category_theory.triangulated.basic ⟷ Mathlib.CategoryTheory.Triangulated.Basic

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Luke Kershaw. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
 -/
-import Data.Int.Basic
+import Algebra.Group.Int
 import CategoryTheory.Shift.Basic
 
 #align_import category_theory.triangulated.basic from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Luke Kershaw. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
 -/
-import Mathbin.Data.Int.Basic
-import Mathbin.CategoryTheory.Shift.Basic
+import Data.Int.Basic
+import CategoryTheory.Shift.Basic
 
 #align_import category_theory.triangulated.basic from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
 

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

@@ -118,12 +118,6 @@ structure TriangleMorphism (T₁ : Triangle C) (T₂ : Triangle C) where
 #align category_theory.pretriangulated.triangle_morphism CategoryTheory.Pretriangulated.TriangleMorphism
 -/
 
-restate_axiom triangle_morphism.comm₁'
-
-restate_axiom triangle_morphism.comm₂'
-
-restate_axiom triangle_morphism.comm₃'
-
 attribute [simp, reassoc] triangle_morphism.comm₁ triangle_morphism.comm₂ triangle_morphism.comm₃
 
 #print CategoryTheory.Pretriangulated.triangleMorphismId /-

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Luke Kershaw. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
-
-! This file was ported from Lean 3 source module category_theory.triangulated.basic
-! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Int.Basic
 import Mathbin.CategoryTheory.Shift.Basic
 
+#align_import category_theory.triangulated.basic from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
+
 /-!
 # Triangles
 

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

@@ -41,6 +41,7 @@ We work in a category `C` equipped with a shift.
 -/
 variable (C : Type u) [Category.{v} C] [HasShift C ℤ]
 
+#print CategoryTheory.Pretriangulated.Triangle /-
 /-- A triangle in `C` is a sextuple `(X,Y,Z,f,g,h)` where `X,Y,Z` are objects of `C`,
 and `f : X ⟶ Y`, `g : Y ⟶ Z`, `h : Z ⟶ X⟦1⟧` are morphisms in `C`.
 See <https://stacks.math.columbia.edu/tag/0144>.
@@ -53,9 +54,11 @@ structure Triangle where mk' ::
   mor₂ : obj₂ ⟶ obj₃
   mor₃ : obj₃ ⟶ obj₁⟦(1 : ℤ)⟧
 #align category_theory.pretriangulated.triangle CategoryTheory.Pretriangulated.Triangle
+-/
 
 variable {C}
 
+#print CategoryTheory.Pretriangulated.Triangle.mk /-
 /-- A triangle `(X,Y,Z,f,g,h)` in `C` is defined by the morphisms `f : X ⟶ Y`, `g : Y ⟶ Z`
 and `h : Z ⟶ X⟦1⟧`.
 -/
@@ -69,6 +72,7 @@ def Triangle.mk {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ X⟦(1 : ℤ)
   mor₂ := g
   mor₃ := h
 #align category_theory.pretriangulated.triangle.mk CategoryTheory.Pretriangulated.Triangle.mk
+-/
 
 section
 
@@ -79,15 +83,18 @@ open scoped ZeroObject
 instance : Inhabited (Triangle C) :=
   ⟨⟨0, 0, 0, 0, 0, 0⟩⟩
 
+#print CategoryTheory.Pretriangulated.contractibleTriangle /-
 /-- For each object in `C`, there is a triangle of the form `(X,X,0,𝟙 X,0,0)`
 -/
 @[simps]
 def contractibleTriangle (X : C) : Triangle C :=
   Triangle.mk (𝟙 X) (0 : X ⟶ 0) 0
 #align category_theory.pretriangulated.contractible_triangle CategoryTheory.Pretriangulated.contractibleTriangle
+-/
 
