (op [i])) ≫ K[X].d i j ≫ s.πSummand (IndexSet.id (op [j]))
+  (s.cofan _).inj (IndexSet.id (op [i])) ≫ K[X].d i j ≫ s.πSummand (IndexSet.id (op [j]))
 #align simplicial_object.splitting.d SimplicialObject.Splitting.d
 
 theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j])) (hA : ¬A.EqId) :
-    s.ιSummand A ≫ K[X].d j k ≫ s.πSummand (IndexSet.id (op [k])) = 0 := by
+    (s.cofan _).inj A ≫ K[X].d j k ≫ s.πSummand (IndexSet.id (op [k])) = 0 := by
   rw [A.eqId_iff_mono] at hA
-  rw [← assoc, ← s.comp_PInfty_eq_zero_iff, assoc, ← PInfty.comm j k, s.ιSummand_eq, assoc,
+  rw [← assoc, ← s.comp_PInfty_eq_zero_iff, assoc, ← PInfty.comm j k, s.cofan_inj_eq, assoc,
     degeneracy_comp_PInfty_assoc X j A.e hA, zero_comp, comp_zero]
 #align simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero
 
@@ -195,10 +191,10 @@ noncomputable def toKaroubiNondegComplexIsoN₁ :
     (toKaroubi _).obj s.nondegComplex ≅ N₁.obj X where
   hom :=
     { f :=
-        { f := fun n => s.ιSummand (IndexSet.id (op [n])) ≫ PInfty.f n
+        { f := fun n => (s.cofan _).inj (IndexSet.id (op [n])) ≫ PInfty.f n
           comm' := fun i j _ => by
             dsimp
-            rw [assoc, assoc, assoc, πSummand_comp_ιSummand_comp_PInfty_eq_PInfty,
+            rw [assoc, assoc, assoc, πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty,
               HomologicalComplex.Hom.comm] }
       comm := by
         ext n
@@ -222,11 +218,11 @@ noncomputable def toKaroubiNondegComplexIsoN₁ :
   hom_inv_id := by
     ext n
     simp only [assoc, PInfty_comp_πSummand_id, Karoubi.comp_f, HomologicalComplex.comp_f,
-      ι_πSummand_eq_id]
+      cofan_inj_πSummand_eq_id]
     rfl
   inv_hom_id := by
     ext n
-    simp only [πSummand_comp_ιSummand_comp_PInfty_eq_PInfty, Karoubi.comp_f,
+    simp only [πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty, Karoubi.comp_f,
       HomologicalComplex.comp_f, N₁_obj_p, Karoubi.id_eq]
 set_option linter.uppercaseLean3 false in
 #align simplicial_object.splitting.to_karoubi_nondeg_complex_iso_N₁ SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁
@@ -246,24 +242,22 @@ noncomputable def nondegComplexFunctor : Split C ⥤ ChainComplex C ℕ where
     { f := Φ.f
       comm' := fun i j _ => by
         dsimp
-        erw [← ιSummand_naturality_symm_assoc Φ (Splitting.IndexSet.id (op [i])),
+        erw [← cofan_inj_naturality_symm_assoc Φ (Splitting.IndexSet.id (op [i])),
           ((alternatingFaceMapComplex C).map Φ.F).comm_assoc i j]
         simp only [assoc]
         congr 2
         apply S₁.s.hom_ext'
         intro A
         dsimp [alternatingFaceMapComplex]
-        erw [ιSummand_naturality_symm_assoc Φ A]
+        erw [cofan_inj_naturality_symm_assoc Φ A]
         by_cases h : A.EqId
         · dsimp at h
           subst h
-          simp only [Splitting.ι_πSummand_eq_id, comp_id, Splitting.ι_πSummand_eq_id_assoc]
-          rfl
-        · have h' : Splitting.IndexSet.id (op [j]) ≠ A := by
-            rw [ne_comm]
-            exact h
-          rw [S₁.s.ι_πSummand_eq_zero_assoc _ _ h', S₂.s.ι_πSummand_eq_zero _ _ h', zero_comp,
-            comp_zero] }
+          rw [Splitting.cofan_inj_πSummand_eq_id]
+          dsimp
+          rw [comp_id, Splitting.cofan_inj_πSummand_eq_id_assoc]
+        · rw [S₁.s.cofan_inj_πSummand_eq_zero_assoc _ _ (Ne.symm h),
+            S₂.s.cofan_inj_πSummand_eq_zero _ _ (Ne.symm h), zero_comp, comp_zero] }
 #align simplicial_object.split.nondeg_complex_functor SimplicialObject.Split.nondegComplexFunctor
 
