algebraic_topology.dold_kan.n_comp_gamma ⟷ Mathlib.AlgebraicTopology.DoldKan.NCompGamma

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

@@ -46,30 +46,30 @@ theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : S
   by
   induction' Δ' using SimplexCategory.rec with m
   obtain ⟨k, hk⟩ :=
-    Nat.exists_eq_add_of_lt (len_lt_of_mono i fun h => by rw [← h] at h₁ ; exact h₁ rfl)
-  simp only [len_mk] at hk 
+    Nat.exists_eq_add_of_lt (len_lt_of_mono i fun h => by rw [← h] at h₁; exact h₁ rfl)
+  simp only [len_mk] at hk
   cases k
-  · change n = m + 1 at hk 
+  · change n = m + 1 at hk
     subst hk; obtain ⟨j, rfl⟩ := eq_δ_of_mono i
-    rw [is_δ₀.iff] at h₂ 
+    rw [is_δ₀.iff] at h₂
     have h₃ : 1 ≤ (j : ℕ) := by
       by_contra
       exact h₂ (by simpa only [Fin.ext_iff, not_le, Nat.lt_one_iff] using h)
     exact (higher_faces_vanish.of_P (m + 1) m).comp_δ_eq_zero j h₂ (by linarith)
-  · simp only [Nat.succ_eq_add_one, ← add_assoc] at hk 
+  · simp only [Nat.succ_eq_add_one, ← add_assoc] at hk
     clear h₂ hi
     subst hk
     obtain ⟨j₁, i, rfl⟩ :=
       eq_comp_δ_of_not_surjective i fun h =>
         by
         have h' := len_le_of_epi (SimplexCategory.epi_iff_surjective.2 h)
-        dsimp at h' 
+        dsimp at h'
         linarith
     obtain ⟨j₂, i, rfl⟩ :=
       eq_comp_δ_of_not_surjective i fun h =>
         by
         have h' := len_le_of_epi (SimplexCategory.epi_iff_surjective.2 h)
-        dsimp at h' 
+        dsimp at h'
         linarith
     by_cases hj₁ : j₁ = 0
     · subst hj₁
@@ -258,7 +258,7 @@ instance : IsIso (Γ₂N₂.natTrans : (N₂ : Karoubi (SimplicialObject C) ⥤
     have : is_iso (N₂.map (Γ₂N₂.nat_trans.app P)) :=
       by
       have h := identity_N₂_objectwise P
-      erw [hom_comp_eq_id] at h 
+      erw [hom_comp_eq_id] at h
       rw [h]
       infer_instance
     exact is_iso_of_reflects_iso _ N₂

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

@@ -172,12 +172,12 @@ def natTrans : (N₁ : SimplicialObject C ⥤ _) ⋙ Γ₂ ⟶ toKaroubi _
 
 end Γ₂N₁
 
-#print AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂ /-
+#print AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso /-
 /-- The compatibility isomorphism relating `N₂ ⋙ Γ₂` and `N₁ ⋙ Γ₂`. -/
 @[simps]
-def compatibility_Γ₂N₁_Γ₂N₂ : toKaroubi (SimplicialObject C) ⋙ N₂ ⋙ Γ₂ ≅ N₁ ⋙ Γ₂ :=
+def Γ₂N₂ToKaroubiIso : toKaroubi (SimplicialObject C) ⋙ N₂ ⋙ Γ₂ ≅ N₁ ⋙ Γ₂ :=
   eqToIso (Functor.congr_obj (functorExtension₁_comp_whiskeringLeft_toKaroubi _ _) (N₁ ⋙ Γ₂))
-#align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂ AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂
+#align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂ AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso
 -/
 
 namespace Γ₂N₂
@@ -185,25 +185,22 @@ namespace Γ₂N₂
 #print AlgebraicTopology.DoldKan.Γ₂N₂.natTrans /-
 /-- The natural transformation `N₂ ⋙ Γ₂ ⟶ 𝟭 (simplicial_object C)`. -/
 def natTrans : (N₂ : Karoubi (SimplicialObject C) ⥤ _) ⋙ Γ₂ ⟶ 𝟭 _ :=
-  ((whiskeringLeft _ _ _).obj _).Preimage (compatibility_Γ₂N₁_Γ₂N₂.Hom ≫ Γ₂N₁.natTrans)
+  ((whiskeringLeft _ _ _).obj _).Preimage (Γ₂N₂ToKaroubiIso.Hom ≫ Γ₂N₁.natTrans)
 #align algebraic_topology.dold_kan.Γ₂N₂.nat_trans AlgebraicTopology.DoldKan.Γ₂N₂.natTrans
 -/
 
