algebraic_topology.dold_kan.functor_gamma

(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

@@ -27,6 +27,8 @@ By construction, `Γ₀.obj K` is a split simplicial object whose splitting is `
 We also construct `Γ₂ : karoubi (chain_complex C ℕ) ⥤ karoubi (simplicial_object C)`
 which shall be an equivalence for any additive category `C`.
 
+(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

@@ -74,7 +74,7 @@ theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i =
 theorem eq_δ₀ {n : ℕ} {i : [n] ⟶ [n + 1]} [Mono i] (hi : Isδ₀ i) : i = SimplexCategory.δ 0 :=
   by
   obtain ⟨j, rfl⟩ := SimplexCategory.eq_δ_of_mono i
-  rw [Iff] at hi 
+  rw [Iff] at hi
   rw [hi]
 #align algebraic_topology.dold_kan.is_δ₀.eq_δ₀ AlgebraicTopology.DoldKan.Isδ₀.eq_δ₀
 -/
@@ -147,7 +147,7 @@ theorem mapMono_δ₀ {n : ℕ} : mapMono K (δ (0 : Fin (n + 2))) = K.d (n + 1)
 
 #print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero /-
 theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i = 0 := by unfold map_mono;
-  rw [Ne.def] at h₁ ; split_ifs; rfl
+  rw [Ne.def] at h₁; split_ifs; rfl
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero
 -/
 
@@ -188,7 +188,7 @@ theorem mapMono_comp : mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i) :=
   · by_contra
     simpa only [self_eq_add_right, h] using Eq
   · by_contra
-    simp only [h.1, add_right_inj] at eq 
+    simp only [h.1, add_right_inj] at eq
     linarith
   -- in all cases, the LHS is also zero, either by definition, or because d ≫ d = 0
   by_cases h₃ : is_δ₀ i
@@ -265,7 +265,7 @@ def obj (K : ChainComplex C ℕ) : SimplicialObject C
     cases A
     have fac : θ.unop ≫ θ'.unop ≫ A.e = (θ' ≫ θ).unop ≫ A.e := by rw [unop_comp, assoc]
     rw [← image.fac (θ'.unop ≫ A.e), ← assoc, ←
-      image.fac (θ.unop ≫ factor_thru_image (θ'.unop ≫ A.e)), assoc] at fac 
+      image.fac (θ.unop ≫ factor_thru_image (θ'.unop ≫ A.e)), assoc] at fac
     simpa only [obj.map_on_summand₀'_assoc K A θ', obj.map_on_summand₀' K _ θ,
       obj.termwise.map_mono_comp_assoc, obj.map_on_summand₀ K A fac]
 #align algebraic_topology.dold_kan.Γ₀.obj AlgebraicTopology.DoldKan.Γ₀.obj
@@ -412,7 +412,7 @@ theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ)
   by
   intro j hj
   have eq := Γ₀.obj.map_mono_on_summand_id K (SimplexCategory.δ j.succ)
-  rw [Γ₀.obj.termwise.map_mono_eq_zero K, zero_comp] at eq ; rotate_left
+  rw [Γ₀.obj.termwise.map_mono_eq_zero K, zero_comp] at eq; rotate_left
   · intro h
     exact (Nat.succ_ne_self n) (congr_arg SimplexCategory.len h)
   · exact fun h => Fin.succ_ne_zero j (by simpa only [is_δ₀.iff] using h)

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -132,6 +132,9 @@ theorem mapMono_δ₀' (hi : Isδ₀ i) : mapMono K i = K.d Δ.len Δ'.len :=
   by
   unfold map_mono
   classical
+  rw [dif_neg, dif_pos hi]
+  rintro rfl
+  simpa only [self_eq_add_right, Nat.one_ne_zero] using hi.1
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀' AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀'
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -132,9 +132,6 @@ theorem mapMono_δ₀' (hi : Isδ₀ i) : mapMono K i = K.d Δ.len Δ'.len :=
   by
   unfold map_mono
   classical
-  rw [dif_neg, dif_pos hi]
-  rintro rfl
-  simpa only [self_eq_add_right, Nat.one_ne_zero] using hi.1
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀' AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀'
 -/

bump to nightly-2023-12-28-06

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

c30f5587

Diff

@@ -272,7 +272,6 @@ def obj (K : ChainComplex C ℕ) : SimplicialObject C
 -/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
-#print AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_id /-
 theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
     SimplicialObject.Splitting.map (Γ₀.obj K)
         (fun n : ℕ => Sigma.ι (Γ₀.Obj.summand K (op [n])) (Splitting.IndexSet.id (op [n]))) Δ =
@@ -290,7 +289,6 @@ theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
     Γ₀.obj.termwise.map_mono_id, A.ext']
   apply id_comp
 #align algebraic_topology.dold_kan.Γ₀.splitting_map_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_id
--/
 
 #print AlgebraicTopology.DoldKan.Γ₀.splitting /-
 /-- By construction, the simplicial `Γ₀.obj K` is equipped with a splitting. -/
@@ -304,12 +302,10 @@ def splitting (K : ChainComplex C ℕ) : SimplicialObject.Splitting (Γ₀.obj K
 #align algebraic_topology.dold_kan.Γ₀.splitting AlgebraicTopology.DoldKan.Γ₀.splitting
 -/
 
-#print AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id /-
 @[simp]
 theorem splitting_iso_hom_eq_id (Δ : SimplexCategoryᵒᵖ) : ((splitting K).Iso Δ).Hom = 𝟙 _ :=
   splitting_map_eq_id K Δ
 #align algebraic_topology.dold_kan.Γ₀.splitting_iso_hom_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id
--/
 
 #print AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand /-
 @[reassoc]

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ 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.DoldKan.SplitSimplicialObject
+import AlgebraicTopology.DoldKan.SplitSimplicialObject
 
 #align_import algebraic_topology.dold_kan.functor_gamma from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"

bump to nightly-2023-08-06-03

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

b0e28731

Diff

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathbin.AlgebraicTopology.DoldKan.SplitSimplicialObject
 
-#align_import algebraic_topology.dold_kan.functor_gamma from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+#align_import algebraic_topology.dold_kan.functor_gamma from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 
@@ -28,6 +28,8 @@ By construction, `Γ₀.obj K` is a split simplicial object whose splitting is `
 We also construct `Γ₂ : karoubi (chain_complex C ℕ) ⥤ karoubi (simplicial_object C)`
 which shall be an equivalence for any additive category `C`.
 
+(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

@@ -2,14 +2,11 @@
 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.functor_gamma
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.DoldKan.SplitSimplicialObject
 
+#align_import algebraic_topology.dold_kan.functor_gamma from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 
 # Construction of the inverse functor of the Dold-Kan equivalence

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -59,6 +59,7 @@ def Isδ₀ {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] : Prop :=
 
 namespace Isδ₀
 
+#print AlgebraicTopology.DoldKan.Isδ₀.iff /-
 theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i = 0 :=
   by
   constructor
@@ -68,13 +69,16 @@ theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i =
   · rintro rfl
     exact ⟨rfl, Fin.succ_ne_zero _⟩
 #align algebraic_topology.dold_kan.is_δ₀.iff AlgebraicTopology.DoldKan.Isδ₀.iff
+-/
 
+#print AlgebraicTopology.DoldKan.Isδ₀.eq_δ₀ /-
 theorem eq_δ₀ {n : ℕ} {i : [n] ⟶ [n + 1]} [Mono i] (hi : Isδ₀ i) : i = SimplexCategory.δ 0 :=
   by
   obtain ⟨j, rfl⟩ := SimplexCategory.eq_δ_of_mono i
   rw [Iff] at hi 
   rw [hi]
 #align algebraic_topology.dold_kan.is_δ₀.eq_δ₀ AlgebraicTopology.DoldKan.Isδ₀.eq_δ₀
+-/
 
 end Isδ₀
 
@@ -124,6 +128,7 @@ theorem mapMono_id : mapMono K (𝟙 Δ) = 𝟙 _ := by unfold map_mono;
 
 variable {Δ}
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀' /-
 theorem mapMono_δ₀' (hi : Isδ₀ i) : mapMono K i = K.d Δ.len Δ'.len :=
   by
   unfold map_mono
@@ -132,15 +137,20 @@ theorem mapMono_δ₀' (hi : Isδ₀ i) : mapMono K i = K.d Δ.len Δ'.len :=
   rintro rfl
   simpa only [self_eq_add_right, Nat.one_ne_zero] using hi.1
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀' AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀'
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀ /-
 @[simp]
 theorem mapMono_δ₀ {n : ℕ} : mapMono K (δ (0 : Fin (n + 2))) = K.d (n + 1) n :=
   mapMono_δ₀' K _ (by rw [is_δ₀.iff])
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀ AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero /-
 theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i = 0 := by unfold map_mono;
   rw [Ne.def] at h₁ ; split_ifs; rfl
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero
+-/
 
 variable {K K'}
 
@@ -159,6 +169,7 @@ theorem mapMono_naturality : mapMono K i ≫ f.f Δ'.len = f.f Δ.len ≫ mapMon
 
 variable (K)
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_comp /-
 @[simp, reassoc]
 theorem mapMono_comp : mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i) :=
   by
@@ -187,6 +198,7 @@ theorem mapMono_comp : mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i) :=
     · simp only [map_mono_eq_zero K i' h₂ h₄, comp_zero]
   · simp only [map_mono_eq_zero K i h₁ h₃, zero_comp]
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_comp AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_comp
+-/
 
 end Termwise
 
@@ -261,6 +273,7 @@ def obj (K : ChainComplex C ℕ) : SimplicialObject C
 -/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
+#print AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_id /-
 theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
     SimplicialObject.Splitting.map (Γ₀.obj K)
         (fun n : ℕ => Sigma.ι (Γ₀.Obj.summand K (op [n])) (Splitting.IndexSet.id (op [n]))) Δ =
@@ -278,6 +291,7 @@ theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
     Γ₀.obj.termwise.map_mono_id, A.ext']
   apply id_comp
 #align algebraic_topology.dold_kan.Γ₀.splitting_map_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_id
+-/
 
 #print AlgebraicTopology.DoldKan.Γ₀.splitting /-
 /-- By construction, the simplicial `Γ₀.obj K` is equipped with a splitting. -/
@@ -291,11 +305,14 @@ def splitting (K : ChainComplex C ℕ) : SimplicialObject.Splitting (Γ₀.obj K
 #align algebraic_topology.dold_kan.Γ₀.splitting AlgebraicTopology.DoldKan.Γ₀.splitting
 -/
 