 end
 
+#print CategoryTheory.Pretriangulated.TriangleMorphism /-
 /-- A morphism of triangles `(X,Y,Z,f,g,h) ⟶ (X',Y',Z',f',g',h')` in `C` is a triple of morphisms
 `a : X ⟶ X'`, `b : Y ⟶ Y'`, `c : Z ⟶ Z'` such that
 `a ≫ f' = f ≫ b`, `b ≫ g' = g ≫ c`, and `a⟦1⟧' ≫ h = h' ≫ c`.
@@ -112,6 +119,7 @@ structure TriangleMorphism (T₁ : Triangle C) (T₂ : Triangle C) where
   comm₂' : T₁.mor₂ ≫ hom₃ = hom₂ ≫ T₂.mor₂ := by obviously
   comm₃' : T₁.mor₃ ≫ hom₁⟦1⟧' = hom₃ ≫ T₂.mor₃ := by obviously
 #align category_theory.pretriangulated.triangle_morphism CategoryTheory.Pretriangulated.TriangleMorphism
+-/
 
 restate_axiom triangle_morphism.comm₁'
 
@@ -121,6 +129,7 @@ restate_axiom triangle_morphism.comm₃'
 
 attribute [simp, reassoc] triangle_morphism.comm₁ triangle_morphism.comm₂ triangle_morphism.comm₃
 
+#print CategoryTheory.Pretriangulated.triangleMorphismId /-
 /-- The identity triangle morphism.
 -/
 @[simps]
@@ -130,12 +139,14 @@ def triangleMorphismId (T : Triangle C) : TriangleMorphism T T
   hom₂ := 𝟙 T.obj₂
   hom₃ := 𝟙 T.obj₃
 #align category_theory.pretriangulated.triangle_morphism_id CategoryTheory.Pretriangulated.triangleMorphismId
+-/
 
 instance (T : Triangle C) : Inhabited (TriangleMorphism T T) :=
   ⟨triangleMorphismId T⟩
 
 variable {T₁ T₂ T₃ : Triangle C}
 
+#print CategoryTheory.Pretriangulated.TriangleMorphism.comp /-
 /-- Composition of triangle morphisms gives a triangle morphism.
 -/
 @[simps]
@@ -145,7 +156,9 @@ def TriangleMorphism.comp (f : TriangleMorphism T₁ T₂) (g : TriangleMorphism
   hom₂ := f.hom₂ ≫ g.hom₂
   hom₃ := f.hom₃ ≫ g.hom₃
 #align category_theory.pretriangulated.triangle_morphism.comp CategoryTheory.Pretriangulated.TriangleMorphism.comp
+-/
 
+#print CategoryTheory.Pretriangulated.triangleCategory /-
 /-- Triangles with triangle morphisms form a category.
 -/
 @[simps]
@@ -155,7 +168,9 @@ instance triangleCategory : Category (Triangle C)
   id A := triangleMorphismId A
   comp A B C f g := f.comp g
 #align category_theory.pretriangulated.triangle_category CategoryTheory.Pretriangulated.triangleCategory
+-/
 
+#print CategoryTheory.Pretriangulated.Triangle.homMk /-
 /-- a constructor for morphisms of triangles -/
 @[simps]
 def Triangle.homMk (A B : Triangle C) (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ : A.obj₂ ⟶ B.obj₂)
@@ -168,7 +183,9 @@ def Triangle.homMk (A B : Triangle C) (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ :
     comm₂' := comm₂
     comm₃' := comm₃ }
 #align category_theory.pretriangulated.triangle.hom_mk CategoryTheory.Pretriangulated.Triangle.homMk
+-/
 
