category_theory.preadditive.opposite ⟷ Mathlib.CategoryTheory.Preadditive.Opposite

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz, Johan Commelin, Joël Riou
 -/
-import Mathbin.CategoryTheory.Preadditive.AdditiveFunctor
-import Mathbin.Logic.Equiv.TransferInstance
+import CategoryTheory.Preadditive.AdditiveFunctor
+import Logic.Equiv.TransferInstance
 
 #align_import category_theory.preadditive.opposite from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
 

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

@@ -41,11 +41,11 @@ instance moduleEndLeft {X : Cᵒᵖ} {Y : C} : Module (End X) (unop X ⟶ Y)
 #align category_theory.module_End_left CategoryTheory.moduleEndLeft
 -/
 
-#print CategoryTheory.unop_zero /-
+#print CategoryTheory.Limits.unop_zero /-
 @[simp]
-theorem unop_zero (X Y : Cᵒᵖ) : (0 : X ⟶ Y).unop = 0 :=
+theorem CategoryTheory.Limits.unop_zero (X Y : Cᵒᵖ) : (0 : X ⟶ Y).unop = 0 :=
   rfl
-#align category_theory.unop_zero CategoryTheory.unop_zero
+#align category_theory.unop_zero CategoryTheory.Limits.unop_zero
 -/
 
 #print CategoryTheory.unop_add /-
@@ -69,11 +69,11 @@ theorem unop_neg {X Y : Cᵒᵖ} (f : X ⟶ Y) : (-f).unop = -f.unop :=
 #align category_theory.unop_neg CategoryTheory.unop_neg
 -/
 
-#print CategoryTheory.op_zero /-
+#print CategoryTheory.Limits.op_zero /-
 @[simp]
-theorem op_zero (X Y : C) : (0 : X ⟶ Y).op = 0 :=
+theorem CategoryTheory.Limits.op_zero (X Y : C) : (0 : X ⟶ Y).op = 0 :=
   rfl
-#align category_theory.op_zero CategoryTheory.op_zero
+#align category_theory.op_zero CategoryTheory.Limits.op_zero
 -/
 
 #print CategoryTheory.op_add /-

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz, Johan Commelin, Joël Riou
-
-! This file was ported from Lean 3 source module category_theory.preadditive.opposite
-! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Preadditive.AdditiveFunctor
 import Mathbin.Logic.Equiv.TransferInstance
 
+#align_import category_theory.preadditive.opposite from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+
 /-!
 # If `C` is preadditive, `Cᵒᵖ` has a natural preadditive structure.
 

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

@@ -34,6 +34,7 @@ instance : Preadditive Cᵒᵖ
   comp_add X Y Z f g g' :=
     congr_arg Quiver.Hom.op (Preadditive.add_comp _ _ _ g.unop g'.unop f.unop)
 
+#print CategoryTheory.moduleEndLeft /-
 instance moduleEndLeft {X : Cᵒᵖ} {Y : C} : Module (End X) (unop X ⟶ Y)
     where
   smul_add r f g := Preadditive.comp_add _ _ _ _ _ _
@@ -41,26 +42,35 @@ instance moduleEndLeft {X : Cᵒᵖ} {Y : C} : Module (End X) (unop X ⟶ Y)
   add_smul r s f := Preadditive.add_comp _ _ _ _ _ _
   zero_smul f := Limits.zero_comp
 #align category_theory.module_End_left CategoryTheory.moduleEndLeft
+-/
 
+#print CategoryTheory.unop_zero /-
 @[simp]
 theorem unop_zero (X Y : Cᵒᵖ) : (0 : X ⟶ Y).unop = 0 :=
   rfl
 #align category_theory.unop_zero CategoryTheory.unop_zero
+-/
 
+#print CategoryTheory.unop_add /-
 @[simp]
 theorem unop_add {X Y : Cᵒᵖ} (f g : X ⟶ Y) : (f + g).unop = f.unop + g.unop :=
   rfl
 #align category_theory.unop_add CategoryTheory.unop_add
+-/
 
+#print CategoryTheory.unop_zsmul /-
 @[simp]
 theorem unop_zsmul {X Y : Cᵒᵖ} (k : ℤ) (f : X ⟶ Y) : (k • f).unop = k • f.unop :=
   rfl
 #align category_theory.unop_zsmul CategoryTheory.unop_zsmul
+-/
 
+#print CategoryTheory.unop_neg /-
 @[simp]
 theorem unop_neg {X Y : Cᵒᵖ} (f : X ⟶ Y) : (-f).unop = -f.unop :=
   rfl
 #align category_theory.unop_neg CategoryTheory.unop_neg
+-/
 
 #print CategoryTheory.op_zero /-
 @[simp]
@@ -69,60 +79,82 @@ theorem op_zero (X Y : C) : (0 : X ⟶ Y).op = 0 :=
 #align category_theory.op_zero CategoryTheory.op_zero
 -/
 