 #print AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app /-
 theorem natTrans_app_f_app (P : Karoubi (SimplicialObject C)) :
     Γ₂N₂.natTrans.app P =
-      (N₂ ⋙ Γ₂).map P.decompId_i ≫
-        (compatibility_Γ₂N₁_Γ₂N₂.Hom ≫ Γ₂N₁.natTrans).app P.pt ≫ P.decompId_p :=
-  whiskeringLeft_obj_preimage_app (compatibility_Γ₂N₁_Γ₂N₂.Hom ≫ Γ₂N₁.natTrans) P
+      (N₂ ⋙ Γ₂).map P.decompId_i ≫ (Γ₂N₂ToKaroubiIso.Hom ≫ Γ₂N₁.natTrans).app P.pt ≫ P.decompId_p :=
+  whiskeringLeft_obj_preimage_app (Γ₂N₂ToKaroubiIso.Hom ≫ Γ₂N₁.natTrans) P
 #align algebraic_topology.dold_kan.Γ₂N₂.nat_trans_app_f_app AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app
 -/
 
 end Γ₂N₂
 
-#print AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans /-
-theorem compatibility_Γ₂N₁_Γ₂N₂_natTrans (X : SimplicialObject C) :
-    Γ₂N₁.natTrans.app X =
-      (compatibility_Γ₂N₁_Γ₂N₂.app X).inv ≫ Γ₂N₂.natTrans.app ((toKaroubi _).obj X) :=
+theorem Γ₂N₂ToKaroubiIso_natTrans (X : SimplicialObject C) :
+    Γ₂N₁.natTrans.app X = (Γ₂N₂ToKaroubiIso.app X).inv ≫ Γ₂N₂.natTrans.app ((toKaroubi _).obj X) :=
   by
   rw [← cancel_epi (compatibility_Γ₂N₁_Γ₂N₂.app X).Hom, iso.hom_inv_id_assoc]
   exact
@@ -211,8 +208,7 @@ theorem compatibility_Γ₂N₁_Γ₂N₂_natTrans (X : SimplicialObject C) :
       (((whiskering_left _ _ _).obj _).image_preimage
           (compatibility_Γ₂N₁_Γ₂N₂.hom ≫ Γ₂N₁.nat_trans : _ ⟶ to_karoubi _ ⋙ 𝟭 _)).symm
       X
-#align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂_nat_trans AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans
--/
+#align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂_nat_trans AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_natTrans
 
 #print AlgebraicTopology.DoldKan.identity_N₂_objectwise /-
 theorem identity_N₂_objectwise (P : Karoubi (SimplicialObject C)) :

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

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

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

@@ -6,7 +6,7 @@ Authors: Joël Riou
 import Mathbin.AlgebraicTopology.DoldKan.GammaCompN
 import Mathbin.AlgebraicTopology.DoldKan.NReflectsIso
 
-#align_import algebraic_topology.dold_kan.n_comp_gamma from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+#align_import algebraic_topology.dold_kan.n_comp_gamma from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
@@ -22,6 +22,8 @@ that it becomes an isomorphism after the application of the functor
 `N₂ : karoubi (simplicial_object C) ⥤ karoubi (chain_complex C ℕ)`
 which reflects isomorphisms.
 
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -71,7 +71,7 @@ theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : S
         linarith
     by_cases hj₁ : j₁ = 0
     · subst hj₁
-      rw [assoc, ← SimplexCategory.δ_comp_δ'' (Fin.zero_le _)]
+      rw [assoc, ← SimplexCategory.δ_comp_δ'' (Fin.zero_le' _)]
       simp only [op_comp, X.map_comp, assoc, P_infty_f]
       erw [(higher_faces_vanish.of_P _ _).comp_δ_eq_zero_assoc _ j₂.succ_ne_zero, zero_comp]
       rw [Fin.val_succ]

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.dold_kan.n_comp_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.GammaCompN
 import Mathbin.AlgebraicTopology.DoldKan.NReflectsIso
 
+#align_import algebraic_topology.dold_kan.n_comp_gamma from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
 > Any changes to this file require a corresponding PR to mathlib4.

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

@@ -41,6 +41,7 @@ namespace DoldKan
 
 variable {C : Type _} [Category C] [Preadditive C]
 
+#print AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero /-
 theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : SimplexCategory}
     (i : Δ' ⟶ [n]) [hi : Mono i] (h₁ : Δ'.len ≠ n) (h₂ : ¬Isδ₀ i) : PInfty.f n ≫ X.map i.op = 0 :=
   by
@@ -83,7 +84,9 @@ theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : S
       by_contra
       exact hj₁ (by simp only [Fin.ext_iff, Fin.val_zero]; linarith)
 #align algebraic_topology.dold_kan.P_infty_comp_map_mono_eq_zero AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty /-
 @[reassoc]
 theorem Γ₀_obj_termwise_mapMono_comp_PInfty (X : SimplicialObject C) {Δ Δ' : SimplexCategory}
     (i : Δ ⟶ Δ') [Mono i] :
@@ -123,11 +126,13 @@ theorem Γ₀_obj_termwise_mapMono_comp_PInfty (X : SimplicialObject C) {Δ Δ'
     · by_contra h'
       exact hi h'
 #align algebraic_topology.dold_kan.Γ₀_obj_termwise_map_mono_comp_P_infty AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty
+-/
 