+#print AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id /-
 @[simp]
 theorem splitting_iso_hom_eq_id (Δ : SimplexCategoryᵒᵖ) : ((splitting K).Iso Δ).Hom = 𝟙 _ :=
   splitting_map_eq_id K Δ
 #align algebraic_topology.dold_kan.Γ₀.splitting_iso_hom_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand /-
 @[reassoc]
 theorem Obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ')
     {Δ'' : SimplexCategory} {e : Δ'.unop ⟶ Δ''} {i : Δ'' ⟶ A.1.unop} [Epi e] [Mono i]
@@ -307,21 +324,27 @@ theorem Obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.Index
   simp only [assoc, Γ₀.splitting_iso_hom_eq_id, id_comp, comp_id]
   exact Γ₀.obj.map_on_summand₀ K A fac
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand' /-
 @[reassoc]
 theorem Obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
     (splitting K).ιSummand A ≫ (obj K).map θ =
       Obj.Termwise.mapMono K (image.ι (θ.unop ≫ A.e)) ≫ (splitting K).ιSummand (A.pull θ) :=
   by apply obj.map_on_summand; apply image.fac
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id /-
 @[reassoc]
 theorem Obj.mapMono_on_summand_id {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
     (splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (obj K).map i.op =
       Obj.Termwise.mapMono K i ≫ (splitting K).ιSummand (Splitting.IndexSet.id (op Δ')) :=
   Obj.map_on_summand K (Splitting.IndexSet.id (op Δ)) i.op (rfl : 𝟙 _ ≫ i = i ≫ 𝟙 _)
 #align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id /-
 @[reassoc]
 theorem Obj.map_epi_on_summand_id {Δ Δ' : SimplexCategory} (e : Δ' ⟶ Δ) [Epi e] :
     (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (Γ₀.obj K).map e.op =
@@ -331,6 +354,7 @@ theorem Obj.map_epi_on_summand_id {Δ Δ' : SimplexCategory} (e : Δ' ⟶ Δ) [E
       (rfl : e ≫ 𝟙 Δ = e ≫ 𝟙 Δ),
     Γ₀.obj.termwise.map_mono_id] using id_comp _
 #align algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id
+-/
 
 #print AlgebraicTopology.DoldKan.Γ₀.map /-
 /-- The functor `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`, on morphisms. -/
@@ -351,6 +375,7 @@ end Γ₀
 
 variable [HasFiniteCoproducts C]
 
+#print AlgebraicTopology.DoldKan.Γ₀' /-
 /-- The functor `Γ₀' : chain_complex C ℕ ⥤ simplicial_object.split C`
 that induces `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`, which
 shall be the inverse functor of the Dold-Kan equivalence for
@@ -364,6 +389,7 @@ def Γ₀' : ChainComplex C ℕ ⥤ SimplicialObject.Split C
       f := f.f
       comm' := fun n => by dsimp; simpa only [← splitting.ι_summand_id, (Γ₀.splitting K).ι_desc] }
 #align algebraic_topology.dold_kan.Γ₀' AlgebraicTopology.DoldKan.Γ₀'
+-/
 
 #print AlgebraicTopology.DoldKan.Γ₀ /-
 /-- The functor `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`, which is
@@ -375,6 +401,7 @@ def Γ₀ : ChainComplex C ℕ ⥤ SimplicialObject C :=
 #align algebraic_topology.dold_kan.Γ₀ AlgebraicTopology.DoldKan.Γ₀
 -/
 
+#print AlgebraicTopology.DoldKan.Γ₂ /-
 /-- The extension of `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`
 on the idempotent completions. It shall be an equivalence of categories
 for any additive category `C`. -/
@@ -382,6 +409,7 @@ for any additive category `C`. -/
 def Γ₂ : Karoubi (ChainComplex C ℕ) ⥤ Karoubi (SimplicialObject C) :=
   (CategoryTheory.Idempotents.functorExtension₂ _ _).obj Γ₀
 #align algebraic_topology.dold_kan.Γ₂ AlgebraicTopology.DoldKan.Γ₂
+-/
 
 #print AlgebraicTopology.DoldKan.HigherFacesVanish.on_Γ₀_summand_id /-
 theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ) :
@@ -397,6 +425,7 @@ theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ)
 #align algebraic_topology.dold_kan.higher_faces_vanish.on_Γ₀_summand_id AlgebraicTopology.DoldKan.HigherFacesVanish.on_Γ₀_summand_id
 -/
 
+#print AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self /-
 @[simp, reassoc]
 theorem PInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n : ℕ} :
     (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) ≫ (PInfty : K[Γ₀.obj K] ⟶ _).f n =
@@ -407,6 +436,7 @@ theorem PInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n :
   · simpa only [P_f_0_eq] using comp_id _
   · exact (higher_faces_vanish.on_Γ₀_summand_id K n).comp_P_eq_self
 #align algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self
+-/
 
 end DoldKan

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -128,9 +128,9 @@ theorem mapMono_δ₀' (hi : Isδ₀ i) : mapMono K i = K.d Δ.len Δ'.len :=
   by
   unfold map_mono
   classical
-    rw [dif_neg, dif_pos hi]
-    rintro rfl
-    simpa only [self_eq_add_right, Nat.one_ne_zero] using hi.1
+  rw [dif_neg, dif_pos hi]
+  rintro rfl
+  simpa only [self_eq_add_right, Nat.one_ne_zero] using hi.1
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀' AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀'
 
 @[simp]

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -36,8 +36,8 @@ which shall be an equivalence for any additive category `C`.
 
 noncomputable section
 
-open
-  CategoryTheory CategoryTheory.Category CategoryTheory.Limits SimplexCategory SimplicialObject Opposite CategoryTheory.Idempotents
+open CategoryTheory CategoryTheory.Category CategoryTheory.Limits SimplexCategory SimplicialObject
+  Opposite CategoryTheory.Idempotents
 
 open scoped Simplicial DoldKan
 
@@ -72,7 +72,7 @@ theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i =
 theorem eq_δ₀ {n : ℕ} {i : [n] ⟶ [n + 1]} [Mono i] (hi : Isδ₀ i) : i = SimplexCategory.δ 0 :=
   by
   obtain ⟨j, rfl⟩ := SimplexCategory.eq_δ_of_mono i
-  rw [Iff] at hi
+  rw [Iff] at hi 
   rw [hi]
 #align algebraic_topology.dold_kan.is_δ₀.eq_δ₀ AlgebraicTopology.DoldKan.Isδ₀.eq_δ₀
 
@@ -107,7 +107,7 @@ zero otherwise. -/
 def mapMono (K : ChainComplex C ℕ) {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
     K.pt Δ.len ⟶ K.pt Δ'.len := by
   by_cases Δ = Δ'
-  · exact eq_to_hom (by congr )
+  · exact eq_to_hom (by congr)
   · by_cases is_δ₀ i
     · exact K.d Δ.len Δ'.len
     · exact 0
@@ -139,7 +139,7 @@ theorem mapMono_δ₀ {n : ℕ} : mapMono K (δ (0 : Fin (n + 2))) = K.d (n + 1)
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀ AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀
 
 theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i = 0 := by unfold map_mono;
-  rw [Ne.def] at h₁; split_ifs; rfl
+  rw [Ne.def] at h₁ ; split_ifs; rfl
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero
 
 variable {K K'}
@@ -178,7 +178,7 @@ theorem mapMono_comp : mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i) :=
   · by_contra
     simpa only [self_eq_add_right, h] using Eq
   · by_contra
-    simp only [h.1, add_right_inj] at eq
+    simp only [h.1, add_right_inj] at eq 
     linarith
   -- in all cases, the LHS is also zero, either by definition, or because d ≫ d = 0
   by_cases h₃ : is_δ₀ i
@@ -254,7 +254,7 @@ def obj (K : ChainComplex C ℕ) : SimplicialObject C
     cases A
     have fac : θ.unop ≫ θ'.unop ≫ A.e = (θ' ≫ θ).unop ≫ A.e := by rw [unop_comp, assoc]
     rw [← image.fac (θ'.unop ≫ A.e), ← assoc, ←
-      image.fac (θ.unop ≫ factor_thru_image (θ'.unop ≫ A.e)), assoc] at fac
+      image.fac (θ.unop ≫ factor_thru_image (θ'.unop ≫ A.e)), assoc] at fac 
     simpa only [obj.map_on_summand₀'_assoc K A θ', obj.map_on_summand₀' K _ θ,
       obj.termwise.map_mono_comp_assoc, obj.map_on_summand₀ K A fac]
 #align algebraic_topology.dold_kan.Γ₀.obj AlgebraicTopology.DoldKan.Γ₀.obj
@@ -389,7 +389,7 @@ theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ)
   by
   intro j hj
   have eq := Γ₀.obj.map_mono_on_summand_id K (SimplexCategory.δ j.succ)
-  rw [Γ₀.obj.termwise.map_mono_eq_zero K, zero_comp] at eq; rotate_left
+  rw [Γ₀.obj.termwise.map_mono_eq_zero K, zero_comp] at eq ; rotate_left
   · intro h
     exact (Nat.succ_ne_self n) (congr_arg SimplexCategory.len h)
   · exact fun h => Fin.succ_ne_zero j (by simpa only [is_δ₀.iff] using h)

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -39,7 +39,7 @@ noncomputable section
 open
   CategoryTheory CategoryTheory.Category CategoryTheory.Limits SimplexCategory SimplicialObject Opposite CategoryTheory.Idempotents
 
-open Simplicial DoldKan
+open scoped Simplicial DoldKan
 
 namespace AlgebraicTopology

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -59,12 +59,6 @@ def Isδ₀ {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] : Prop :=
 
 namespace Isδ₀
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.is_δ₀.iff AlgebraicTopology.DoldKan.Isδ₀.iffₓ'. -/
 theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i = 0 :=
   by
   constructor
@@ -75,12 +69,6 @@ theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i =
     exact ⟨rfl, Fin.succ_ne_zero _⟩
 #align algebraic_topology.dold_kan.is_δ₀.iff AlgebraicTopology.DoldKan.Isδ₀.iff
 
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 theorem eq_δ₀ {n : ℕ} {i : [n] ⟶ [n + 1]} [Mono i] (hi : Isδ₀ i) : i = SimplexCategory.δ 0 :=
   by
   obtain ⟨j, rfl⟩ := SimplexCategory.eq_δ_of_mono i
@@ -136,12 +124,6 @@ theorem mapMono_id : mapMono K (𝟙 Δ) = 𝟙 _ := by unfold map_mono;
 
 variable {Δ}
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀' AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀'ₓ'. -/
 theorem mapMono_δ₀' (hi : Isδ₀ i) : mapMono K i = K.d Δ.len Δ'.len :=
   by
   unfold map_mono
@@ -151,20 +133,11 @@ theorem mapMono_δ₀' (hi : Isδ₀ i) : mapMono K i = K.d Δ.len Δ'.len :=
     simpa only [self_eq_add_right, Nat.one_ne_zero] using hi.1
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀' AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀'
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀ AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀ₓ'. -/
 @[simp]
 theorem mapMono_δ₀ {n : ℕ} : mapMono K (δ (0 : Fin (n + 2))) = K.d (n + 1) n :=
   mapMono_δ₀' K _ (by rw [is_δ₀.iff])
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀ AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀
 