 /-- The natural isomorphism (in `Karoubi (ChainComplex C ℕ)`) between the chain complex
@@ -278,7 +272,7 @@ noncomputable def toKaroubiNondegComplexFunctorIsoN₁ :
     simp only [Karoubi.comp_f, toKaroubi_map_f, HomologicalComplex.comp_f,
       nondegComplexFunctor_map_f, Splitting.toKaroubiNondegComplexIsoN₁_hom_f_f, N₁_map_f,
       AlternatingFaceMapComplex.map_f, assoc, PInfty_f_idem_assoc]
-    erw [← Split.ιSummand_naturality_symm_assoc Φ (Splitting.IndexSet.id (op [n]))]
+    erw [← Split.cofan_inj_naturality_symm_assoc Φ (Splitting.IndexSet.id (op [n]))]
     rw [PInfty_f_naturality]
 set_option linter.uppercaseLean3 false in
 #align simplicial_object.split.to_karoubi_nondeg_complex_functor_iso_N₁ SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁

chore: add missing hypothesis names to by_cases (#8533)

I've also got a change to make this required, but I'd like to land this first.

2009db69

Diff

@@ -38,7 +38,7 @@ by a splitting of a simplicial object. -/
 noncomputable def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     X.obj Δ ⟶ s.N A.1.unop.len := by
   refine' (s.iso Δ).inv ≫ Sigma.desc fun B => _
-  by_cases B = A
+  by_cases h : B = A
   · exact eqToHom (by subst h; rfl)
   · exact 0
 #align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummand
@@ -254,7 +254,7 @@ noncomputable def nondegComplexFunctor : Split C ⥤ ChainComplex C ℕ where
         intro A
         dsimp [alternatingFaceMapComplex]
         erw [ιSummand_naturality_symm_assoc Φ A]
-        by_cases A.EqId
+        by_cases h : A.EqId
         · dsimp at h
           subst h
           simp only [Splitting.ι_πSummand_eq_id, comp_id, Splitting.ι_πSummand_eq_id_assoc]

chore: fix some cases in names (#7469)

And fix some names in comments where this revealed issues

be0d066c

Diff

@@ -164,7 +164,7 @@ theorem ιSummand_comp_d_comp_πSummand_eq_zero (j k : ℕ) (A : IndexSet (op [j
 #align simplicial_object.splitting.ι_summand_comp_d_comp_π_summand_eq_zero SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero
 
 /-- If `s` is a splitting of a simplicial object `X` in a preadditive category,
-`s.nondeg_complex` is a chain complex which is given in degree `n` by
+`s.nondegComplex` is a chain complex which is given in degree `n` by
 the nondegenerate `n`-simplices of `X`. -/
 @[simps]
 noncomputable def nondegComplex : ChainComplex C ℕ where

chore: fix SHA for Dold-Kan equivalence files (#6834)

cf01bdac

Diff

@@ -7,7 +7,7 @@ import Mathlib.AlgebraicTopology.SplitSimplicialObject
 import Mathlib.AlgebraicTopology.DoldKan.Degeneracies
 import Mathlib.AlgebraicTopology.DoldKan.FunctorN
 
-#align_import algebraic_topology.dold_kan.split_simplicial_object from "leanprover-community/mathlib"@"31019c2504b17f85af7e0577585fad996935a317"
+#align_import algebraic_topology.dold_kan.split_simplicial_object from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!

feat: forward port of Mathlib.AlgebraicTopology.DoldKan.Equivalence (#6444)

In this PR (which is a forward port of https://github.com/leanprover-community/mathlib/pull/17926), the Dold-Kan equivalence between simplicial objects and chain complexes in abelian categories is constructed.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

c532d7b8

Diff

@@ -17,6 +17,8 @@ In this file we define a functor `nondegComplex : SimplicialObject.Split C ⥤ C
 when `C` is a preadditive category with finite coproducts, and get an isomorphism
 `toKaroubiNondegComplexFunctorIsoN₁ : nondegComplex ⋙ toKaroubi _ ≅ forget C ⋙ DoldKan.N₁`.
 