+#print CategoryTheory.op_add /-
 @[simp]
 theorem op_add {X Y : C} (f g : X ⟶ Y) : (f + g).op = f.op + g.op :=
   rfl
 #align category_theory.op_add CategoryTheory.op_add
+-/
 
+#print CategoryTheory.op_zsmul /-
 @[simp]
 theorem op_zsmul {X Y : C} (k : ℤ) (f : X ⟶ Y) : (k • f).op = k • f.op :=
   rfl
 #align category_theory.op_zsmul CategoryTheory.op_zsmul
+-/
 
+#print CategoryTheory.op_neg /-
 @[simp]
 theorem op_neg {X Y : C} (f : X ⟶ Y) : (-f).op = -f.op :=
   rfl
 #align category_theory.op_neg CategoryTheory.op_neg
+-/
 
 variable {C}
 
+#print CategoryTheory.unopHom /-
 /-- `unop` induces morphisms of monoids on hom groups of a preadditive category -/
 @[simps]
 def unopHom (X Y : Cᵒᵖ) : (X ⟶ Y) →+ (Opposite.unop Y ⟶ Opposite.unop X) :=
   AddMonoidHom.mk' (fun f => f.unop) fun f g => unop_add _ f g
 #align category_theory.unop_hom CategoryTheory.unopHom
+-/
 
+#print CategoryTheory.unop_sum /-
 @[simp]
 theorem unop_sum (X Y : Cᵒᵖ) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.Sum f).unop = s.Sum fun i => (f i).unop :=
   (unopHom X Y).map_sum _ _
 #align category_theory.unop_sum CategoryTheory.unop_sum
+-/
 
+#print CategoryTheory.opHom /-
 /-- `op` induces morphisms of monoids on hom groups of a preadditive category -/
 @[simps]
 def opHom (X Y : C) : (X ⟶ Y) →+ (Opposite.op Y ⟶ Opposite.op X) :=
   AddMonoidHom.mk' (fun f => f.op) fun f g => op_add _ f g
 #align category_theory.op_hom CategoryTheory.opHom
+-/
 
+#print CategoryTheory.op_sum /-
 @[simp]
 theorem op_sum (X Y : C) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.Sum f).op = s.Sum fun i => (f i).op :=
   (opHom X Y).map_sum _ _
 #align category_theory.op_sum CategoryTheory.op_sum
+-/
 
 variable {D : Type _} [Category D] [Preadditive D]
 
+#print CategoryTheory.Functor.op_additive /-
 instance Functor.op_additive (F : C ⥤ D) [F.Additive] : F.op.Additive where
 #align category_theory.functor.op_additive CategoryTheory.Functor.op_additive
+-/
 
+#print CategoryTheory.Functor.rightOp_additive /-
 instance Functor.rightOp_additive (F : Cᵒᵖ ⥤ D) [F.Additive] : F.rightOp.Additive where
 #align category_theory.functor.right_op_additive CategoryTheory.Functor.rightOp_additive
+-/
 
+#print CategoryTheory.Functor.leftOp_additive /-
 instance Functor.leftOp_additive (F : C ⥤ Dᵒᵖ) [F.Additive] : F.leftOp.Additive where
 #align category_theory.functor.left_op_additive CategoryTheory.Functor.leftOp_additive
+-/
 
+#print CategoryTheory.Functor.unop_additive /-
 instance Functor.unop_additive (F : Cᵒᵖ ⥤ Dᵒᵖ) [F.Additive] : F.unop.Additive where
 #align category_theory.functor.unop_additive CategoryTheory.Functor.unop_additive
+-/
 
 end CategoryTheory
 

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

@@ -34,12 +34,6 @@ instance : Preadditive Cᵒᵖ
   comp_add X Y Z f g g' :=
     congr_arg Quiver.Hom.op (Preadditive.add_comp _ _ _ g.unop g'.unop f.unop)
 
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 instance moduleEndLeft {X : Cᵒᵖ} {Y : C} : Module (End X) (unop X ⟶ Y)
     where
   smul_add r f g := Preadditive.comp_add _ _ _ _ _ _
@@ -48,42 +42,21 @@ instance moduleEndLeft {X : Cᵒᵖ} {Y : C} : Module (End X) (unop X ⟶ Y)
   zero_smul f := Limits.zero_comp
 #align category_theory.module_End_left CategoryTheory.moduleEndLeft
 
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 @[simp]
 theorem unop_zero (X Y : Cᵒᵖ) : (0 : X ⟶ Y).unop = 0 :=
   rfl
 #align category_theory.unop_zero CategoryTheory.unop_zero
 