-/- warning: algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero -> AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zeroₓ'. -/
 theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i = 0 := by unfold map_mono;
   rw [Ne.def] at h₁; split_ifs; rfl
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero
@@ -186,12 +159,6 @@ theorem mapMono_naturality : mapMono K i ≫ f.f Δ'.len = f.f Δ.len ≫ mapMon
 
 variable (K)
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_comp AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_compₓ'. -/
 @[simp, reassoc]
 theorem mapMono_comp : mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i) :=
   by
@@ -293,12 +260,6 @@ def obj (K : ChainComplex C ℕ) : SimplicialObject C
 #align algebraic_topology.dold_kan.Γ₀.obj AlgebraicTopology.DoldKan.Γ₀.obj
 -/
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.splitting_map_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_idₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
 theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
     SimplicialObject.Splitting.map (Γ₀.obj K)
@@ -330,20 +291,11 @@ def splitting (K : ChainComplex C ℕ) : SimplicialObject.Splitting (Γ₀.obj K
 #align algebraic_topology.dold_kan.Γ₀.splitting AlgebraicTopology.DoldKan.Γ₀.splitting
 -/
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.splitting_iso_hom_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_idₓ'. -/
 @[simp]
 theorem splitting_iso_hom_eq_id (Δ : SimplexCategoryᵒᵖ) : ((splitting K).Iso Δ).Hom = 𝟙 _ :=
   splitting_map_eq_id K Δ
 #align algebraic_topology.dold_kan.Γ₀.splitting_iso_hom_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id
 
-/- warning: algebraic_topology.dold_kan.Γ₀.obj.map_on_summand -> AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summandₓ'. -/
 @[reassoc]
 theorem Obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ')
     {Δ'' : SimplexCategory} {e : Δ'.unop ⟶ Δ''} {i : Δ'' ⟶ A.1.unop} [Epi e] [Mono i]
@@ -356,9 +308,6 @@ theorem Obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.Index
   exact Γ₀.obj.map_on_summand₀ K A fac
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand
 
-/- warning: algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' -> AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'ₓ'. -/
 @[reassoc]
 theorem Obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
     (splitting K).ιSummand A ≫ (obj K).map θ =
@@ -366,9 +315,6 @@ theorem Obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.Inde
   by apply obj.map_on_summand; apply image.fac
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'
 
-/- warning: algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id -> AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_idₓ'. -/
 @[reassoc]
 theorem Obj.mapMono_on_summand_id {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
     (splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (obj K).map i.op =
@@ -376,9 +322,6 @@ theorem Obj.mapMono_on_summand_id {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [M
   Obj.map_on_summand K (Splitting.IndexSet.id (op Δ)) i.op (rfl : 𝟙 _ ≫ i = i ≫ 𝟙 _)
 #align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id
 
-/- warning: algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id -> AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_idₓ'. -/
 @[reassoc]
 theorem Obj.map_epi_on_summand_id {Δ Δ' : SimplexCategory} (e : Δ' ⟶ Δ) [Epi e] :
     (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (Γ₀.obj K).map e.op =
@@ -408,12 +351,6 @@ end Γ₀
 
 variable [HasFiniteCoproducts C]
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀' AlgebraicTopology.DoldKan.Γ₀'ₓ'. -/
 /-- The functor `Γ₀' : chain_complex C ℕ ⥤ simplicial_object.split C`
 that induces `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`, which
 shall be the inverse functor of the Dold-Kan equivalence for
@@ -438,12 +375,6 @@ def Γ₀ : ChainComplex C ℕ ⥤ SimplicialObject C :=
 #align algebraic_topology.dold_kan.Γ₀ AlgebraicTopology.DoldKan.Γ₀
 -/
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂ AlgebraicTopology.DoldKan.Γ₂ₓ'. -/
 /-- The extension of `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`
 on the idempotent completions. It shall be an equivalence of categories
 for any additive category `C`. -/
@@ -466,9 +397,6 @@ theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ)
 #align algebraic_topology.dold_kan.higher_faces_vanish.on_Γ₀_summand_id AlgebraicTopology.DoldKan.HigherFacesVanish.on_Γ₀_summand_id
 -/
 
-/- warning: algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self -> AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_selfₓ'. -/
 @[simp, reassoc]
 theorem PInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n : ℕ} :
     (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) ≫ (PInfty : K[Γ₀.obj K] ⟶ _).f n =

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -129,9 +129,7 @@ def mapMono (K : ChainComplex C ℕ) {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ)
 variable (Δ)
 
 #print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_id /-
-theorem mapMono_id : mapMono K (𝟙 Δ) = 𝟙 _ :=
-  by
-  unfold map_mono
+theorem mapMono_id : mapMono K (𝟙 Δ) = 𝟙 _ := by unfold map_mono;
   simp only [eq_self_iff_true, eq_to_hom_refl, dite_eq_ite, if_true]
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_id AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_id
 -/
@@ -167,12 +165,8 @@ theorem mapMono_δ₀ {n : ℕ} : mapMono K (δ (0 : Fin (n + 2))) = K.d (n + 1)
 /- warning: algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero -> AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zeroₓ'. -/
-theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i = 0 :=
-  by
-  unfold map_mono
-  rw [Ne.def] at h₁
-  split_ifs
-  rfl
+theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i = 0 := by unfold map_mono;
+  rw [Ne.def] at h₁; split_ifs; rfl
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero
 
 variable {K K'}
@@ -369,9 +363,7 @@ Case conversion may be inaccurate. Consider using '#align algebraic_topology.dol
 theorem Obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
     (splitting K).ιSummand A ≫ (obj K).map θ =
       Obj.Termwise.mapMono K (image.ι (θ.unop ≫ A.e)) ≫ (splitting K).ιSummand (A.pull θ) :=
-  by
-  apply obj.map_on_summand
-  apply image.fac
+  by apply obj.map_on_summand; apply image.fac
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'
 
 /- warning: algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id -> AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id is a dubious translation:
@@ -433,9 +425,7 @@ def Γ₀' : ChainComplex C ℕ ⥤ SimplicialObject.Split C
   map K K' f :=
     { f := Γ₀.map f
       f := f.f
-      comm' := fun n => by
-        dsimp
-        simpa only [← splitting.ι_summand_id, (Γ₀.splitting K).ι_desc] }
+      comm' := fun n => by dsimp; simpa only [← splitting.ι_summand_id, (Γ₀.splitting K).ι_desc] }
 #align algebraic_topology.dold_kan.Γ₀' AlgebraicTopology.DoldKan.Γ₀'
 
 #print AlgebraicTopology.DoldKan.Γ₀ /-

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -165,10 +165,7 @@ theorem mapMono_δ₀ {n : ℕ} : mapMono K (δ (0 : Fin (n + 2))) = K.d (n + 1)
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀ AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀
 
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SimplexCategory Δ' Δ) -> (Not (AlgebraicTopology.DoldKan.Isδ₀ Δ' Δ i _inst_4)) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat 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(HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zeroₓ'. -/
 theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i = 0 :=
   by
@@ -351,10 +348,7 @@ theorem splitting_iso_hom_eq_id (Δ : SimplexCategoryᵒᵖ) : ((splitting K).Is
 #align algebraic_topology.dold_kan.Γ₀.splitting_iso_hom_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id
 
 /- warning: algebraic_topology.dold_kan.Γ₀.obj.map_on_summand -> AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand is a dubious translation:
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(SimplicialObject.Splitting.IndexSet.mk (Opposite.unop.{1} SimplexCategory Δ') Δ'' e _inst_6))))
-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] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} {Δ' : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ') {Δ'' : SimplexCategory} {e : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') Δ''} {i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))} [_inst_6 : CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') Δ'' e] [_inst_7 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) i], (Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} 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SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A))) -> (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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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, 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(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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ Δ' θ)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.X.{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)) K (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)))) (HomologicalComplex.X.{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)) K (SimplexCategory.len 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ'))) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) i _inst_7) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ')) (SimplicialObject.Splitting.IndexSet.mk (Opposite.unop.{1} SimplexCategory Δ') Δ'' e _inst_6))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summandₓ'. -/
 @[reassoc]
 theorem Obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ')
@@ -369,10 +363,7 @@ theorem Obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.Index
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand
 
 /- warning: algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' -> AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand' 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] (K : 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) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} {Δ' : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ'), Eq.{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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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} 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SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)))) (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)) 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SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (CategoryTheory.Limits.HasImages.has_image.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.instHasStrongEpiMonoFactorisationsSimplexCategorySmallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} 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CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (CategoryTheory.Limits.HasImages.has_image.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.instHasStrongEpiMonoFactorisationsSimplexCategorySmallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} 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SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A))))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ' (SimplicialObject.Splitting.IndexSet.pull Δ A Δ' θ)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'ₓ'. -/
 @[reassoc]
 theorem Obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
@@ -384,10 +375,7 @@ theorem Obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.Inde
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'
 
 /- warning: algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id -> AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id 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] (K : 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) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : SimplexCategory} {Δ' : SimplexCategory} (i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ) [_inst_6 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ' Δ i], 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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 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 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(SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ)))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ')) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ))) 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K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ') (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ'))))
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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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ')) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ' Δ i _inst_6) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ') (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ'))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_idₓ'. -/
 @[reassoc]
 theorem Obj.mapMono_on_summand_id {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
@@ -397,10 +385,7 @@ theorem Obj.mapMono_on_summand_id {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [M
 #align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id
 
 /- warning: algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id -> AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_idₓ'. -/
 @[reassoc]
 theorem Obj.map_epi_on_summand_id {Δ Δ' : SimplexCategory} (e : Δ' ⟶ Δ) [Epi e] :
@@ -492,10 +477,7 @@ theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ)
 -/
 
 /- warning: algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self -> AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self is a dubious translation:
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(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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (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_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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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_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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n)) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_selfₓ'. -/
 @[simp, reassoc]
 theorem PInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n : ℕ} :

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -181,7 +181,7 @@ theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i =
 variable {K K'}
 
 #print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem mapMono_naturality : mapMono K i ≫ f.f Δ'.len = f.f Δ.len ≫ mapMono K' i :=
   by
   unfold map_mono
@@ -201,7 +201,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (K : 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)) {Δ'' : SimplexCategory} {Δ' : SimplexCategory} {Δ : SimplexCategory} (i' : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ') (_inst_3 : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ'') [i : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ Δ' i'] [_inst_4 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ' Δ'' _inst_3], Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ'')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ'')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ)) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ' Δ'' _inst_3 _inst_4) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ Δ' i' i)) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ Δ'' (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) Δ Δ' Δ'' i' _inst_3) (CategoryTheory.mono_comp.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ Δ' Δ'' i' i _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_comp AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_compₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem mapMono_comp : mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i) :=
   by
   -- case where i : Δ' ⟶ Δ is the identity
@@ -246,7 +246,7 @@ def map (K : ChainComplex C ℕ) {Δ' Δ : SimplexCategoryᵒᵖ} (θ : Δ ⟶ 
 -/
 
 #print AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀ /-
-@[reassoc.1]
+@[reassoc]
 theorem map_on_summand₀ {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) {θ : Δ ⟶ Δ'}
     {Δ'' : SimplexCategory} {e : Δ'.unop ⟶ Δ''} {i : Δ'' ⟶ A.1.unop} [Epi e] [Mono i]
     (fac : e ≫ i = θ.unop ≫ A.e) :
@@ -265,7 +265,7 @@ theorem map_on_summand₀ {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexS
 -/
 