 variable [HasFiniteCoproducts C]
 
 namespace Γ₂N₁
 
+#print AlgebraicTopology.DoldKan.Γ₂N₁.natTrans /-
 /-- The natural transformation `N₁ ⋙ Γ₂ ⟶ to_karoubi (simplicial_object C)`. -/
 @[simps]
 def natTrans : (N₁ : SimplicialObject C ⥤ _) ⋙ Γ₂ ⟶ toKaroubi _
@@ -164,31 +169,39 @@ def natTrans : (N₁ : SimplicialObject C ⥤ _) ⋙ Γ₂ ⟶ toKaroubi _
       HomologicalComplex.comp_f, alternating_face_map_complex.map_f, P_infty_f_naturality_assoc,
       nat_trans.naturality]
 #align algebraic_topology.dold_kan.Γ₂N₁.nat_trans AlgebraicTopology.DoldKan.Γ₂N₁.natTrans
+-/
 
 end Γ₂N₁
 
+#print AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂ /-
 /-- The compatibility isomorphism relating `N₂ ⋙ Γ₂` and `N₁ ⋙ Γ₂`. -/
 @[simps]
 def compatibility_Γ₂N₁_Γ₂N₂ : toKaroubi (SimplicialObject C) ⋙ N₂ ⋙ Γ₂ ≅ N₁ ⋙ Γ₂ :=
   eqToIso (Functor.congr_obj (functorExtension₁_comp_whiskeringLeft_toKaroubi _ _) (N₁ ⋙ Γ₂))
 #align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂ AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂
+-/
 
 namespace Γ₂N₂
 
+#print AlgebraicTopology.DoldKan.Γ₂N₂.natTrans /-
 /-- The natural transformation `N₂ ⋙ Γ₂ ⟶ 𝟭 (simplicial_object C)`. -/
 def natTrans : (N₂ : Karoubi (SimplicialObject C) ⥤ _) ⋙ Γ₂ ⟶ 𝟭 _ :=
   ((whiskeringLeft _ _ _).obj _).Preimage (compatibility_Γ₂N₁_Γ₂N₂.Hom ≫ Γ₂N₁.natTrans)
 #align algebraic_topology.dold_kan.Γ₂N₂.nat_trans AlgebraicTopology.DoldKan.Γ₂N₂.natTrans
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app /-
 theorem natTrans_app_f_app (P : Karoubi (SimplicialObject C)) :
     Γ₂N₂.natTrans.app P =
       (N₂ ⋙ Γ₂).map P.decompId_i ≫
         (compatibility_Γ₂N₁_Γ₂N₂.Hom ≫ Γ₂N₁.natTrans).app P.pt ≫ P.decompId_p :=
   whiskeringLeft_obj_preimage_app (compatibility_Γ₂N₁_Γ₂N₂.Hom ≫ Γ₂N₁.natTrans) P
 #align algebraic_topology.dold_kan.Γ₂N₂.nat_trans_app_f_app AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app
+-/
 
 end Γ₂N₂
 
+#print AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans /-
 theorem compatibility_Γ₂N₁_Γ₂N₂_natTrans (X : SimplicialObject C) :
     Γ₂N₁.natTrans.app X =
       (compatibility_Γ₂N₁_Γ₂N₂.app X).inv ≫ Γ₂N₂.natTrans.app ((toKaroubi _).obj X) :=
@@ -200,7 +213,9 @@ theorem compatibility_Γ₂N₁_Γ₂N₂_natTrans (X : SimplicialObject C) :
           (compatibility_Γ₂N₁_Γ₂N₂.hom ≫ Γ₂N₁.nat_trans : _ ⟶ to_karoubi _ ⋙ 𝟭 _)).symm
       X
 #align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂_nat_trans AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans
+-/
 
+#print AlgebraicTopology.DoldKan.identity_N₂_objectwise /-
 theorem identity_N₂_objectwise (P : Karoubi (SimplicialObject C)) :
     N₂Γ₂.inv.app (N₂.obj P) ≫ N₂.map (Γ₂N₂.natTrans.app P) = 𝟙 (N₂.obj P) :=
   by
@@ -230,12 +245,15 @@ theorem identity_N₂_objectwise (P : Karoubi (SimplicialObject C)) :
   simp only [karoubi.comp_f, HomologicalComplex.comp_f, karoubi.id_eq, N₂_obj_p_f, assoc, eq₁, eq₂,
     P_infty_f_naturality_assoc, app_idem, P_infty_f_idem_assoc]
 #align algebraic_topology.dold_kan.identity_N₂_objectwise AlgebraicTopology.DoldKan.identity_N₂_objectwise
+-/
 