-/- warning: category_theory.unop_add -> CategoryTheory.unop_add is a dubious translation:
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 @[simp]
 theorem unop_add {X Y : Cᵒᵖ} (f g : X ⟶ Y) : (f + g).unop = f.unop + g.unop :=
   rfl
 #align category_theory.unop_add CategoryTheory.unop_add
 
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 @[simp]
 theorem unop_zsmul {X Y : Cᵒᵖ} (k : ℤ) (f : X ⟶ Y) : (k • f).unop = k • f.unop :=
   rfl
 #align category_theory.unop_zsmul CategoryTheory.unop_zsmul
 
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 @[simp]
 theorem unop_neg {X Y : Cᵒᵖ} (f : X ⟶ Y) : (-f).unop = -f.unop :=
   rfl
@@ -96,31 +69,16 @@ theorem op_zero (X Y : C) : (0 : X ⟶ Y).op = 0 :=
 #align category_theory.op_zero CategoryTheory.op_zero
 -/
 
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 @[simp]
 theorem op_add {X Y : C} (f g : X ⟶ Y) : (f + g).op = f.op + g.op :=
   rfl
 #align category_theory.op_add CategoryTheory.op_add
 
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 @[simp]
 theorem op_zsmul {X Y : C} (k : ℤ) (f : X ⟶ Y) : (k • f).op = k • f.op :=
   rfl
 #align category_theory.op_zsmul CategoryTheory.op_zsmul
 
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 @[simp]
 theorem op_neg {X Y : C} (f : X ⟶ Y) : (-f).op = -f.op :=
   rfl
@@ -128,48 +86,24 @@ theorem op_neg {X Y : C} (f : X ⟶ Y) : (-f).op = -f.op :=
 
 variable {C}
 
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 /-- `unop` induces morphisms of monoids on hom groups of a preadditive category -/
 @[simps]
 def unopHom (X Y : Cᵒᵖ) : (X ⟶ Y) →+ (Opposite.unop Y ⟶ Opposite.unop X) :=
   AddMonoidHom.mk' (fun f => f.unop) fun f g => unop_add _ f g
 #align category_theory.unop_hom CategoryTheory.unopHom
 
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 @[simp]
 theorem unop_sum (X Y : Cᵒᵖ) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.Sum f).unop = s.Sum fun i => (f i).unop :=
   (unopHom X Y).map_sum _ _
 #align category_theory.unop_sum CategoryTheory.unop_sum
 
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 /-- `op` induces morphisms of monoids on hom groups of a preadditive category -/
 @[simps]
 def opHom (X Y : C) : (X ⟶ Y) →+ (Opposite.op Y ⟶ Opposite.op X) :=
   AddMonoidHom.mk' (fun f => f.op) fun f g => op_add _ f g
 #align category_theory.op_hom CategoryTheory.opHom
 
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 @[simp]
 theorem op_sum (X Y : C) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.Sum f).op = s.Sum fun i => (f i).op :=
@@ -178,39 +112,15 @@ theorem op_sum (X Y : C) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
 
 variable {D : Type _} [Category D] [Preadditive D]
 
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 instance Functor.op_additive (F : C ⥤ D) [F.Additive] : F.op.Additive where
 #align category_theory.functor.op_additive CategoryTheory.Functor.op_additive
 
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 instance Functor.rightOp_additive (F : Cᵒᵖ ⥤ D) [F.Additive] : F.rightOp.Additive where
 #align category_theory.functor.right_op_additive CategoryTheory.Functor.rightOp_additive
 
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 instance Functor.leftOp_additive (F : C ⥤ Dᵒᵖ) [F.Additive] : F.leftOp.Additive where
 #align category_theory.functor.left_op_additive CategoryTheory.Functor.leftOp_additive
 
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 instance Functor.unop_additive (F : Cᵒᵖ ⥤ Dᵒᵖ) [F.Additive] : F.unop.Additive where
 #align category_theory.functor.unop_additive CategoryTheory.Functor.unop_additive
 

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

@@ -60,10 +60,7 @@ theorem unop_zero (X Y : Cᵒᵖ) : (0 : X ⟶ Y).unop = 0 :=
 #align category_theory.unop_zero CategoryTheory.unop_zero
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.unop_add CategoryTheory.unop_addₓ'. -/
 @[simp]
 theorem unop_add {X Y : Cᵒᵖ} (f g : X ⟶ Y) : (f + g).unop = f.unop + g.unop :=
@@ -100,10 +97,7 @@ theorem op_zero (X Y : C) : (0 : X ⟶ Y).op = 0 :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.op_add CategoryTheory.op_addₓ'. -/
 @[simp]
 theorem op_add {X Y : C} (f g : X ⟶ Y) : (f + g).op = f.op + g.op :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz, Johan Commelin, Joël Riou
 
 ! This file was ported from Lean 3 source module category_theory.preadditive.opposite
-! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Logic.Equiv.TransferInstance
 /-!
 # If `C` is preadditive, `Cᵒᵖ` has a natural preadditive structure.
 