 #print AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀' /-
-@[reassoc.1]
+@[reassoc]
 theorem map_on_summand₀' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
     Sigma.ι (summand K Δ) A ≫ map K θ =
       Termwise.mapMono K (image.ι (θ.unop ≫ A.e)) ≫ Sigma.ι (summand K _) (A.pull θ) :=
@@ -356,7 +356,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} {Δ' : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ') {Δ'' : SimplexCategory} {e : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') Δ''} {i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))} [_inst_6 : CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') Δ'' e] [_inst_7 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) i], (Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) e i) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A))) -> (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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ')) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ') (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ A) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ Δ' θ)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.X.{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)) K (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)))) (HomologicalComplex.X.{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)) K (SimplexCategory.len 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ'))) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) i _inst_7) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ')) (SimplicialObject.Splitting.IndexSet.mk (Opposite.unop.{1} SimplexCategory Δ') Δ'' e _inst_6))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summandₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem Obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ')
     {Δ'' : SimplexCategory} {e : Δ'.unop ⟶ Δ''} {i : Δ'' ⟶ A.1.unop} [Epi e] [Mono i]
     (fac : e ≫ i = θ.unop ≫ A.e) :
@@ -374,7 +374,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} {Δ' : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ'), Eq.{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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ')) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ') (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ A) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ Δ' θ)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.X.{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 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SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (HomologicalComplex.X.{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)) K (SimplexCategory.len (CategoryTheory.Limits.image.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (CategoryTheory.Limits.HasImages.has_image.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.instHasStrongEpiMonoFactorisationsSimplexCategorySmallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)))))) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ') (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K (CategoryTheory.Limits.image.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (CategoryTheory.Limits.HasImages.has_image.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.instHasStrongEpiMonoFactorisationsSimplexCategorySmallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)))) (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.Limits.image.ι.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (CategoryTheory.Limits.HasImages.has_image.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.instHasStrongEpiMonoFactorisationsSimplexCategorySmallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)))) (CategoryTheory.Limits.instMonoImageι.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (CategoryTheory.Limits.HasImages.has_image.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.instHasStrongEpiMonoFactorisationsSimplexCategorySmallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A))))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ' (SimplicialObject.Splitting.IndexSet.pull Δ A Δ' θ)))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem Obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
     (splitting K).ιSummand A ≫ (obj K).map θ =
       Obj.Termwise.mapMono K (image.ι (θ.unop ≫ A.e)) ≫ (splitting K).ιSummand (A.pull θ) :=
@@ -389,7 +389,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : SimplexCategory} {Δ' : SimplexCategory} (i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ) [_inst_6 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ' Δ i], 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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 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 (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ'))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 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 (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ')) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ))) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ) (Opposite.op.{1} SimplexCategory Δ') (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ i))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ)) (HomologicalComplex.X.{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)) K (SimplexCategory.len 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ')) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ' Δ i _inst_6) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ') (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ'))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_idₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem Obj.mapMono_on_summand_id {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
     (splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (obj K).map i.op =
       Obj.Termwise.mapMono K i ≫ (splitting K).ιSummand (Splitting.IndexSet.id (op Δ')) :=
@@ -402,7 +402,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : SimplexCategory} {Δ' : SimplexCategory} (e : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ) [_inst_6 : CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ' Δ e], 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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 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 (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ'))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 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 (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ')) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ))) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ) (Opposite.op.{1} SimplexCategory Δ') (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ e))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ') (SimplicialObject.Splitting.IndexSet.mk Δ' Δ e _inst_6))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_idₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem Obj.map_epi_on_summand_id {Δ Δ' : SimplexCategory} (e : Δ' ⟶ Δ) [Epi e] :
     (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (Γ₀.obj K).map e.op =
       (Γ₀.splitting K).ιSummand (Splitting.IndexSet.mk e) :=
@@ -497,7 +497,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] (K : 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)) {n : Nat}, Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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_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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (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_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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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_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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n)) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_selfₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem PInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n : ℕ} :
     (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) ≫ (PInfty : K[Γ₀.obj K] ⟶ _).f n =
       (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) :=

bump to nightly-2023-04-28-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

473bb540

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.functor_gamma
-! leanprover-community/mathlib commit 5b8284148e8149728f4b90624888d98c36284454
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.AlgebraicTopology.DoldKan.SplitSimplicialObject
 
 # Construction of the inverse functor of the Dold-Kan equivalence
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 
 In this file, we construct the functor `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`
 which shall be the inverse functor of the Dold-Kan equivalence in the case of abelian categories,

bump to nightly-2023-04-22-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0

21a90077

Diff

@@ -45,15 +45,23 @@ namespace DoldKan
 variable {C : Type _} [Category C] [Preadditive C] (K K' : ChainComplex C ℕ) (f : K ⟶ K')
   {Δ'' Δ' Δ : SimplexCategory} (i' : Δ'' ⟶ Δ') [Mono i'] (i : Δ' ⟶ Δ) [Mono i]
 
+#print AlgebraicTopology.DoldKan.Isδ₀ /-
 /-- `is_δ₀ i` is a simple condition used to check whether a monomorphism `i` in
 `simplex_category` identifies to the coface map `δ 0`. -/
 @[nolint unused_arguments]
 def Isδ₀ {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] : Prop :=
   Δ.len = Δ'.len + 1 ∧ i.toOrderHom 0 ≠ 0
 #align algebraic_topology.dold_kan.is_δ₀ AlgebraicTopology.DoldKan.Isδ₀
+-/
 
 namespace Isδ₀
 
+/- warning: algebraic_topology.dold_kan.is_δ₀.iff -> AlgebraicTopology.DoldKan.Isδ₀.iff is a dubious translation:
+lean 3 declaration is
+  forall {j : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, Iff (AlgebraicTopology.DoldKan.Isδ₀ (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SimplexCategory.mk j) (SimplexCategory.δ j i) (SimplexCategory.δ.CategoryTheory.mono j i)) (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall {j : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) j (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, Iff (AlgebraicTopology.DoldKan.Isδ₀ (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) j (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk j) (SimplexCategory.δ j i) (SimplexCategory.instMonoSimplexCategorySmallCategoryMkHAddNatInstHAddInstAddNatOfNatInstOfNatNatδ j i)) (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) j (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) j (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) j (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) j (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.is_δ₀.iff AlgebraicTopology.DoldKan.Isδ₀.iffₓ'. -/
 theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i = 0 :=
   by
   constructor
@@ -64,6 +72,12 @@ theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i =
     exact ⟨rfl, Fin.succ_ne_zero _⟩
 #align algebraic_topology.dold_kan.is_δ₀.iff AlgebraicTopology.DoldKan.Isδ₀.iff
 
+/- warning: algebraic_topology.dold_kan.is_δ₀.eq_δ₀ -> AlgebraicTopology.DoldKan.Isδ₀.eq_δ₀ is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat} {i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))} [_inst_5 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i], (AlgebraicTopology.DoldKan.Isδ₀ (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SimplexCategory.mk n) i _inst_5) -> (Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) i (SimplexCategory.δ n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (NeZero.succ (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 {n : Nat} {i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))} [_inst_5 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i], (AlgebraicTopology.DoldKan.Isδ₀ (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) i _inst_5) -> (Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) i (SimplexCategory.δ n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (NeZero.succ (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 algebraic_topology.dold_kan.is_δ₀.eq_δ₀ AlgebraicTopology.DoldKan.Isδ₀.eq_δ₀ₓ'. -/
 theorem eq_δ₀ {n : ℕ} {i : [n] ⟶ [n + 1]} [Mono i] (hi : Isδ₀ i) : i = SimplexCategory.δ 0 :=
   by
   obtain ⟨j, rfl⟩ := SimplexCategory.eq_δ_of_mono i
@@ -77,20 +91,25 @@ namespace Γ₀
 
 namespace Obj
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.summand /-
 /-- In the definition of `(Γ₀.obj K).obj Δ` as a direct sum indexed by `A : splitting.index_set Δ`,
 the summand `summand K Δ A` is `K.X A.1.len`. -/
 def summand (Δ : SimplexCategoryᵒᵖ) (A : Splitting.IndexSet Δ) : C :=
   K.pt A.1.unop.len
 #align algebraic_topology.dold_kan.Γ₀.obj.summand AlgebraicTopology.DoldKan.Γ₀.Obj.summand
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.obj₂ /-
 /-- The functor `Γ₀` sends a chain complex `K` to the simplicial object which
 sends `Δ` to the direct sum of the objects `summand K Δ A` for all `A : splitting.index_set Δ` -/
 def obj₂ (K : ChainComplex C ℕ) (Δ : SimplexCategoryᵒᵖ) [HasFiniteCoproducts C] : C :=
   ∐ fun A : Splitting.IndexSet Δ => summand K Δ A
 #align algebraic_topology.dold_kan.Γ₀.obj.obj₂ AlgebraicTopology.DoldKan.Γ₀.Obj.obj₂
+-/
 
 namespace Termwise
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono /-
 /-- A monomorphism `i : Δ' ⟶ Δ` induces a morphism `K.X Δ.len ⟶ K.X Δ'.len` which
 is the identity if `Δ = Δ'`, the differential on the complex `K` if `i = δ 0`, and
 zero otherwise. -/
@@ -102,17 +121,26 @@ def mapMono (K : ChainComplex C ℕ) {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ)
     · exact K.d Δ.len Δ'.len
     · exact 0
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono
+-/
 
 variable (Δ)
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_id /-
 theorem mapMono_id : mapMono K (𝟙 Δ) = 𝟙 _ :=
   by
   unfold map_mono
   simp only [eq_self_iff_true, eq_to_hom_refl, dite_eq_ite, if_true]
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_id AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_id
+-/
 
 variable {Δ}
 
+/- warning: algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀' -> AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀' 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] (K : 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) {Δ' : SimplexCategory} {Δ : SimplexCategory} (i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ) [_inst_4 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ' Δ i], (AlgebraicTopology.DoldKan.Isδ₀ Δ Δ' i _inst_4) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ'))) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ' Δ i _inst_4) (HomologicalComplex.d.{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) K (SimplexCategory.len Δ) (SimplexCategory.len Δ')))
+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] (K : 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)) {Δ' : SimplexCategory} {Δ : SimplexCategory} (i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ') [_inst_4 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ Δ' i], (AlgebraicTopology.DoldKan.Isδ₀ Δ' Δ i _inst_4) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ))) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ Δ' i _inst_4) (HomologicalComplex.d.{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)) K (SimplexCategory.len Δ') (SimplexCategory.len Δ)))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀' AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀'ₓ'. -/
 theorem mapMono_δ₀' (hi : Isδ₀ i) : mapMono K i = K.d Δ.len Δ'.len :=
   by
   unfold map_mono
@@ -122,11 +150,23 @@ theorem mapMono_δ₀' (hi : Isδ₀ i) : mapMono K i = K.d Δ.len Δ'.len :=
     simpa only [self_eq_add_right, Nat.one_ne_zero] using hi.1
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀' AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀'
 