+#print AlgebraicTopology.DoldKan.identity_N₂ /-
 theorem identity_N₂ :
     ((𝟙 (N₂ : Karoubi (SimplicialObject C) ⥤ _) ◫ N₂Γ₂.inv) ≫ Γ₂N₂.natTrans ◫ 𝟙 N₂ : N₂ ⟶ N₂) =
       𝟙 N₂ :=
   by ext P : 2; dsimp; rw [Γ₂.map_id, N₂.map_id, comp_id, id_comp, identity_N₂_objectwise P]
 #align algebraic_topology.dold_kan.identity_N₂ AlgebraicTopology.DoldKan.identity_N₂
+-/
 
 instance : IsIso (Γ₂N₂.natTrans : (N₂ : Karoubi (SimplicialObject C) ⥤ _) ⋙ _ ⟶ _) :=
   by
@@ -260,17 +278,21 @@ instance : IsIso (Γ₂N₁.natTrans : (N₁ : SimplicialObject C ⥤ _) ⋙ _ 
     infer_instance
   apply nat_iso.is_iso_of_is_iso_app
 
+#print AlgebraicTopology.DoldKan.Γ₂N₂ /-
 /-- The unit isomorphism of the Dold-Kan equivalence. -/
 @[simp]
 def Γ₂N₂ : 𝟭 _ ≅ (N₂ : Karoubi (SimplicialObject C) ⥤ _) ⋙ Γ₂ :=
   (asIso Γ₂N₂.natTrans).symm
 #align algebraic_topology.dold_kan.Γ₂N₂ AlgebraicTopology.DoldKan.Γ₂N₂
+-/
 
+#print AlgebraicTopology.DoldKan.Γ₂N₁ /-
 /-- The natural isomorphism `to_karoubi (simplicial_object C) ≅ N₁ ⋙ Γ₂`. -/
 @[simps]
 def Γ₂N₁ : toKaroubi _ ≅ (N₁ : SimplicialObject C ⥤ _) ⋙ Γ₂ :=
   (asIso Γ₂N₁.natTrans).symm
 #align algebraic_topology.dold_kan.Γ₂N₁ AlgebraicTopology.DoldKan.Γ₂N₁
+-/
 
 end DoldKan
 

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

@@ -30,8 +30,8 @@ which reflects isomorphisms.
 
 noncomputable section
 
-open
-  CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Idempotents SimplexCategory Opposite SimplicialObject
+open CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Idempotents
+  SimplexCategory Opposite SimplicialObject
 
 open scoped Simplicial DoldKan
 
@@ -46,30 +46,30 @@ theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : S
   by
   induction' Δ' using SimplexCategory.rec with m
   obtain ⟨k, hk⟩ :=
-    Nat.exists_eq_add_of_lt (len_lt_of_mono i fun h => by rw [← h] at h₁; exact h₁ rfl)
-  simp only [len_mk] at hk
+    Nat.exists_eq_add_of_lt (len_lt_of_mono i fun h => by rw [← h] at h₁ ; exact h₁ rfl)
+  simp only [len_mk] at hk 
   cases k
-  · change n = m + 1 at hk
+  · change n = m + 1 at hk 
     subst hk; obtain ⟨j, rfl⟩ := eq_δ_of_mono i
-    rw [is_δ₀.iff] at h₂
+    rw [is_δ₀.iff] at h₂ 
     have h₃ : 1 ≤ (j : ℕ) := by
       by_contra
       exact h₂ (by simpa only [Fin.ext_iff, not_le, Nat.lt_one_iff] using h)
     exact (higher_faces_vanish.of_P (m + 1) m).comp_δ_eq_zero j h₂ (by linarith)
-  · simp only [Nat.succ_eq_add_one, ← add_assoc] at hk
+  · simp only [Nat.succ_eq_add_one, ← add_assoc] at hk 
     clear h₂ hi
     subst hk
     obtain ⟨j₁, i, rfl⟩ :=
       eq_comp_δ_of_not_surjective i fun h =>
         by
         have h' := len_le_of_epi (SimplexCategory.epi_iff_surjective.2 h)
-        dsimp at h'
+        dsimp at h' 
         linarith
     obtain ⟨j₂, i, rfl⟩ :=
       eq_comp_δ_of_not_surjective i fun h =>
         by
         have h' := len_le_of_epi (SimplexCategory.epi_iff_surjective.2 h)
-        dsimp at h'
+        dsimp at h' 
         linarith
     by_cases hj₁ : j₁ = 0
     · subst hj₁
@@ -245,7 +245,7 @@ instance : IsIso (Γ₂N₂.natTrans : (N₂ : Karoubi (SimplicialObject C) ⥤
     have : is_iso (N₂.map (Γ₂N₂.nat_trans.app P)) :=
       by
       have h := identity_N₂_objectwise P
-      erw [hom_comp_eq_id] at h
+      erw [hom_comp_eq_id] at h 
       rw [h]
       infer_instance
     exact is_iso_of_reflects_iso _ N₂

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

@@ -33,7 +33,7 @@ noncomputable section
 open
   CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Idempotents SimplexCategory Opposite SimplicialObject
 
-open Simplicial DoldKan
+open scoped Simplicial DoldKan
 
 namespace AlgebraicTopology
 

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

@@ -41,9 +41,6 @@ namespace DoldKan
 
 variable {C : Type _} [Category C] [Preadditive C]
 