+> 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/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

@@ -31,6 +31,12 @@ instance : Preadditive Cᵒᵖ
   comp_add X Y Z f g g' :=
     congr_arg Quiver.Hom.op (Preadditive.add_comp _ _ _ g.unop g'.unop f.unop)
 
+/- warning: category_theory.module_End_left -> CategoryTheory.moduleEndLeft is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.module_End_left CategoryTheory.moduleEndLeftₓ'. -/
 instance moduleEndLeft {X : Cᵒᵖ} {Y : C} : Module (End X) (unop X ⟶ Y)
     where
   smul_add r f g := Preadditive.comp_add _ _ _ _ _ _
@@ -39,41 +45,85 @@ instance moduleEndLeft {X : Cᵒᵖ} {Y : C} : Module (End X) (unop X ⟶ Y)
   zero_smul f := Limits.zero_comp
 #align category_theory.module_End_left CategoryTheory.moduleEndLeft
 
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 @[simp]
 theorem unop_zero (X Y : Cᵒᵖ) : (0 : X ⟶ Y).unop = 0 :=
   rfl
 #align category_theory.unop_zero CategoryTheory.unop_zero
 
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 @[simp]
 theorem unop_add {X Y : Cᵒᵖ} (f g : X ⟶ Y) : (f + g).unop = f.unop + g.unop :=
   rfl
 #align category_theory.unop_add CategoryTheory.unop_add
 
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 @[simp]
 theorem unop_zsmul {X Y : Cᵒᵖ} (k : ℤ) (f : X ⟶ Y) : (k • f).unop = k • f.unop :=
   rfl
 #align category_theory.unop_zsmul CategoryTheory.unop_zsmul
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.unop_neg CategoryTheory.unop_negₓ'. -/
 @[simp]
 theorem unop_neg {X Y : Cᵒᵖ} (f : X ⟶ Y) : (-f).unop = -f.unop :=
   rfl
 #align category_theory.unop_neg CategoryTheory.unop_neg
 
+#print CategoryTheory.op_zero /-
 @[simp]
 theorem op_zero (X Y : C) : (0 : X ⟶ Y).op = 0 :=
   rfl
 #align category_theory.op_zero CategoryTheory.op_zero
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.op_add CategoryTheory.op_addₓ'. -/
 @[simp]
 theorem op_add {X Y : C} (f g : X ⟶ Y) : (f + g).op = f.op + g.op :=
   rfl
 #align category_theory.op_add CategoryTheory.op_add
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.op_zsmul CategoryTheory.op_zsmulₓ'. -/
 @[simp]
 theorem op_zsmul {X Y : C} (k : ℤ) (f : X ⟶ Y) : (k • f).op = k • f.op :=
   rfl
 #align category_theory.op_zsmul CategoryTheory.op_zsmul
 
+/- warning: category_theory.op_neg -> CategoryTheory.op_neg is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.op_neg CategoryTheory.op_negₓ'. -/
 @[simp]
 theorem op_neg {X Y : C} (f : X ⟶ Y) : (-f).op = -f.op :=
   rfl
@@ -81,24 +131,48 @@ theorem op_neg {X Y : C} (f : X ⟶ Y) : (-f).op = -f.op :=
 
 variable {C}
 
+/- warning: category_theory.unop_hom -> CategoryTheory.unopHom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.unop_hom CategoryTheory.unopHomₓ'. -/
 /-- `unop` induces morphisms of monoids on hom groups of a preadditive category -/
 @[simps]
 def unopHom (X Y : Cᵒᵖ) : (X ⟶ Y) →+ (Opposite.unop Y ⟶ Opposite.unop X) :=
   AddMonoidHom.mk' (fun f => f.unop) fun f g => unop_add _ f g
 #align category_theory.unop_hom CategoryTheory.unopHom
 
+/- warning: category_theory.unop_sum -> CategoryTheory.unop_sum is a dubious translation:
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 @[simp]
 theorem unop_sum (X Y : Cᵒᵖ) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.Sum f).unop = s.Sum fun i => (f i).unop :=
   (unopHom X Y).map_sum _ _
 #align category_theory.unop_sum CategoryTheory.unop_sum
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.op_hom CategoryTheory.opHomₓ'. -/
 /-- `op` induces morphisms of monoids on hom groups of a preadditive category -/
 @[simps]
 def opHom (X Y : C) : (X ⟶ Y) →+ (Opposite.op Y ⟶ Opposite.op X) :=
   AddMonoidHom.mk' (fun f => f.op) fun f g => op_add _ f g
 #align category_theory.op_hom CategoryTheory.opHom
 