+/- warning: algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀ -> AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀ 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 algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀ AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀ₓ'. -/
 @[simp]
 theorem mapMono_δ₀ {n : ℕ} : mapMono K (δ (0 : Fin (n + 2))) = K.d (n + 1) n :=
   mapMono_δ₀' K _ (by rw [is_δ₀.iff])
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_δ₀ AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀
 
+/- warning: algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero -> AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero is a dubious translation:
+lean 3 declaration is
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(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) K (SimplexCategory.len Δ'))) 0 (OfNat.mk.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ'))) 0 (Zero.zero.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ'))) (CategoryTheory.Limits.HasZeroMorphisms.hasZero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ')))))))
+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] (K : 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)) {Δ' : SimplexCategory} {Δ : SimplexCategory} (i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ') [_inst_4 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ Δ' i], (Ne.{1} SimplexCategory Δ' Δ) -> (Not (AlgebraicTopology.DoldKan.Isδ₀ Δ' Δ i _inst_4)) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ))) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ Δ' i _inst_4) (OfNat.ofNat.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ))) 0 (Zero.toOfNat0.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zeroₓ'. -/
 theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i = 0 :=
   by
   unfold map_mono
@@ -137,6 +177,7 @@ theorem mapMono_eq_zero (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i =
 
 variable {K K'}
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality /-
 @[simp, reassoc.1]
 theorem mapMono_naturality : mapMono K i ≫ f.f Δ'.len = f.f Δ.len ≫ mapMono K' i :=
   by
@@ -147,9 +188,16 @@ theorem mapMono_naturality : mapMono K i ≫ f.f Δ'.len = f.f Δ.len ≫ mapMon
   · rw [HomologicalComplex.Hom.comm]
   · rw [zero_comp, comp_zero]
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_naturality AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality
+-/
 
 variable (K)
 
+/- warning: algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_comp -> AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_comp 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] (K : 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) {Δ'' : SimplexCategory} {Δ' : SimplexCategory} {Δ : SimplexCategory} (i' : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ'' Δ') [_inst_3 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ'' Δ' i'] (i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ) [_inst_4 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ' Δ i], Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ''))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ)) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ')) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ'')) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ' Δ i _inst_4) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ'' Δ' i' _inst_3)) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ'' Δ (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) Δ'' Δ' Δ i' i) (CategoryTheory.mono_comp.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ'' Δ' Δ i' _inst_3 i _inst_4))
+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] (K : 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)) {Δ'' : SimplexCategory} {Δ' : SimplexCategory} {Δ : SimplexCategory} (i' : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ') (_inst_3 : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ'') [i : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ Δ' i'] [_inst_4 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ' Δ'' _inst_3], Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ'')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ'')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ')) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ)) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ' Δ'' _inst_3 _inst_4) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ Δ' i' i)) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ Δ'' (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) Δ Δ' Δ'' i' _inst_3) (CategoryTheory.mono_comp.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ Δ' Δ'' i' i _inst_3 _inst_4))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_comp AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_compₓ'. -/
 @[simp, reassoc.1]
 theorem mapMono_comp : mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i) :=
   by
@@ -183,6 +231,7 @@ end Termwise
 
 variable [HasFiniteCoproducts C]
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.map /-
 /-- The simplicial morphism on the simplicial object `Γ₀.obj K` induced by
 a morphism `Δ' → Δ` in `simplex_category` is defined on each summand
 associated to an `A : Γ_index_set Δ` in terms of the epi-mono factorisation
@@ -191,7 +240,9 @@ def map (K : ChainComplex C ℕ) {Δ' Δ : SimplexCategoryᵒᵖ} (θ : Δ ⟶ 
   Sigma.desc fun A =>
     Termwise.mapMono K (image.ι (θ.unop ≫ A.e)) ≫ Sigma.ι (summand K Δ') (A.pull θ)
 #align algebraic_topology.dold_kan.Γ₀.obj.map AlgebraicTopology.DoldKan.Γ₀.Obj.map
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀ /-
 @[reassoc.1]
 theorem map_on_summand₀ {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) {θ : Δ ⟶ Δ'}
     {Δ'' : SimplexCategory} {e : Δ'.unop ⟶ Δ''} {i : Δ'' ⟶ A.1.unop} [Epi e] [Mono i]
@@ -208,18 +259,22 @@ theorem map_on_summand₀ {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexS
     congr
     exact SimplexCategory.factorThruImage_eq fac
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand₀ AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀' /-
 @[reassoc.1]
 theorem map_on_summand₀' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
     Sigma.ι (summand K Δ) A ≫ map K θ =
       Termwise.mapMono K (image.ι (θ.unop ≫ A.e)) ≫ Sigma.ι (summand K _) (A.pull θ) :=
   map_on_summand₀ K A (A.fac_pull θ)
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand₀' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀'
+-/
 
 end Obj
 
 variable [HasFiniteCoproducts C]
 
+#print AlgebraicTopology.DoldKan.Γ₀.obj /-
 /-- The functor `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`, on objects. -/
 @[simps]
 def obj (K : ChainComplex C ℕ) : SimplicialObject C
@@ -242,7 +297,14 @@ def obj (K : ChainComplex C ℕ) : SimplicialObject C
     simpa only [obj.map_on_summand₀'_assoc K A θ', obj.map_on_summand₀' K _ θ,
       obj.termwise.map_mono_comp_assoc, obj.map_on_summand₀ K A fac]
 #align algebraic_topology.dold_kan.Γ₀.obj AlgebraicTopology.DoldKan.Γ₀.obj
+-/
 
+/- warning: algebraic_topology.dold_kan.Γ₀.splitting_map_eq_id -> AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_id 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] (K : 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) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{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)) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (fun (n : Nat) => AlgebraicTopology.DoldKan.Γ₀.Obj.summand.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) Δ _inst_5) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ)) (SimplicialObject.Splitting.map.{u1, u2} C _inst_1 (fun (n : Nat) => AlgebraicTopology.DoldKan.Γ₀.Obj.summand.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (fun (n : Nat) => CategoryTheory.Limits.Sigma.ι.{0, u2, u1} (SimplicialObject.Splitting.IndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.Obj.summand.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (AlgebraicTopology.DoldKan.Γ₀.Obj.obj₂._proof_1.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) _inst_5) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) _inst_5 Δ) (CategoryTheory.CategoryStruct.id.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (fun (n : Nat) => AlgebraicTopology.DoldKan.Γ₀.Obj.summand.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) Δ _inst_5))
+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] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{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)) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (fun (n : Nat) => AlgebraicTopology.DoldKan.Γ₀.Obj.summand.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) Δ _inst_5) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ)) (SimplicialObject.Splitting.map.{u1, u2} C _inst_1 (fun (n : Nat) => AlgebraicTopology.DoldKan.Γ₀.Obj.summand.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (fun (n : Nat) => CategoryTheory.Limits.Sigma.ι.{0, u2, u1} (SimplicialObject.Splitting.IndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.Obj.summand.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Limits.hasColimitOfHasColimitsOfShape.{0, 0, u2, u1} C _inst_1 (CategoryTheory.Discrete.{0} (SimplicialObject.Splitting.IndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.discreteCategory.{0} (SimplicialObject.Splitting.IndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.Limits.hasColimitsOfShape_discrete.{0, u2, u1} C _inst_1 _inst_5 (SimplicialObject.Splitting.IndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Finite.of_fintype.{0} (SimplicialObject.Splitting.IndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (SimplicialObject.Splitting.IndexSet.instFintypeIndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))) (CategoryTheory.Discrete.functor.{u2, 0, u1} C _inst_1 (SimplicialObject.Splitting.IndexSet (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (AlgebraicTopology.DoldKan.Γ₀.Obj.summand.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) _inst_5 Δ) (CategoryTheory.CategoryStruct.id.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (fun (n : Nat) => AlgebraicTopology.DoldKan.Γ₀.Obj.summand.{u1, u2} C _inst_1 _inst_2 K (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) Δ _inst_5))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.splitting_map_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_idₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
 theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
     SimplicialObject.Splitting.map (Γ₀.obj K)
@@ -262,6 +324,7 @@ theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
   apply id_comp
 #align algebraic_topology.dold_kan.Γ₀.splitting_map_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_id
 
+#print AlgebraicTopology.DoldKan.Γ₀.splitting /-
 /-- By construction, the simplicial `Γ₀.obj K` is equipped with a splitting. -/
 def splitting (K : ChainComplex C ℕ) : SimplicialObject.Splitting (Γ₀.obj K)
     where
@@ -271,14 +334,27 @@ def splitting (K : ChainComplex C ℕ) : SimplicialObject.Splitting (Γ₀.obj K
     rw [Γ₀.splitting_map_eq_id]
     apply is_iso.id
 #align algebraic_topology.dold_kan.Γ₀.splitting AlgebraicTopology.DoldKan.Γ₀.splitting
+-/
 
+/- warning: algebraic_topology.dold_kan.Γ₀.splitting_iso_hom_eq_id -> AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id 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] (K : 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) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{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)) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ _inst_5) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ)) (CategoryTheory.Iso.hom.{u2, u1} C _inst_1 (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ _inst_5) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ) (SimplicialObject.Splitting.iso.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ)) (CategoryTheory.CategoryStruct.id.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ _inst_5))
+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] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{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)) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ _inst_5) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ)) (CategoryTheory.Iso.hom.{u2, u1} C _inst_1 (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ _inst_5) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ) (SimplicialObject.Splitting.iso.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ)) (CategoryTheory.CategoryStruct.id.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.coprod.{u1, u2} C _inst_1 (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) Δ _inst_5))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.splitting_iso_hom_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_idₓ'. -/
 @[simp]
 theorem splitting_iso_hom_eq_id (Δ : SimplexCategoryᵒᵖ) : ((splitting K).Iso Δ).Hom = 𝟙 _ :=
   splitting_map_eq_id K Δ
 #align algebraic_topology.dold_kan.Γ₀.splitting_iso_hom_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id
 