-/- warning: algebraic_topology.dold_kan.P_infty_comp_map_mono_eq_zero -> AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_comp_map_mono_eq_zero AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zeroₓ'. -/
 theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : SimplexCategory}
     (i : Δ' ⟶ [n]) [hi : Mono i] (h₁ : Δ'.len ≠ n) (h₂ : ¬Isδ₀ i) : PInfty.f n ≫ X.map i.op = 0 :=
   by
@@ -87,9 +84,6 @@ theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : S
       exact hj₁ (by simp only [Fin.ext_iff, Fin.val_zero]; linarith)
 #align algebraic_topology.dold_kan.P_infty_comp_map_mono_eq_zero AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero
 
-/- warning: algebraic_topology.dold_kan.Γ₀_obj_termwise_map_mono_comp_P_infty -> AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀_obj_termwise_map_mono_comp_P_infty AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInftyₓ'. -/
 @[reassoc]
 theorem Γ₀_obj_termwise_mapMono_comp_PInfty (X : SimplicialObject C) {Δ Δ' : SimplexCategory}
     (i : Δ ⟶ Δ') [Mono i] :
@@ -134,9 +128,6 @@ variable [HasFiniteCoproducts C]
 
 namespace Γ₂N₁
 
-/- warning: algebraic_topology.dold_kan.Γ₂N₁.nat_trans -> AlgebraicTopology.DoldKan.Γ₂N₁.natTrans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂N₁.nat_trans AlgebraicTopology.DoldKan.Γ₂N₁.natTransₓ'. -/
 /-- The natural transformation `N₁ ⋙ Γ₂ ⟶ to_karoubi (simplicial_object C)`. -/
 @[simps]
 def natTrans : (N₁ : SimplicialObject C ⥤ _) ⋙ Γ₂ ⟶ toKaroubi _
@@ -176,9 +167,6 @@ def natTrans : (N₁ : SimplicialObject C ⥤ _) ⋙ Γ₂ ⟶ toKaroubi _
 
 end Γ₂N₁
 
-/- warning: algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂ -> AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂ AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂ₓ'. -/
 /-- The compatibility isomorphism relating `N₂ ⋙ Γ₂` and `N₁ ⋙ Γ₂`. -/
 @[simps]
 def compatibility_Γ₂N₁_Γ₂N₂ : toKaroubi (SimplicialObject C) ⋙ N₂ ⋙ Γ₂ ≅ N₁ ⋙ Γ₂ :=
@@ -187,17 +175,11 @@ def compatibility_Γ₂N₁_Γ₂N₂ : toKaroubi (SimplicialObject C) ⋙ N₂
 
 namespace Γ₂N₂
 
-/- warning: algebraic_topology.dold_kan.Γ₂N₂.nat_trans -> AlgebraicTopology.DoldKan.Γ₂N₂.natTrans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂N₂.nat_trans AlgebraicTopology.DoldKan.Γ₂N₂.natTransₓ'. -/
 /-- The natural transformation `N₂ ⋙ Γ₂ ⟶ 𝟭 (simplicial_object C)`. -/
 def natTrans : (N₂ : Karoubi (SimplicialObject C) ⥤ _) ⋙ Γ₂ ⟶ 𝟭 _ :=
   ((whiskeringLeft _ _ _).obj _).Preimage (compatibility_Γ₂N₁_Γ₂N₂.Hom ≫ Γ₂N₁.natTrans)
 #align algebraic_topology.dold_kan.Γ₂N₂.nat_trans AlgebraicTopology.DoldKan.Γ₂N₂.natTrans
 
-/- warning: algebraic_topology.dold_kan.Γ₂N₂.nat_trans_app_f_app -> AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂N₂.nat_trans_app_f_app AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_appₓ'. -/
 theorem natTrans_app_f_app (P : Karoubi (SimplicialObject C)) :
     Γ₂N₂.natTrans.app P =
       (N₂ ⋙ Γ₂).map P.decompId_i ≫
@@ -207,9 +189,6 @@ theorem natTrans_app_f_app (P : Karoubi (SimplicialObject C)) :
 
 end Γ₂N₂
 
-/- warning: algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂_nat_trans -> AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂_nat_trans AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTransₓ'. -/
 theorem compatibility_Γ₂N₁_Γ₂N₂_natTrans (X : SimplicialObject C) :
     Γ₂N₁.natTrans.app X =
       (compatibility_Γ₂N₁_Γ₂N₂.app X).inv ≫ Γ₂N₂.natTrans.app ((toKaroubi _).obj X) :=
@@ -222,9 +201,6 @@ theorem compatibility_Γ₂N₁_Γ₂N₂_natTrans (X : SimplicialObject C) :
       X
 #align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂_nat_trans AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans
 