+#print CategoryTheory.Pretriangulated.Triangle.isoMk /-
 /-- a constructor for isomorphisms of triangles -/
 @[simps]
 def Triangle.isoMk (A B : Triangle C) (iso₁ : A.obj₁ ≅ B.obj₁) (iso₂ : A.obj₂ ≅ B.obj₂)
@@ -189,6 +206,7 @@ def Triangle.isoMk (A B : Triangle C) (iso₁ : A.obj₁ ≅ B.obj₁) (iso₂ :
         simp only [← cancel_mono (iso₁.hom⟦(1 : ℤ)⟧'), assoc, ← functor.map_comp, iso.inv_hom_id,
           CategoryTheory.Functor.map_id, comp_id, comm₃, iso.inv_hom_id_assoc])
 #align category_theory.pretriangulated.triangle.iso_mk CategoryTheory.Pretriangulated.Triangle.isoMk
+-/
 
 end CategoryTheory.Pretriangulated
 

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

@@ -74,7 +74,7 @@ section
 
 variable [HasZeroObject C] [HasZeroMorphisms C]
 
-open ZeroObject
+open scoped ZeroObject
 
 instance : Inhabited (Triangle C) :=
   ⟨⟨0, 0, 0, 0, 0, 0⟩⟩

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

@@ -41,12 +41,6 @@ We work in a category `C` equipped with a shift.
 -/
 variable (C : Type u) [Category.{v} C] [HasShift C ℤ]
 
-/- warning: category_theory.pretriangulated.triangle -> CategoryTheory.Pretriangulated.Triangle is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid], Sort.{max (succ u2) (succ u1)}
-but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt], Sort.{max (succ u2) (succ u1)}
-Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle CategoryTheory.Pretriangulated.Triangleₓ'. -/
 /-- A triangle in `C` is a sextuple `(X,Y,Z,f,g,h)` where `X,Y,Z` are objects of `C`,
 and `f : X ⟶ Y`, `g : Y ⟶ Z`, `h : Z ⟶ X⟦1⟧` are morphisms in `C`.
 See <https://stacks.math.columbia.edu/tag/0144>.
@@ -62,12 +56,6 @@ structure Triangle where mk' ::
 
 variable {C}
 
-/- warning: category_theory.pretriangulated.triangle.mk -> CategoryTheory.Pretriangulated.Triangle.mk is a dubious translation:
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-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt] {X : C} {Y : C} {Z : C}, (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Z (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.shiftFunctor.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt _inst_2 (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) X)) -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
-Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle.mk CategoryTheory.Pretriangulated.Triangle.mkₓ'. -/
 /-- A triangle `(X,Y,Z,f,g,h)` in `C` is defined by the morphisms `f : X ⟶ Y`, `g : Y ⟶ Z`
 and `h : Z ⟶ X⟦1⟧`.
 -/
@@ -91,12 +79,6 @@ open ZeroObject
 instance : Inhabited (Triangle C) :=
   ⟨⟨0, 0, 0, 0, 0, 0⟩⟩
 
-/- warning: category_theory.pretriangulated.contractible_triangle -> CategoryTheory.Pretriangulated.contractibleTriangle is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1], C -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1], C -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
-Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.contractible_triangle CategoryTheory.Pretriangulated.contractibleTriangleₓ'. -/
 /-- For each object in `C`, there is a triangle of the form `(X,X,0,𝟙 X,0,0)`
 -/
 @[simps]
@@ -106,12 +88,6 @@ def contractibleTriangle (X : C) : Triangle C :=
 
 end
 
-/- warning: category_theory.pretriangulated.triangle_morphism -> CategoryTheory.Pretriangulated.TriangleMorphism is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid], (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2) -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2) -> Type.{u1}
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt], (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2) -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2) -> Type.{u1}
-Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle_morphism CategoryTheory.Pretriangulated.TriangleMorphismₓ'. -/
 /-- A morphism of triangles `(X,Y,Z,f,g,h) ⟶ (X',Y',Z',f',g',h')` in `C` is a triple of morphisms
 `a : X ⟶ X'`, `b : Y ⟶ Y'`, `c : Z ⟶ Z'` such that
 `a ≫ f' = f ≫ b`, `b ≫ g' = g ≫ c`, and `a⟦1⟧' ≫ h = h' ≫ c`.
@@ -145,12 +121,6 @@ restate_axiom triangle_morphism.comm₃'
 
 attribute [simp, reassoc] triangle_morphism.comm₁ triangle_morphism.comm₂ triangle_morphism.comm₃
 