+/- warning: algebraic_topology.dold_kan.Γ₀.obj.map_on_summand -> AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand 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] (K : 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) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} {Δ' : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ') {Δ'' : SimplexCategory} {e : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') Δ''} {i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))} [_inst_6 : CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') Δ'' e] [_inst_7 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) i], (Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) e i) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A))) -> (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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ')) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ') (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ A) (CategoryTheory.Functor.map.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ Δ' θ)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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)))) (HomologicalComplex.x.{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) K (SimplexCategory.len Δ'')) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ') (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) i _inst_7) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ')) (SimplicialObject.Splitting.IndexSet.mk (Opposite.unop.{1} SimplexCategory Δ') Δ'' e _inst_6))))
+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] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} {Δ' : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory))) Δ Δ') {Δ'' : SimplexCategory} {e : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') Δ''} {i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))} [_inst_6 : CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') Δ'' e] [_inst_7 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) i], (Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') Δ'' (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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(SimplicialObject.Splitting.IndexSet.e Δ 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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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, 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SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)))) (HomologicalComplex.X.{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)) K (SimplexCategory.len 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory (Opposite.unop.{1} SimplexCategory Δ'))) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ'' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory 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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summandₓ'. -/
 @[reassoc.1]
-theorem obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ')
+theorem Obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ')
     {Δ'' : SimplexCategory} {e : Δ'.unop ⟶ Δ''} {i : Δ'' ⟶ A.1.unop} [Epi e] [Mono i]
     (fac : e ≫ i = θ.unop ≫ A.e) :
     (Γ₀.splitting K).ιSummand A ≫ (Γ₀.obj K).map θ =
@@ -287,34 +363,53 @@ theorem obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.Index
   dsimp only [SimplicialObject.Splitting.ιSummand, SimplicialObject.Splitting.ιCoprod]
   simp only [assoc, Γ₀.splitting_iso_hom_eq_id, id_comp, comp_id]
   exact Γ₀.obj.map_on_summand₀ K A fac
-#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.obj.map_on_summand
-
+#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand
+
+/- warning: algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' -> AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand' is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ') (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K (CategoryTheory.Limits.image.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (CategoryTheory.Limits.HasImages.hasImage.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.CategoryTheory.Limits.hasStrongEpiMonoFactorisations) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)))) (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.Limits.image.ι.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (CategoryTheory.Limits.HasImages.hasImage.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.CategoryTheory.Limits.hasStrongEpiMonoFactorisations) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)))) (CategoryTheory.Limits.image.ι.CategoryTheory.mono.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)) (CategoryTheory.Limits.HasImages.hasImage.{0, 0} SimplexCategory SimplexCategory.smallCategory (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{0, 0} SimplexCategory SimplexCategory.smallCategory SimplexCategory.CategoryTheory.Limits.hasStrongEpiMonoFactorisations) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ') α)) A)) (Quiver.Hom.unop.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A))))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ' (SimplicialObject.Splitting.IndexSet.pull Δ' Δ A θ)))
+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] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : Opposite.{1} SimplexCategory} {Δ' : Opposite.{1} SimplexCategory} (A : SimplicialObject.Splitting.IndexSet Δ) (θ : Quiver.Hom.{1, 0} (Opposite.{1} SimplexCategory) (Quiver.opposite.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory 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(CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A)))) (CategoryTheory.Limits.instMonoImageι.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory Δ') (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) (fun (α : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory Δ) (Opposite.unop.{1} SimplexCategory Δ')) => 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SimplexCategory.smallCategory)) Δ Δ' θ) (SimplicialObject.Splitting.IndexSet.e Δ A))))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) Δ' (SimplicialObject.Splitting.IndexSet.pull Δ A Δ' θ)))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'ₓ'. -/
 @[reassoc.1]
-theorem obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
+theorem Obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
     (splitting K).ιSummand A ≫ (obj K).map θ =
       Obj.Termwise.mapMono K (image.ι (θ.unop ≫ A.e)) ≫ (splitting K).ιSummand (A.pull θ) :=
   by
   apply obj.map_on_summand
   apply image.fac
-#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.obj.map_on_summand'
-
+#align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'
+
+/- warning: algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id -> AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id 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] (K : 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) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : SimplexCategory} {Δ' : SimplexCategory} (i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ) [_inst_6 : CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ' Δ i], 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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 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 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(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) K (SimplexCategory.len Δ')) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ')) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ' (Opposite.unop.{1} SimplexCategory (Sigma.fst.{0, 0} (Opposite.{1} SimplexCategory) (fun (Δ' : Opposite.{1} SimplexCategory) => Subtype.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (Opposite.unop.{1} SimplexCategory (Opposite.op.{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 (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ')) => CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory Δ)) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ)))) i _inst_6) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ') (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ'))))
+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] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : SimplexCategory} {Δ' : SimplexCategory} (i : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ) [_inst_6 : CategoryTheory.Mono.{0, 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(AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ) (Opposite.op.{1} SimplexCategory Δ') (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ i))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.X.{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)) K (SimplexCategory.len Δ)) (HomologicalComplex.X.{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)) K (SimplexCategory.len 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ')) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 K Δ' Δ i _inst_6) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ') (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ'))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_idₓ'. -/
 @[reassoc.1]
-theorem obj.mapMono_on_summand_id {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
+theorem Obj.mapMono_on_summand_id {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
     (splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (obj K).map i.op =
       Obj.Termwise.mapMono K i ≫ (splitting K).ιSummand (Splitting.IndexSet.id (op Δ')) :=
-  obj.map_on_summand K (Splitting.IndexSet.id (op Δ)) i.op (rfl : 𝟙 _ ≫ i = i ≫ 𝟙 _)
-#align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.obj.mapMono_on_summand_id
-
+  Obj.map_on_summand K (Splitting.IndexSet.id (op Δ)) i.op (rfl : 𝟙 _ ≫ i = i ≫ 𝟙 _)
+#align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id
+
+/- warning: algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id -> AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id 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] (K : 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) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : SimplexCategory} {Δ' : SimplexCategory} (e : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ) [_inst_6 : CategoryTheory.Epi.{0, 0} SimplexCategory SimplexCategory.smallCategory Δ' Δ e], 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_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 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 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+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] (K : 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)) [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] {Δ : SimplexCategory} {Δ' : SimplexCategory} (e : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ) [_inst_6 : CategoryTheory.Epi.{0, 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(CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ'))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 Δ)) (Opposite.unop.{1} SimplexCategory Δ')) (fun 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C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory 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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ')) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory Δ))) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (Opposite.op.{1} SimplexCategory Δ) (Opposite.op.{1} SimplexCategory Δ') (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ' Δ e))) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory Δ') (SimplicialObject.Splitting.IndexSet.mk Δ' Δ e _inst_6))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_idₓ'. -/
 @[reassoc.1]
-theorem obj.map_epi_on_summand_id {Δ Δ' : SimplexCategory} (e : Δ' ⟶ Δ) [Epi e] :
+theorem Obj.map_epi_on_summand_id {Δ Δ' : SimplexCategory} (e : Δ' ⟶ Δ) [Epi e] :
     (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (Γ₀.obj K).map e.op =
       (Γ₀.splitting K).ιSummand (Splitting.IndexSet.mk e) :=
   by
   simpa only [Γ₀.obj.map_on_summand K (splitting.index_set.id (op Δ)) e.op
       (rfl : e ≫ 𝟙 Δ = e ≫ 𝟙 Δ),
     Γ₀.obj.termwise.map_mono_id] using id_comp _
-#align algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id AlgebraicTopology.DoldKan.Γ₀.obj.map_epi_on_summand_id
+#align algebraic_topology.dold_kan.Γ₀.obj.map_epi_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id
 
+#print AlgebraicTopology.DoldKan.Γ₀.map /-
 /-- The functor `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`, on morphisms. -/
 @[simps]
 def map {K K' : ChainComplex C ℕ} (f : K ⟶ K') : obj K ⟶ obj K'
@@ -327,11 +422,18 @@ def map {K K' : ChainComplex C ℕ} (f : K ⟶ K') : obj K ⟶ obj K'
       assoc, obj.map_on_summand' K' _ θ]
     apply obj.termwise.map_mono_naturality_assoc
 #align algebraic_topology.dold_kan.Γ₀.map AlgebraicTopology.DoldKan.Γ₀.map
+-/
 
 end Γ₀
 
 variable [HasFiniteCoproducts C]
 
+/- warning: algebraic_topology.dold_kan.Γ₀' -> AlgebraicTopology.DoldKan.Γ₀' 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_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], CategoryTheory.Functor.{u2, u2, max u1 u2, max u1 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))))) 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)) (SimplicialObject.Split.{u1, u2} C _inst_1 _inst_5) (SimplicialObject.Split.CategoryTheory.category.{u1, u2} C _inst_1 _inst_5)
+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_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], CategoryTheory.Functor.{u2, u2, max u1 u2, max u2 u1} (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.{u1, u2} C _inst_1 _inst_5) (SimplicialObject.instCategorySplit.{u1, u2} C _inst_1 _inst_5)
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀' AlgebraicTopology.DoldKan.Γ₀'ₓ'. -/
 /-- The functor `Γ₀' : chain_complex C ℕ ⥤ simplicial_object.split C`
 that induces `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`, which
 shall be the inverse functor of the Dold-Kan equivalence for
@@ -348,6 +450,7 @@ def Γ₀' : ChainComplex C ℕ ⥤ SimplicialObject.Split C
         simpa only [← splitting.ι_summand_id, (Γ₀.splitting K).ι_desc] }
 #align algebraic_topology.dold_kan.Γ₀' AlgebraicTopology.DoldKan.Γ₀'
 
+#print AlgebraicTopology.DoldKan.Γ₀ /-
 /-- The functor `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`, which is
 the inverse functor of the Dold-Kan equivalence when `C` is an abelian
 category, or more generally a pseudoabelian category. -/
@@ -355,7 +458,14 @@ category, or more generally a pseudoabelian category. -/
 def Γ₀ : ChainComplex C ℕ ⥤ SimplicialObject C :=
   Γ₀' ⋙ Split.forget _
 #align algebraic_topology.dold_kan.Γ₀ AlgebraicTopology.DoldKan.Γ₀
+-/
 
+/- warning: algebraic_topology.dold_kan.Γ₂ -> AlgebraicTopology.DoldKan.Γ₂ 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_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], CategoryTheory.Functor.{u2, u2, max u1 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_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))) (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_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))) (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1], CategoryTheory.Functor.{u2, u2, max u1 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_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.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂ AlgebraicTopology.DoldKan.Γ₂ₓ'. -/
 /-- The extension of `Γ₀ : chain_complex C ℕ ⥤ simplicial_object C`
 on the idempotent completions. It shall be an equivalence of categories
 for any additive category `C`. -/
@@ -364,6 +474,7 @@ def Γ₂ : Karoubi (ChainComplex C ℕ) ⥤ Karoubi (SimplicialObject C) :=
   (CategoryTheory.Idempotents.functorExtension₂ _ _).obj Γ₀
 #align algebraic_topology.dold_kan.Γ₂ AlgebraicTopology.DoldKan.Γ₂
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.on_Γ₀_summand_id /-
 theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ) :
     HigherFacesVanish (n + 1) ((Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n + 1]))) :=
   by
@@ -375,9 +486,16 @@ theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ)
   · exact fun h => Fin.succ_ne_zero j (by simpa only [is_δ₀.iff] using h)
   exact Eq
 #align algebraic_topology.dold_kan.higher_faces_vanish.on_Γ₀_summand_id AlgebraicTopology.DoldKan.HigherFacesVanish.on_Γ₀_summand_id
+-/
 