+(See `Equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/

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

@@ -28,7 +28,7 @@ namespace SimplicialObject
 
 namespace Splitting
 
-variable {C : Type _} [Category C] [HasFiniteCoproducts C] {X : SimplicialObject C}
+variable {C : Type*} [Category C] [HasFiniteCoproducts C] {X : SimplicialObject C}
   (s : Splitting X)
 
 /-- The projection on a summand of the coproduct decomposition given
@@ -233,7 +233,7 @@ end Splitting
 
 namespace Split
 
-variable {C : Type _} [Category C] [Preadditive C] [HasFiniteCoproducts C]
+variable {C : Type*} [Category C] [Preadditive C] [HasFiniteCoproducts C]
 
 /-- The functor which sends a split simplicial object in a preadditive category to
 the chain complex which consists of nondegenerate simplices. -/

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

@@ -2,16 +2,13 @@
 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.dold_kan.split_simplicial_object
-! leanprover-community/mathlib commit 31019c2504b17f85af7e0577585fad996935a317
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.SplitSimplicialObject
 import Mathlib.AlgebraicTopology.DoldKan.Degeneracies
 import Mathlib.AlgebraicTopology.DoldKan.FunctorN
 
+#align_import algebraic_topology.dold_kan.split_simplicial_object from "leanprover-community/mathlib"@"31019c2504b17f85af7e0577585fad996935a317"
+
 /-!
 
 # Split simplicial objects in preadditive categories

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

@@ -47,7 +47,7 @@ noncomputable def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A
 @[reassoc (attr := simp)]
 theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A : IndexSet Δ) :
     s.ιSummand A ≫ s.πSummand A = 𝟙 _ := by
-  dsimp [ιSummand, πSummand]
+  dsimp only [ιSummand, iso_hom, πSummand, iso_inv, summand]
   simp only [summand, assoc, IsIso.hom_inv_id_assoc]
   erw [colimit.ι_desc, Cofan.mk_ι_app]
   dsimp
@@ -57,7 +57,7 @@ theorem ι_πSummand_eq_id [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A
 @[reassoc (attr := simp)]
 theorem ι_πSummand_eq_zero [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A B : IndexSet Δ)
     (h : B ≠ A) : s.ιSummand A ≫ s.πSummand B = 0 := by
-  dsimp [ιSummand, πSummand]
+  dsimp only [ιSummand, iso_hom, πSummand, iso_inv, summand]
   simp only [summand, assoc, IsIso.hom_inv_id_assoc]
   erw [colimit.ι_desc, Cofan.mk_ι_app]
   exact dif_neg h.symm

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -40,7 +40,7 @@ noncomputable def πSummand [HasZeroMorphisms C] {Δ : SimplexCategoryᵒᵖ} (A
     X.obj Δ ⟶ s.N A.1.unop.len := by
   refine' (s.iso Δ).inv ≫ Sigma.desc fun B => _
   by_cases B = A
-  · exact eqToHom (by subst h ; rfl)
+  · exact eqToHom (by subst h; rfl)
   · exact 0
 #align simplicial_object.splitting.π_summand SimplicialObject.Splitting.πSummand

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

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

0b676a27

Diff

@@ -11,7 +11,6 @@ Authors: Joël Riou
 import Mathlib.AlgebraicTopology.SplitSimplicialObject
 import Mathlib.AlgebraicTopology.DoldKan.Degeneracies
 import Mathlib.AlgebraicTopology.DoldKan.FunctorN
-import Mathlib.Tactic.LibrarySearch
 
 /-!