+/- warning: category_theory.op_sum -> CategoryTheory.op_sum 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] (X : C) (Y : C) {ι : Type.{u3}} (s : Finset.{u3} ι) (f : ι -> (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y)), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} (Opposite.{succ u1} C) (Quiver.opposite.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1))) (Opposite.op.{succ u1} C Y) (Opposite.op.{succ u1} C X)) (Quiver.Hom.op.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y (Finset.sum.{u2, u3} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y) ι (AddCommGroup.toAddCommMonoid.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y) (CategoryTheory.Preadditive.homGroup.{u2, u1} C _inst_1 _inst_2 X Y)) s f)) (Finset.sum.{u2, u3} (Quiver.Hom.{succ u2, u1} (Opposite.{succ u1} C) (Quiver.opposite.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1))) (Opposite.op.{succ u1} C Y) (Opposite.op.{succ u1} C X)) ι (AddCommGroup.toAddCommMonoid.{u2} (Quiver.Hom.{succ u2, u1} (Opposite.{succ u1} C) (Quiver.opposite.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1))) (Opposite.op.{succ u1} C Y) (Opposite.op.{succ u1} C X)) (CategoryTheory.Preadditive.homGroup.{u2, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) (CategoryTheory.Opposite.preadditive.{u1, u2} C _inst_1 _inst_2) (Opposite.op.{succ u1} C Y) (Opposite.op.{succ u1} C X))) s (fun (i : ι) => Quiver.Hom.op.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y (f i)))
+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] (X : C) (Y : C) {ι : Type.{u3}} (s : Finset.{u3} ι) (f : ι -> (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y)), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} (Opposite.{succ u1} C) (Quiver.opposite.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1))) (Opposite.op.{succ u1} C Y) (Opposite.op.{succ u1} C X)) (Quiver.Hom.op.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y (Finset.sum.{u2, u3} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y) ι (AddCommGroup.toAddCommMonoid.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y) (CategoryTheory.Preadditive.homGroup.{u2, u1} C _inst_1 _inst_2 X Y)) s f)) (Finset.sum.{u2, u3} (Quiver.Hom.{succ u2, u1} (Opposite.{succ u1} C) (Quiver.opposite.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1))) (Opposite.op.{succ u1} C Y) (Opposite.op.{succ u1} C X)) ι (AddCommGroup.toAddCommMonoid.{u2} (Quiver.Hom.{succ u2, u1} (Opposite.{succ u1} C) (Quiver.opposite.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1))) (Opposite.op.{succ u1} C Y) (Opposite.op.{succ u1} C X)) (CategoryTheory.Preadditive.homGroup.{u2, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) (CategoryTheory.instPreadditiveOppositeOpposite.{u1, u2} C _inst_1 _inst_2) (Opposite.op.{succ u1} C Y) (Opposite.op.{succ u1} C X))) s (fun (i : ι) => Quiver.Hom.op.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) X Y (f i)))
+Case conversion may be inaccurate. Consider using '#align category_theory.op_sum CategoryTheory.op_sumₓ'. -/
 @[simp]
 theorem op_sum (X Y : C) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.Sum f).op = s.Sum fun i => (f i).op :=
@@ -107,15 +181,39 @@ theorem op_sum (X Y : C) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
 
 variable {D : Type _} [Category D] [Preadditive D]
 
+/- warning: category_theory.functor.op_additive -> CategoryTheory.Functor.op_additive 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] {D : Type.{u3}} [_inst_3 : CategoryTheory.Category.{u4, u3} D] [_inst_4 : CategoryTheory.Preadditive.{u4, u3} D _inst_3] (F : CategoryTheory.Functor.{u2, u4, u1, u3} C _inst_1 D _inst_3) [_inst_5 : CategoryTheory.Functor.Additive.{u1, u3, u2, u4} C D _inst_1 _inst_3 _inst_2 _inst_4 F], CategoryTheory.Functor.Additive.{u1, u3, u2, u4} (Opposite.{succ u1} C) (Opposite.{succ u3} D) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) (CategoryTheory.Category.opposite.{u4, u3} D _inst_3) (CategoryTheory.Opposite.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Opposite.preadditive.{u3, u4} D _inst_3 _inst_4) (CategoryTheory.Functor.op.{u2, u4, u1, u3} C _inst_1 D _inst_3 F)
+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] {D : Type.{u3}} [_inst_3 : CategoryTheory.Category.{u4, u3} D] [_inst_4 : CategoryTheory.Preadditive.{u4, u3} D _inst_3] (F : CategoryTheory.Functor.{u2, u4, u1, u3} C _inst_1 D _inst_3) [_inst_5 : CategoryTheory.Functor.Additive.{u1, u3, u2, u4} C D _inst_1 _inst_3 _inst_2 _inst_4 F], CategoryTheory.Functor.Additive.{u1, u3, u2, u4} (Opposite.{succ u1} C) (Opposite.{succ u3} D) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) (CategoryTheory.Category.opposite.{u4, u3} D _inst_3) (CategoryTheory.instPreadditiveOppositeOpposite.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.instPreadditiveOppositeOpposite.{u3, u4} D _inst_3 _inst_4) (CategoryTheory.Functor.op.{u2, u4, u1, u3} C _inst_1 D _inst_3 F)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.op_additive CategoryTheory.Functor.op_additiveₓ'. -/
 instance Functor.op_additive (F : C ⥤ D) [F.Additive] : F.op.Additive where
 #align category_theory.functor.op_additive CategoryTheory.Functor.op_additive
 