+/- warning: algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self -> AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self 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_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] (K : 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) {n : Nat}, Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.n.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 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SimplexCategory.smallCategory (Opposite.unop.{1} SimplexCategory (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Opposite.unop.{1} SimplexCategory Δ') α)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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_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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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_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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n)) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasFiniteCoproducts.{u2, u1} C _inst_1] (K : 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)) {n : Nat}, Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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_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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (SimplicialObject.Splitting.N.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (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_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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (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_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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K)) n)) (SimplicialObject.Splitting.ιSummand.{u1, u2} C _inst_1 _inst_5 (AlgebraicTopology.DoldKan.Γ₀.obj.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (AlgebraicTopology.DoldKan.Γ₀.splitting.{u1, u2} C _inst_1 _inst_2 _inst_5 K) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (SimplicialObject.Splitting.IndexSet.id (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_selfₓ'. -/
 @[simp, reassoc.1]
-theorem pInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n : ℕ} :
+theorem PInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n : ℕ} :
     (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) ≫ (PInfty : K[Γ₀.obj K] ⟶ _).f n =
       (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) :=
   by
@@ -385,7 +503,7 @@ theorem pInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n :
   cases n
   · simpa only [P_f_0_eq] using comp_id _
   · exact (higher_faces_vanish.on_Γ₀_summand_id K n).comp_P_eq_self
-#align algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self AlgebraicTopology.DoldKan.pInfty_on_Γ₀_splitting_summand_eq_self
+#align algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self
 
 end DoldKan

bump to nightly-2023-04-20-20

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

e863e061

Diff

@@ -378,7 +378,7 @@ theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ)
 
 @[simp, reassoc.1]
 theorem pInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n : ℕ} :
-    (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) ≫ (pInfty : K[Γ₀.obj K] ⟶ _).f n =
+    (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) ≫ (PInfty : K[Γ₀.obj K] ⟶ _).f n =
       (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) :=
   by
   rw [P_infty_f]

bump to nightly-2023-04-20-16

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

3940090c

Diff

@@ -384,7 +384,7 @@ theorem pInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n :
   rw [P_infty_f]
   cases n
   · simpa only [P_f_0_eq] using comp_id _
-  · exact (higher_faces_vanish.on_Γ₀_summand_id K n).comp_p_eq_self
+  · exact (higher_faces_vanish.on_Γ₀_summand_id K n).comp_P_eq_self
 #align algebraic_topology.dold_kan.P_infty_on_Γ₀_splitting_summand_eq_self AlgebraicTopology.DoldKan.pInfty_on_Γ₀_splitting_summand_eq_self
 
 end DoldKan

bump to nightly-2023-04-18-06

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

c37d1701

Diff

@@ -252,7 +252,7 @@ theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
   ext A
   trace
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[]"
-  induction Δ using Opposite.rec
+  induction Δ using Opposite.rec'
   induction' Δ with n
   dsimp
   simp only [colimit.ι_desc, cofan.mk_ι_app, comp_id, Γ₀.obj_map]

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -243,7 +243,7 @@ def obj (K : ChainComplex C ℕ) : SimplicialObject C
       obj.termwise.map_mono_comp_assoc, obj.map_on_summand₀ K A fac]
 #align algebraic_topology.dold_kan.Γ₀.obj AlgebraicTopology.DoldKan.Γ₀.obj
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `discrete_cases #[] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[] -/
 theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
     SimplicialObject.Splitting.map (Γ₀.obj K)
         (fun n : ℕ => Sigma.ι (Γ₀.Obj.summand K (op [n])) (Splitting.IndexSet.id (op [n]))) Δ =
@@ -251,7 +251,7 @@ theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
   by
   ext A
   trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `discrete_cases #[]"
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `discrete_cases #[]"
   induction Δ using Opposite.rec
   induction' Δ with n
   dsimp

bump to nightly-2023-02-28-22

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

1fb1623f

Diff

@@ -80,7 +80,7 @@ namespace Obj
 /-- In the definition of `(Γ₀.obj K).obj Δ` as a direct sum indexed by `A : splitting.index_set Δ`,
 the summand `summand K Δ A` is `K.X A.1.len`. -/
 def summand (Δ : SimplexCategoryᵒᵖ) (A : Splitting.IndexSet Δ) : C :=
-  K.x A.1.unop.len
+  K.pt A.1.unop.len
 #align algebraic_topology.dold_kan.Γ₀.obj.summand AlgebraicTopology.DoldKan.Γ₀.Obj.summand
 
 /-- The functor `Γ₀` sends a chain complex `K` to the simplicial object which
@@ -95,7 +95,7 @@ namespace Termwise
 is the identity if `Δ = Δ'`, the differential on the complex `K` if `i = δ 0`, and
 zero otherwise. -/
 def mapMono (K : ChainComplex C ℕ) {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
-    K.x Δ.len ⟶ K.x Δ'.len := by
+    K.pt Δ.len ⟶ K.pt Δ'.len := by
   by_cases Δ = Δ'
   · exact eq_to_hom (by congr )
   · by_cases is_δ₀ i
@@ -265,7 +265,7 @@ theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
 /-- By construction, the simplicial `Γ₀.obj K` is equipped with a splitting. -/
 def splitting (K : ChainComplex C ℕ) : SimplicialObject.Splitting (Γ₀.obj K)
     where
-  n n := K.x n
+  n n := K.pt n
   ι n := Sigma.ι (Γ₀.Obj.summand K (op [n])) (Splitting.IndexSet.id (op [n]))
   map_is_iso' Δ := by
     rw [Γ₀.splitting_map_eq_id]

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -124,7 +124,7 @@ theorem mapMono_δ₀ {n : ℕ} : mapMono K (δ (0 : Fin (n + 2))) = K.d (n + 1)
 
 theorem mapMono_eq_zero (i : Δ' ⟶ Δ) [Mono i] (h₁ : Δ ≠ Δ') (h₂ : ¬Isδ₀ i) : mapMono K i = 0 := by
   unfold mapMono
-  rw [Ne.def] at h₁
+  rw [Ne] at h₁
   split_ifs
   rfl
 #align algebraic_topology.dold_kan.Γ₀.obj.termwise.map_mono_eq_zero AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero

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

@@ -158,13 +158,13 @@ theorem mapMono_comp (i' : Δ'' ⟶ Δ') (i : Δ' ⟶ Δ) [Mono i'] [Mono i] :
   -- then the RHS is always zero
   obtain ⟨k, hk⟩ := Nat.exists_eq_add_of_lt (len_lt_of_mono i h₁)
   obtain ⟨k', hk'⟩ := Nat.exists_eq_add_of_lt (len_lt_of_mono i' h₂)
-  have eq : Δ.len = Δ''.len + (k + k' + 2) := by linarith
+  have eq : Δ.len = Δ''.len + (k + k' + 2) := by omega
   rw [mapMono_eq_zero K (i' ≫ i) _ _]; rotate_left
   · by_contra h
     simp only [self_eq_add_right, h, add_eq_zero_iff, and_false] at eq
   · by_contra h
     simp only [h.1, add_right_inj] at eq
-    linarith
+    omega
   -- in all cases, the LHS is also zero, either by definition, or because d ≫ d = 0
   by_cases h₃ : Isδ₀ i
   · by_cases h₄ : Isδ₀ i'

chore: reduce imports (#9830)

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

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

f4c4ca61

Diff

@@ -3,7 +3,8 @@ Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
-import Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject
+import Mathlib.AlgebraicTopology.SplitSimplicialObject
+import Mathlib.AlgebraicTopology.DoldKan.PInfty
 
 #align_import algebraic_topology.dold_kan.functor_gamma from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"

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

@@ -231,65 +231,56 @@ def obj (K : ChainComplex C ℕ) : SimplicialObject C where
     rfl)
 #align algebraic_topology.dold_kan.Γ₀.obj AlgebraicTopology.DoldKan.Γ₀.obj
 
-
-theorem splitting_map_eq_id (Δ : SimplexCategoryᵒᵖ) :
-    SimplicialObject.Splitting.map (Γ₀.obj K)
-        (fun n : ℕ => Sigma.ι (Γ₀.Obj.summand K (op [n])) (Splitting.IndexSet.id (op [n]))) Δ =
-      𝟙 _ := colimit.hom_ext (fun ⟨A⟩ => by
-  induction' Δ using Opposite.rec' with Δ
-  induction' Δ using SimplexCategory.rec with n
-  dsimp [Splitting.map]
-  simp only [colimit.ι_desc, Cofan.mk_ι_app, Γ₀.obj_map]
-  erw [Γ₀.Obj.map_on_summand₀ K (SimplicialObject.Splitting.IndexSet.id A.1)
-      (show A.e ≫ 𝟙 _ = A.e.op.unop ≫ 𝟙 _ by rfl),
-    Γ₀.Obj.Termwise.mapMono_id, A.ext', id_comp, comp_id]
-  rfl)
-#align algebraic_topology.dold_kan.Γ₀.splitting_map_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_id
-
 /-- By construction, the simplicial `Γ₀.obj K` is equipped with a splitting. -/
 def splitting (K : ChainComplex C ℕ) : SimplicialObject.Splitting (Γ₀.obj K) where
   N n := K.X n
   ι n := Sigma.ι (Γ₀.Obj.summand K (op [n])) (Splitting.IndexSet.id (op [n]))
-  map_isIso Δ := by
-    rw [Γ₀.splitting_map_eq_id]
-    apply IsIso.id
+  isColimit' Δ := IsColimit.ofIsoColimit (colimit.isColimit _) (Cofan.ext (Iso.refl _) (by
+      intro A
+      dsimp [Splitting.cofan']
+      rw [comp_id, Γ₀.Obj.map_on_summand₀ K (SimplicialObject.Splitting.IndexSet.id A.1)
+        (show A.e ≫ 𝟙 _ = A.e.op.unop ≫ 𝟙 _ by rfl), Γ₀.Obj.Termwise.mapMono_id]
+      dsimp
+      rw [id_comp]
+      rfl))
 #align algebraic_topology.dold_kan.Γ₀.splitting AlgebraicTopology.DoldKan.Γ₀.splitting
 
-@[simp 1100]
-theorem splitting_iso_hom_eq_id (Δ : SimplexCategoryᵒᵖ) : ((splitting K).iso Δ).hom = 𝟙 _ :=
-  splitting_map_eq_id K Δ
-#align algebraic_topology.dold_kan.Γ₀.splitting_iso_hom_eq_id AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id
-
 @[reassoc]
 theorem Obj.map_on_summand {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ')
     {Δ'' : SimplexCategory} {e : Δ'.unop ⟶ Δ''} {i : Δ'' ⟶ A.1.unop} [Epi e] [Mono i]
     (fac : e ≫ i = θ.unop ≫ A.e) :
-    (Γ₀.splitting K).ιSummand A ≫ (Γ₀.obj K).map θ =
-      Γ₀.Obj.Termwise.mapMono K i ≫ (Γ₀.splitting K).ιSummand (Splitting.IndexSet.mk e) := by
-  dsimp only [SimplicialObject.Splitting.ιSummand, SimplicialObject.Splitting.ιCoprod]
-  simp only [assoc, Γ₀.splitting_iso_hom_eq_id, id_comp, comp_id]
-  exact Γ₀.Obj.map_on_summand₀ K A fac
+    ((Γ₀.splitting K).cofan Δ).inj A ≫ (Γ₀.obj K).map θ =
+      Γ₀.Obj.Termwise.mapMono K i ≫ ((Γ₀.splitting K).cofan Δ').inj (Splitting.IndexSet.mk e) := by
+  dsimp [Splitting.cofan]
+  change (_ ≫ (Γ₀.obj K).map A.e.op) ≫ (Γ₀.obj K).map θ = _
+  rw [assoc, ← Functor.map_comp]
+  dsimp [splitting]
+  erw [Γ₀.Obj.map_on_summand₀ K (Splitting.IndexSet.id A.1)
+    (show e ≫ i = ((Splitting.IndexSet.e A).op ≫ θ).unop ≫ 𝟙 _ by rw [comp_id, fac]; rfl),
+    Γ₀.Obj.map_on_summand₀ K (Splitting.IndexSet.id (op Δ''))
+      (show e ≫ 𝟙 Δ'' = e.op.unop ≫ 𝟙 _ by simp), Termwise.mapMono_id, id_comp]
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand
 