-/- warning: algebraic_topology.dold_kan.identity_N₂_objectwise -> AlgebraicTopology.DoldKan.identity_N₂_objectwise is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.identity_N₂_objectwise AlgebraicTopology.DoldKan.identity_N₂_objectwiseₓ'. -/
 theorem identity_N₂_objectwise (P : Karoubi (SimplicialObject C)) :
     N₂Γ₂.inv.app (N₂.obj P) ≫ N₂.map (Γ₂N₂.natTrans.app P) = 𝟙 (N₂.obj P) :=
   by
@@ -255,9 +231,6 @@ theorem identity_N₂_objectwise (P : Karoubi (SimplicialObject C)) :
     P_infty_f_naturality_assoc, app_idem, P_infty_f_idem_assoc]
 #align algebraic_topology.dold_kan.identity_N₂_objectwise AlgebraicTopology.DoldKan.identity_N₂_objectwise
 
-/- warning: algebraic_topology.dold_kan.identity_N₂ -> AlgebraicTopology.DoldKan.identity_N₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.identity_N₂ AlgebraicTopology.DoldKan.identity_N₂ₓ'. -/
 theorem identity_N₂ :
     ((𝟙 (N₂ : Karoubi (SimplicialObject C) ⥤ _) ◫ N₂Γ₂.inv) ≫ Γ₂N₂.natTrans ◫ 𝟙 N₂ : N₂ ⟶ N₂) =
       𝟙 N₂ :=
@@ -287,21 +260,12 @@ instance : IsIso (Γ₂N₁.natTrans : (N₁ : SimplicialObject C ⥤ _) ⋙ _ 
     infer_instance
   apply nat_iso.is_iso_of_is_iso_app
 
-/- warning: algebraic_topology.dold_kan.Γ₂N₂ -> AlgebraicTopology.DoldKan.Γ₂N₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂N₂ AlgebraicTopology.DoldKan.Γ₂N₂ₓ'. -/
 /-- The unit isomorphism of the Dold-Kan equivalence. -/
 @[simp]
 def Γ₂N₂ : 𝟭 _ ≅ (N₂ : Karoubi (SimplicialObject C) ⥤ _) ⋙ Γ₂ :=
   (asIso Γ₂N₂.natTrans).symm
 #align algebraic_topology.dold_kan.Γ₂N₂ AlgebraicTopology.DoldKan.Γ₂N₂
 
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 /-- The natural isomorphism `to_karoubi (simplicial_object C) ≅ N₁ ⋙ Γ₂`. -/
 @[simps]
 def Γ₂N₁ : toKaroubi _ ≅ (N₁ : SimplicialObject C ⥤ _) ⋙ Γ₂ :=

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

@@ -49,15 +49,11 @@ theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : S
   by
   induction' Δ' using SimplexCategory.rec with m
   obtain ⟨k, hk⟩ :=
-    Nat.exists_eq_add_of_lt
-      (len_lt_of_mono i fun h => by
-        rw [← h] at h₁
-        exact h₁ rfl)
+    Nat.exists_eq_add_of_lt (len_lt_of_mono i fun h => by rw [← h] at h₁; exact h₁ rfl)
   simp only [len_mk] at hk
   cases k
   · change n = m + 1 at hk
-    subst hk
-    obtain ⟨j, rfl⟩ := eq_δ_of_mono i
+    subst hk; obtain ⟨j, rfl⟩ := eq_δ_of_mono i
     rw [is_δ₀.iff] at h₂
     have h₃ : 1 ≤ (j : ℕ) := by
       by_contra
@@ -88,11 +84,7 @@ theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : S
     · simp only [op_comp, X.map_comp, assoc, P_infty_f]
       erw [(higher_faces_vanish.of_P _ _).comp_δ_eq_zero_assoc _ hj₁, zero_comp]
       by_contra
-      exact
-        hj₁
-          (by
-            simp only [Fin.ext_iff, Fin.val_zero]
-            linarith)
+      exact hj₁ (by simp only [Fin.ext_iff, Fin.val_zero]; linarith)
 #align algebraic_topology.dold_kan.P_infty_comp_map_mono_eq_zero AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero
 