+/- warning: category_theory.functor.right_op_additive -> CategoryTheory.Functor.rightOp_additive 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] {D : Type.{u3}} [_inst_3 : CategoryTheory.Category.{u4, u3} D] [_inst_4 : CategoryTheory.Preadditive.{u4, u3} D _inst_3] (F : CategoryTheory.Functor.{u2, u4, u1, u3} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) D _inst_3) [_inst_5 : CategoryTheory.Functor.Additive.{u1, u3, u2, u4} (Opposite.{succ u1} C) D (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) _inst_3 (CategoryTheory.Opposite.preadditive.{u1, u2} C _inst_1 _inst_2) _inst_4 F], CategoryTheory.Functor.Additive.{u1, u3, u2, u4} C (Opposite.{succ u3} D) _inst_1 (CategoryTheory.Category.opposite.{u4, u3} D _inst_3) _inst_2 (CategoryTheory.Opposite.preadditive.{u3, u4} D _inst_3 _inst_4) (CategoryTheory.Functor.rightOp.{u2, u4, u1, u3} C _inst_1 D _inst_3 F)
+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] {D : Type.{u3}} [_inst_3 : CategoryTheory.Category.{u4, u3} D] [_inst_4 : CategoryTheory.Preadditive.{u4, u3} D _inst_3] (F : CategoryTheory.Functor.{u2, u4, u1, u3} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) D _inst_3) [_inst_5 : CategoryTheory.Functor.Additive.{u1, u3, u2, u4} (Opposite.{succ u1} C) D (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) _inst_3 (CategoryTheory.instPreadditiveOppositeOpposite.{u1, u2} C _inst_1 _inst_2) _inst_4 F], CategoryTheory.Functor.Additive.{u1, u3, u2, u4} C (Opposite.{succ u3} D) _inst_1 (CategoryTheory.Category.opposite.{u4, u3} D _inst_3) _inst_2 (CategoryTheory.instPreadditiveOppositeOpposite.{u3, u4} D _inst_3 _inst_4) (CategoryTheory.Functor.rightOp.{u2, u4, u1, u3} C _inst_1 D _inst_3 F)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.right_op_additive CategoryTheory.Functor.rightOp_additiveₓ'. -/
 instance Functor.rightOp_additive (F : Cᵒᵖ ⥤ D) [F.Additive] : F.rightOp.Additive where
 #align category_theory.functor.right_op_additive CategoryTheory.Functor.rightOp_additive
 
+/- warning: category_theory.functor.left_op_additive -> CategoryTheory.Functor.leftOp_additive 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] {D : Type.{u3}} [_inst_3 : CategoryTheory.Category.{u4, u3} D] [_inst_4 : CategoryTheory.Preadditive.{u4, u3} D _inst_3] (F : CategoryTheory.Functor.{u2, u4, u1, u3} C _inst_1 (Opposite.{succ u3} D) (CategoryTheory.Category.opposite.{u4, u3} D _inst_3)) [_inst_5 : CategoryTheory.Functor.Additive.{u1, u3, u2, u4} C (Opposite.{succ u3} D) _inst_1 (CategoryTheory.Category.opposite.{u4, u3} D _inst_3) _inst_2 (CategoryTheory.Opposite.preadditive.{u3, u4} D _inst_3 _inst_4) F], CategoryTheory.Functor.Additive.{u1, u3, u2, u4} (Opposite.{succ u1} C) D (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) _inst_3 (CategoryTheory.Opposite.preadditive.{u1, u2} C _inst_1 _inst_2) _inst_4 (CategoryTheory.Functor.leftOp.{u2, u4, u1, u3} C _inst_1 D _inst_3 F)
+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] {D : Type.{u3}} [_inst_3 : CategoryTheory.Category.{u4, u3} D] [_inst_4 : CategoryTheory.Preadditive.{u4, u3} D _inst_3] (F : CategoryTheory.Functor.{u2, u4, u1, u3} C _inst_1 (Opposite.{succ u3} D) (CategoryTheory.Category.opposite.{u4, u3} D _inst_3)) [_inst_5 : CategoryTheory.Functor.Additive.{u1, u3, u2, u4} C (Opposite.{succ u3} D) _inst_1 (CategoryTheory.Category.opposite.{u4, u3} D _inst_3) _inst_2 (CategoryTheory.instPreadditiveOppositeOpposite.{u3, u4} D _inst_3 _inst_4) F], CategoryTheory.Functor.Additive.{u1, u3, u2, u4} (Opposite.{succ u1} C) D (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) _inst_3 (CategoryTheory.instPreadditiveOppositeOpposite.{u1, u2} C _inst_1 _inst_2) _inst_4 (CategoryTheory.Functor.leftOp.{u2, u4, u1, u3} C _inst_1 D _inst_3 F)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.left_op_additive CategoryTheory.Functor.leftOp_additiveₓ'. -/
 instance Functor.leftOp_additive (F : C ⥤ Dᵒᵖ) [F.Additive] : F.leftOp.Additive where
 #align category_theory.functor.left_op_additive CategoryTheory.Functor.leftOp_additive
 