 @[reassoc]
 theorem Obj.map_on_summand' {Δ Δ' : SimplexCategoryᵒᵖ} (A : Splitting.IndexSet Δ) (θ : Δ ⟶ Δ') :
-    (splitting K).ιSummand A ≫ (obj K).map θ =
-      Obj.Termwise.mapMono K (image.ι (θ.unop ≫ A.e)) ≫ (splitting K).ιSummand (A.pull θ) := by
+    ((splitting K).cofan Δ).inj A ≫ (obj K).map θ =
+      Obj.Termwise.mapMono K (image.ι (θ.unop ≫ A.e)) ≫
+        ((splitting K).cofan Δ').inj (A.pull θ) := by
   apply Obj.map_on_summand
   apply image.fac
 #align algebraic_topology.dold_kan.Γ₀.obj.map_on_summand' AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'
 
 @[reassoc]
 theorem Obj.mapMono_on_summand_id {Δ Δ' : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
-    (splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (obj K).map i.op =
-      Obj.Termwise.mapMono K i ≫ (splitting K).ιSummand (Splitting.IndexSet.id (op Δ')) :=
+    ((splitting K).cofan _).inj (Splitting.IndexSet.id (op Δ)) ≫ (obj K).map i.op =
+      Obj.Termwise.mapMono K i ≫ ((splitting K).cofan _).inj (Splitting.IndexSet.id (op Δ')) :=
   Obj.map_on_summand K (Splitting.IndexSet.id (op Δ)) i.op (rfl : 𝟙 _ ≫ i = i ≫ 𝟙 _)
 #align algebraic_topology.dold_kan.Γ₀.obj.map_mono_on_summand_id AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id
 
 @[reassoc]
 theorem Obj.map_epi_on_summand_id {Δ Δ' : SimplexCategory} (e : Δ' ⟶ Δ) [Epi e] :
-    (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op Δ)) ≫ (Γ₀.obj K).map e.op =
-      (Γ₀.splitting K).ιSummand (Splitting.IndexSet.mk e) := by
+    ((Γ₀.splitting K).cofan _).inj (Splitting.IndexSet.id (op Δ)) ≫ (Γ₀.obj K).map e.op =
+      ((Γ₀.splitting K).cofan _).inj (Splitting.IndexSet.mk e) := by
   simpa only [Γ₀.Obj.map_on_summand K (Splitting.IndexSet.id (op Δ)) e.op
       (rfl : e ≫ 𝟙 Δ = e ≫ 𝟙 Δ),
     Γ₀.Obj.Termwise.mapMono_id] using id_comp _
@@ -298,7 +289,8 @@ theorem Obj.map_epi_on_summand_id {Δ Δ' : SimplexCategory} (e : Δ' ⟶ Δ) [E
 /-- The functor `Γ₀ : ChainComplex C ℕ ⥤ SimplicialObject C`, on morphisms. -/
 @[simps]
 def map {K K' : ChainComplex C ℕ} (f : K ⟶ K') : obj K ⟶ obj K' where
-  app Δ := (Γ₀.splitting K).desc Δ fun A => f.f A.1.unop.len ≫ (Γ₀.splitting K').ιSummand A
+  app Δ := (Γ₀.splitting K).desc Δ fun A => f.f A.1.unop.len ≫
+    ((Γ₀.splitting K').cofan _).inj A
   naturality {Δ' Δ} θ := by
     apply (Γ₀.splitting K).hom_ext'
     intro A
@@ -323,7 +315,7 @@ def Γ₀' : ChainComplex C ℕ ⥤ SimplicialObject.Split C where
       f := f.f
       comm := fun n => by
         dsimp
-        simp only [← Splitting.ιSummand_id, (Γ₀.splitting K).ι_desc]
+        simp only [← Splitting.cofan_inj_id, (Γ₀.splitting K).ι_desc]
         rfl }
 #align algebraic_topology.dold_kan.Γ₀' AlgebraicTopology.DoldKan.Γ₀'
 
@@ -344,7 +336,8 @@ def Γ₂ : Karoubi (ChainComplex C ℕ) ⥤ Karoubi (SimplicialObject C) :=
 #align algebraic_topology.dold_kan.Γ₂ AlgebraicTopology.DoldKan.Γ₂
 
 theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ) :
-    HigherFacesVanish (n + 1) ((Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n + 1]))) := by
+    @HigherFacesVanish C _ _ (Γ₀.obj K) _ n (n + 1)
+      (((Γ₀.splitting K).cofan _).inj (Splitting.IndexSet.id (op [n + 1]))) := by
   intro j _
   have eq := Γ₀.Obj.mapMono_on_summand_id K (SimplexCategory.δ j.succ)
   rw [Γ₀.Obj.Termwise.mapMono_eq_zero K, zero_comp] at eq; rotate_left
@@ -356,8 +349,9 @@ theorem HigherFacesVanish.on_Γ₀_summand_id (K : ChainComplex C ℕ) (n : ℕ)
 
 @[reassoc (attr := simp)]
 theorem PInfty_on_Γ₀_splitting_summand_eq_self (K : ChainComplex C ℕ) {n : ℕ} :
-    (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) ≫ (PInfty : K[Γ₀.obj K] ⟶ _).f n =
-      (Γ₀.splitting K).ιSummand (Splitting.IndexSet.id (op [n])) := by
+    ((Γ₀.splitting K).cofan _).inj (Splitting.IndexSet.id (op [n])) ≫
+      (PInfty : K[Γ₀.obj K] ⟶ _).f n =
+      ((Γ₀.splitting K).cofan _).inj (Splitting.IndexSet.id (op [n])) := by
   rw [PInfty_f]
   rcases n with _|n
   · simpa only [P_f_0_eq] using comp_id _

chore: cleanup some spaces (#7484)

Purely cosmetic PR.

c93575a3

Diff

@@ -93,7 +93,7 @@ zero otherwise. -/
 def mapMono (K : ChainComplex C ℕ) {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ) [Mono i] :
     K.X Δ.len ⟶ K.X Δ'.len := by
   by_cases Δ = Δ'
-  · exact eqToHom (by congr )
+  · exact eqToHom (by congr)
   · by_cases Isδ₀ i
     · exact K.d Δ.len Δ'.len
     · exact 0

chore: only four spaces for subsequent lines (#7286)

Co-authored-by: Moritz Firsching <firsching@google.com>

0c7d6fa5

Diff

@@ -132,7 +132,7 @@ variable {K K'}
 
 @[reassoc (attr := simp)]
 theorem mapMono_naturality (i : Δ ⟶ Δ') [Mono i] :
-  mapMono K i ≫ f.f Δ.len = f.f Δ'.len ≫ mapMono K' i := by
+    mapMono K i ≫ f.f Δ.len = f.f Δ'.len ≫ mapMono K' i := by
   unfold mapMono
   split_ifs with h
   · subst h
@@ -145,7 +145,7 @@ variable (K)
 
 @[reassoc (attr := simp)]
 theorem mapMono_comp (i' : Δ'' ⟶ Δ') (i : Δ' ⟶ Δ) [Mono i'] [Mono i] :
-  mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i) := by
+    mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i) := by
   -- case where i : Δ' ⟶ Δ is the identity
   by_cases h₁ : Δ = Δ'
   · subst h₁

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

cf01bdac

Diff

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject
 
-#align_import algebraic_topology.dold_kan.functor_gamma from "leanprover-community/mathlib"@"5b8284148e8149728f4b90624888d98c36284454"
+#align_import algebraic_topology.dold_kan.functor_gamma 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

@@ -25,6 +25,8 @@ By construction, `Γ₀.obj K` is a split simplicial object whose splitting is `
 We also construct `Γ₂ : Karoubi (ChainComplex C ℕ) ⥤ Karoubi (SimplicialObject C)`
 which shall be an equivalence for any additive category `C`.
 
+(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

@@ -37,7 +37,7 @@ namespace AlgebraicTopology
 
 namespace DoldKan
 
-variable {C : Type _} [Category C] [Preadditive C] (K K' : ChainComplex C ℕ) (f : K ⟶ K')
+variable {C : Type*} [Category C] [Preadditive C] (K K' : ChainComplex C ℕ) (f : K ⟶ K')
   {Δ Δ' Δ'' : SimplexCategory}
 
 /-- `Isδ₀ i` is a simple condition used to check whether a monomorphism `i` in

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

@@ -2,14 +2,11 @@
 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.functor_gamma
-! leanprover-community/mathlib commit 5b8284148e8149728f4b90624888d98c36284454
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject
 
+#align_import algebraic_topology.dold_kan.functor_gamma from "leanprover-community/mathlib"@"5b8284148e8149728f4b90624888d98c36284454"
+
 /-!
 
 # Construction of the inverse functor of the Dold-Kan equivalence

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

@@ -58,7 +58,7 @@ theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i =
     by_contra h
     exact h₂ (Fin.succAbove_ne_zero_zero h)
   · rintro rfl
-    exact ⟨rfl, by dsimp ; exact Fin.succ_ne_zero (0 : Fin (j + 1))⟩
+    exact ⟨rfl, by dsimp; exact Fin.succ_ne_zero (0 : Fin (j + 1))⟩
 #align algebraic_topology.dold_kan.is_δ₀.iff AlgebraicTopology.DoldKan.Isδ₀.iff
 
 theorem eq_δ₀ {n : ℕ} {i : ([n] : SimplexCategory) ⟶ [n + 1]} [Mono i] (hi : Isδ₀ i) :

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -58,7 +58,7 @@ theorem iff {j : ℕ} {i : Fin (j + 2)} : Isδ₀ (SimplexCategory.δ i) ↔ i =
     by_contra h
     exact h₂ (Fin.succAbove_ne_zero_zero h)
   · rintro rfl
-    exact ⟨rfl, by dsimp ; exact Fin.succ_ne_zero 0⟩
+    exact ⟨rfl, by dsimp ; exact Fin.succ_ne_zero (0 : Fin (j + 1))⟩
 #align algebraic_topology.dold_kan.is_δ₀.iff AlgebraicTopology.DoldKan.Isδ₀.iff
 
 theorem eq_δ₀ {n : ℕ} {i : ([n] : SimplexCategory) ⟶ [n + 1]} [Mono i] (hi : Isδ₀ i) :