 /- warning: algebraic_topology.dold_kan.Γ₀_obj_termwise_map_mono_comp_P_infty -> AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty is a dubious translation:
@@ -121,20 +113,15 @@ theorem Γ₀_obj_termwise_mapMono_comp_PInfty (X : SimplicialObject C) {Δ Δ'
     dsimp
     rw [← P_infty.comm' _ n rfl, alternating_face_map_complex.obj_d_eq]
     simp only [eq_self_iff_true, id_comp, if_true, preadditive.comp_sum]
-    rw [Finset.sum_eq_single (0 : Fin (n + 2))]
-    rotate_left
+    rw [Finset.sum_eq_single (0 : Fin (n + 2))]; rotate_left
     · intro b hb hb'
       rw [preadditive.comp_zsmul]
-      erw [P_infty_comp_map_mono_eq_zero X (SimplexCategory.δ b) h
-          (by
-            rw [is_δ₀.iff]
-            exact hb'),
+      erw [P_infty_comp_map_mono_eq_zero X (SimplexCategory.δ b) h (by rw [is_δ₀.iff]; exact hb'),
         zsmul_zero]
     · simp only [Finset.mem_univ, not_true, IsEmpty.forall_iff]
     · simpa only [hi.eq_δ₀, Fin.val_zero, pow_zero, one_zsmul]
   -- The case `i ≠ δ 0`
-  · rw [Γ₀.obj.termwise.map_mono_eq_zero _ i _ hi, zero_comp]
-    swap
+  · rw [Γ₀.obj.termwise.map_mono_eq_zero _ i _ hi, zero_comp]; swap
     · by_contra h'
       exact h (congr_arg SimplexCategory.len h'.symm)
     rw [P_infty_comp_map_mono_eq_zero]
@@ -274,10 +261,7 @@ Case conversion may be inaccurate. Consider using '#align algebraic_topology.dol
 theorem identity_N₂ :
     ((𝟙 (N₂ : Karoubi (SimplicialObject C) ⥤ _) ◫ N₂Γ₂.inv) ≫ Γ₂N₂.natTrans ◫ 𝟙 N₂ : N₂ ⟶ N₂) =
       𝟙 N₂ :=
-  by
-  ext P : 2
-  dsimp
-  rw [Γ₂.map_id, N₂.map_id, comp_id, id_comp, identity_N₂_objectwise P]
+  by ext P : 2; dsimp; rw [Γ₂.map_id, N₂.map_id, comp_id, id_comp, identity_N₂_objectwise P]
 #align algebraic_topology.dold_kan.identity_N₂ AlgebraicTopology.DoldKan.identity_N₂
 
 instance : IsIso (Γ₂N₂.natTrans : (N₂ : Karoubi (SimplicialObject C) ⥤ _) ⋙ _ ⟶ _) :=

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

@@ -42,10 +42,7 @@ namespace DoldKan
 variable {C : Type _} [Category C] [Preadditive C]
 
 /- warning: algebraic_topology.dold_kan.P_infty_comp_map_mono_eq_zero -> AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_comp_map_mono_eq_zero AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zeroₓ'. -/
 theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : SimplexCategory}
     (i : Δ' ⟶ [n]) [hi : Mono i] (h₁ : Δ'.len ≠ n) (h₂ : ¬Isδ₀ i) : PInfty.f n ≫ X.map i.op = 0 :=
@@ -99,10 +96,7 @@ theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : S
 #align algebraic_topology.dold_kan.P_infty_comp_map_mono_eq_zero AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero
 
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_inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 X) (SimplexCategory.len Δ')) (CategoryTheory.Functor.map.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len Δ'))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len Δ))) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) Δ Δ' i)))
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(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 X) (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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (SimplexCategory.len Δ)) (AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono.{u1, u2} C _inst_1 _inst_2 (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) Δ Δ' i _inst_3) (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 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) 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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 X) (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 X) (Opposite.op.{1} SimplexCategory Δ)) (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 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 X) (SimplexCategory.len 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 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (SimplexCategory.len 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)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₀_obj_termwise_map_mono_comp_P_infty AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInftyₓ'. -/
 @[reassoc]
 theorem Γ₀_obj_termwise_mapMono_comp_PInfty (X : SimplicialObject C) {Δ Δ' : SimplexCategory}
@@ -154,10 +148,7 @@ variable [HasFiniteCoproducts C]
 namespace Γ₂N₁
 
 /- warning: algebraic_topology.dold_kan.Γ₂N₁.nat_trans -> AlgebraicTopology.DoldKan.Γ₂N₁.natTrans is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂N₁.nat_trans AlgebraicTopology.DoldKan.Γ₂N₁.natTransₓ'. -/
 /-- The natural transformation `N₁ ⋙ Γ₂ ⟶ to_karoubi (simplicial_object C)`. -/
 @[simps]
@@ -199,10 +190,7 @@ def natTrans : (N₁ : SimplicialObject C ⥤ _) ⋙ Γ₂ ⟶ toKaroubi _
 end Γ₂N₁
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂ AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂ₓ'. -/
 /-- The compatibility isomorphism relating `N₂ ⋙ Γ₂` and `N₁ ⋙ Γ₂`. -/
 @[simps]
@@ -213,10 +201,7 @@ def compatibility_Γ₂N₁_Γ₂N₂ : toKaroubi (SimplicialObject C) ⋙ N₂
 namespace Γ₂N₂
 
 /- warning: algebraic_topology.dold_kan.Γ₂N₂.nat_trans -> AlgebraicTopology.DoldKan.Γ₂N₂.natTrans is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂N₂.nat_trans AlgebraicTopology.DoldKan.Γ₂N₂.natTransₓ'. -/
 /-- The natural transformation `N₂ ⋙ Γ₂ ⟶ 𝟭 (simplicial_object C)`. -/
 def natTrans : (N₂ : Karoubi (SimplicialObject C) ⥤ _) ⋙ Γ₂ ⟶ 𝟭 _ :=
@@ -224,10 +209,7 @@ def natTrans : (N₂ : Karoubi (SimplicialObject C) ⥤ _) ⋙ Γ₂ ⟶ 𝟭 _
 #align algebraic_topology.dold_kan.Γ₂N₂.nat_trans AlgebraicTopology.DoldKan.Γ₂N₂.natTrans
 