+/- warning: category_theory.functor.unop_additive -> CategoryTheory.Functor.unop_additive 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] {D : Type.{u3}} [_inst_3 : CategoryTheory.Category.{u4, u3} D] [_inst_4 : CategoryTheory.Preadditive.{u4, u3} D _inst_3] (F : CategoryTheory.Functor.{u2, u4, u1, u3} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) (Opposite.{succ u3} D) (CategoryTheory.Category.opposite.{u4, u3} D _inst_3)) [_inst_5 : CategoryTheory.Functor.Additive.{u1, u3, u2, u4} (Opposite.{succ u1} C) (Opposite.{succ u3} D) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) (CategoryTheory.Category.opposite.{u4, u3} D _inst_3) (CategoryTheory.Opposite.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Opposite.preadditive.{u3, u4} D _inst_3 _inst_4) F], CategoryTheory.Functor.Additive.{u1, u3, u2, u4} C D _inst_1 _inst_3 _inst_2 _inst_4 (CategoryTheory.Functor.unop.{u2, u4, u1, u3} C _inst_1 D _inst_3 F)
+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] {D : Type.{u3}} [_inst_3 : CategoryTheory.Category.{u4, u3} D] [_inst_4 : CategoryTheory.Preadditive.{u4, u3} D _inst_3] (F : CategoryTheory.Functor.{u2, u4, u1, u3} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) (Opposite.{succ u3} D) (CategoryTheory.Category.opposite.{u4, u3} D _inst_3)) [_inst_5 : CategoryTheory.Functor.Additive.{u1, u3, u2, u4} (Opposite.{succ u1} C) (Opposite.{succ u3} D) (CategoryTheory.Category.opposite.{u2, u1} C _inst_1) (CategoryTheory.Category.opposite.{u4, u3} D _inst_3) (CategoryTheory.instPreadditiveOppositeOpposite.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.instPreadditiveOppositeOpposite.{u3, u4} D _inst_3 _inst_4) F], CategoryTheory.Functor.Additive.{u1, u3, u2, u4} C D _inst_1 _inst_3 _inst_2 _inst_4 (CategoryTheory.Functor.unop.{u2, u4, u1, u3} C _inst_1 D _inst_3 F)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.unop_additive CategoryTheory.Functor.unop_additiveₓ'. -/
 instance Functor.unop_additive (F : Cᵒᵖ ⥤ Dᵒᵖ) [F.Additive] : F.unop.Additive where
 #align category_theory.functor.unop_additive CategoryTheory.Functor.unop_additive
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a

@@ -4,11 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz, Johan Commelin, Joël Riou
 
 ! This file was ported from Lean 3 source module category_theory.preadditive.opposite
-! leanprover-community/mathlib commit 829895f162a1f29d0133f4b3538f4cd1fb5bffd3
+! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.CategoryTheory.Preadditive.Basic
 import Mathbin.CategoryTheory.Preadditive.AdditiveFunctor
 import Mathbin.Logic.Equiv.TransferInstance
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -27,9 +27,9 @@ variable (C : Type _) [Category C] [Preadditive C]
 instance : Preadditive Cᵒᵖ
     where
   homGroup X Y := Equiv.addCommGroup (opEquiv X Y)
-  add_comp' X Y Z f f' g :=
+  add_comp X Y Z f f' g :=
     congr_arg Quiver.Hom.op (Preadditive.comp_add _ _ _ g.unop f.unop f'.unop)
-  comp_add' X Y Z f g g' :=
+  comp_add X Y Z f g g' :=
     congr_arg Quiver.Hom.op (Preadditive.add_comp _ _ _ g.unop g'.unop f.unop)
 
 instance moduleEndLeft {X : Cᵒᵖ} {Y : C} : Module (End X) (unop X ⟶ Y)