 /- warning: algebraic_topology.dold_kan.Γ₂N₂.nat_trans_app_f_app -> AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app is a dubious translation:
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_inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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))))) 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(CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) P)) (CategoryTheory.Idempotents.Karoubi.decompId_p.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) P)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂N₂.nat_trans_app_f_app AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_appₓ'. -/
 theorem natTrans_app_f_app (P : Karoubi (SimplicialObject C)) :
     Γ₂N₂.natTrans.app P =
@@ -239,10 +221,7 @@ theorem natTrans_app_f_app (P : Karoubi (SimplicialObject C)) :
 end Γ₂N₂
 
 /- warning: algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂_nat_trans -> AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans is a dubious translation:
-lean 3 declaration is
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(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 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(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))) (AlgebraicTopology.DoldKan.Γ₂N₂.natTrans.{u1, u2} C _inst_1 _inst_2 _inst_3) (Prefunctor.obj.{succ u2, succ u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (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)))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (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)) (CategoryTheory.Idempotents.toKaroubi.{max u1 u2, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))) X)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂_nat_trans AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTransₓ'. -/
 theorem compatibility_Γ₂N₁_Γ₂N₂_natTrans (X : SimplicialObject C) :
     Γ₂N₁.natTrans.app X =
@@ -257,10 +236,7 @@ theorem compatibility_Γ₂N₁_Γ₂N₂_natTrans (X : SimplicialObject C) :
 #align algebraic_topology.dold_kan.compatibility_Γ₂N₁_Γ₂N₂_nat_trans AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans
 
 /- warning: algebraic_topology.dold_kan.identity_N₂_objectwise -> AlgebraicTopology.DoldKan.identity_N₂_objectwise 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))) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_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) 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Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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 u2 u1, u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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 u2 u1, u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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.DoldKan.N₂.{u2, u1} C _inst_1 _inst_2)) P))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.identity_N₂_objectwise AlgebraicTopology.DoldKan.identity_N₂_objectwiseₓ'. -/
 theorem identity_N₂_objectwise (P : Karoubi (SimplicialObject C)) :
     N₂Γ₂.inv.app (N₂.obj P) ≫ N₂.map (Γ₂N₂.natTrans.app P) = 𝟙 (N₂.obj P) :=
@@ -293,10 +269,7 @@ theorem identity_N₂_objectwise (P : Karoubi (SimplicialObject C)) :
 #align algebraic_topology.dold_kan.identity_N₂_objectwise AlgebraicTopology.DoldKan.identity_N₂_objectwise
 
 /- warning: algebraic_topology.dold_kan.identity_N₂ -> AlgebraicTopology.DoldKan.identity_N₂ is a dubious translation:
-lean 3 declaration is
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(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.CategoryStruct.toQuiver.{max u2 u1, max u2 (max u2 u1) u1 u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, max u1 u2} (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)) (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 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_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.Functor.category.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) 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(AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))))) (AlgebraicTopology.DoldKan.N₂.{u1, u2} C _inst_1 _inst_2) (AlgebraicTopology.DoldKan.N₂.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.CategoryStruct.comp.{max u2 u1, max u2 (max u2 u1) u1 u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, max u1 u2} (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)) (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.Category.toCategoryStruct.{max u2 u1, max u2 (max u2 u1) u1 u2} (CategoryTheory.Functor.{u2, u2, max u2 u1, max u1 u2} (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)) (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 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_inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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.DoldKan.N₂.{u2, u1} C _inst_1 _inst_2))))) (CategoryTheory.CategoryStruct.id.{max u1 u2, max u1 u2} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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 u2 u1, u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} 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.DoldKan.N₂.{u2, u1} C _inst_1 _inst_2))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.identity_N₂ AlgebraicTopology.DoldKan.identity_N₂ₓ'. -/
 theorem identity_N₂ :
     ((𝟙 (N₂ : Karoubi (SimplicialObject C) ⥤ _) ◫ N₂Γ₂.inv) ≫ Γ₂N₂.natTrans ◫ 𝟙 N₂ : N₂ ⟶ N₂) =
@@ -331,10 +304,7 @@ instance : IsIso (Γ₂N₁.natTrans : (N₁ : SimplicialObject C ⥤ _) ⋙ _ 
   apply nat_iso.is_iso_of_is_iso_app
 
 /- warning: algebraic_topology.dold_kan.Γ₂N₂ -> AlgebraicTopology.DoldKan.Γ₂N₂ is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Γ₂N₂ AlgebraicTopology.DoldKan.Γ₂N₂ₓ'. -/
 /-- The unit isomorphism of the Dold-Kan equivalence. -/
 @[simp]