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

@@ -73,7 +73,7 @@ def unopHom (X Y : Cᵒᵖ) : (X ⟶ Y) →+ (Opposite.unop Y ⟶ Opposite.unop
 @[simp]
 theorem unop_sum (X Y : Cᵒᵖ) {ι : Type*} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.sum f).unop = s.sum fun i => (f i).unop :=
-  (unopHom X Y).map_sum _ _
+  map_sum (unopHom X Y) _ _
 #align category_theory.unop_sum CategoryTheory.unop_sum
 
 /-- `op` induces morphisms of monoids on hom groups of a preadditive category -/
@@ -85,7 +85,7 @@ def opHom (X Y : C) : (X ⟶ Y) →+ (Opposite.op Y ⟶ Opposite.op X) :=
 @[simp]
 theorem op_sum (X Y : C) {ι : Type*} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.sum f).op = s.sum fun i => (f i).op :=
-  (opHom X Y).map_sum _ _
+  map_sum (opHom X Y) _ _
 #align category_theory.op_sum CategoryTheory.op_sum
 
 variable {D : Type*} [Category D] [Preadditive D]

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

This has nice performance benefits.

@@ -18,7 +18,7 @@ open Opposite
 
 namespace CategoryTheory
 
-variable (C : Type _) [Category C] [Preadditive C]
+variable (C : Type*) [Category C] [Preadditive C]
 
 instance : Preadditive Cᵒᵖ where
   homGroup X Y := Equiv.addCommGroup (opEquiv X Y)
@@ -71,7 +71,7 @@ def unopHom (X Y : Cᵒᵖ) : (X ⟶ Y) →+ (Opposite.unop Y ⟶ Opposite.unop
 #align category_theory.unop_hom CategoryTheory.unopHom
 
 @[simp]
-theorem unop_sum (X Y : Cᵒᵖ) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
+theorem unop_sum (X Y : Cᵒᵖ) {ι : Type*} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.sum f).unop = s.sum fun i => (f i).unop :=
   (unopHom X Y).map_sum _ _
 #align category_theory.unop_sum CategoryTheory.unop_sum
@@ -83,12 +83,12 @@ def opHom (X Y : C) : (X ⟶ Y) →+ (Opposite.op Y ⟶ Opposite.op X) :=
 #align category_theory.op_hom CategoryTheory.opHom
 
 @[simp]
-theorem op_sum (X Y : C) {ι : Type _} (s : Finset ι) (f : ι → (X ⟶ Y)) :
+theorem op_sum (X Y : C) {ι : Type*} (s : Finset ι) (f : ι → (X ⟶ Y)) :
     (s.sum f).op = s.sum fun i => (f i).op :=
   (opHom X Y).map_sum _ _
 #align category_theory.op_sum CategoryTheory.op_sum
 
-variable {D : Type _} [Category D] [Preadditive D]
+variable {D : Type*} [Category D] [Preadditive D]
 
 instance Functor.op_additive (F : C ⥤ D) [F.Additive] : F.op.Additive where
 #align category_theory.functor.op_additive CategoryTheory.Functor.op_additive

This PR shows that left and right homology data of short complexes are dual notions.

@@ -32,11 +32,6 @@ instance moduleEndLeft {X : Cᵒᵖ} {Y : C} : Module (End X) (unop X ⟶ Y) whe
   zero_smul _ := Limits.zero_comp
 #align category_theory.module_End_left CategoryTheory.moduleEndLeft
 
-@[simp]
-theorem unop_zero (X Y : Cᵒᵖ) : (0 : X ⟶ Y).unop = 0 :=
-  rfl
-#align category_theory.unop_zero CategoryTheory.unop_zero
-
 @[simp]
 theorem unop_add {X Y : Cᵒᵖ} (f g : X ⟶ Y) : (f + g).unop = f.unop + g.unop :=
   rfl
@@ -52,11 +47,6 @@ theorem unop_neg {X Y : Cᵒᵖ} (f : X ⟶ Y) : (-f).unop = -f.unop :=
   rfl
 #align category_theory.unop_neg CategoryTheory.unop_neg
 
-@[simp]
-theorem op_zero (X Y : C) : (0 : X ⟶ Y).op = 0 :=
-  rfl
-#align category_theory.op_zero CategoryTheory.op_zero
-
 @[simp]
 theorem op_add {X Y : C} (f g : X ⟶ Y) : (f + g).op = f.op + g.op :=
   rfl

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz, Johan Commelin, Joël Riou
-
-! This file was ported from Lean 3 source module category_theory.preadditive.opposite
-! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
 import Mathlib.Logic.Equiv.TransferInstance
 
+#align_import category_theory.preadditive.opposite from "leanprover-community/mathlib"@"f8d8465c3c392a93b9ed226956e26dee00975946"
+
 /-!
 # If `C` is preadditive, `Cᵒᵖ` has a natural preadditive structure.
 

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