-/- warning: category_theory.pretriangulated.triangle_morphism_id -> CategoryTheory.Pretriangulated.triangleMorphismId is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid] (T : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2), CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T T
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt] (T : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2), CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T T
-Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle_morphism_id CategoryTheory.Pretriangulated.triangleMorphismIdₓ'. -/
 /-- The identity triangle morphism.
 -/
 @[simps]
@@ -166,12 +136,6 @@ instance (T : Triangle C) : Inhabited (TriangleMorphism T T) :=
 
 variable {T₁ T₂ T₃ : Triangle C}
 
-/- warning: category_theory.pretriangulated.triangle_morphism.comp -> CategoryTheory.Pretriangulated.TriangleMorphism.comp is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid] {T₁ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2} {T₂ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2} {T₃ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2}, (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₁ T₂) -> (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₂ T₃) -> (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₁ T₃)
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt] {T₁ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2} {T₂ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2} {T₃ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2}, (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₁ T₂) -> (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₂ T₃) -> (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₁ T₃)
-Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle_morphism.comp CategoryTheory.Pretriangulated.TriangleMorphism.compₓ'. -/
 /-- Composition of triangle morphisms gives a triangle morphism.
 -/
 @[simps]
@@ -182,12 +146,6 @@ def TriangleMorphism.comp (f : TriangleMorphism T₁ T₂) (g : TriangleMorphism
   hom₃ := f.hom₃ ≫ g.hom₃
 #align category_theory.pretriangulated.triangle_morphism.comp CategoryTheory.Pretriangulated.TriangleMorphism.comp
 
-/- warning: category_theory.pretriangulated.triangle_category -> CategoryTheory.Pretriangulated.triangleCategory is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid], CategoryTheory.Category.{u1, max u2 u1} (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt], CategoryTheory.Category.{u1, max u2 u1} (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
-Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle_category CategoryTheory.Pretriangulated.triangleCategoryₓ'. -/
 /-- Triangles with triangle morphisms form a category.
 -/
 @[simps]
@@ -198,9 +156,6 @@ instance triangleCategory : Category (Triangle C)
   comp A B C f g := f.comp g
 #align category_theory.pretriangulated.triangle_category CategoryTheory.Pretriangulated.triangleCategory
 
-/- warning: category_theory.pretriangulated.triangle.hom_mk -> CategoryTheory.Pretriangulated.Triangle.homMk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle.hom_mk CategoryTheory.Pretriangulated.Triangle.homMkₓ'. -/
 /-- a constructor for morphisms of triangles -/
 @[simps]
 def Triangle.homMk (A B : Triangle C) (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ : A.obj₂ ⟶ B.obj₂)
@@ -214,9 +169,6 @@ def Triangle.homMk (A B : Triangle C) (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ :
     comm₃' := comm₃ }
 #align category_theory.pretriangulated.triangle.hom_mk CategoryTheory.Pretriangulated.Triangle.homMk
 
-/- warning: category_theory.pretriangulated.triangle.iso_mk -> CategoryTheory.Pretriangulated.Triangle.isoMk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle.iso_mk CategoryTheory.Pretriangulated.Triangle.isoMkₓ'. -/
 /-- a constructor for isomorphisms of triangles -/
 @[simps]
 def Triangle.isoMk (A B : Triangle C) (iso₁ : A.obj₁ ≅ B.obj₁) (iso₂ : A.obj₂ ≅ B.obj₂)

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

@@ -199,10 +199,7 @@ instance triangleCategory : Category (Triangle C)
 #align category_theory.pretriangulated.triangle_category CategoryTheory.Pretriangulated.triangleCategory
 
 /- warning: category_theory.pretriangulated.triangle.hom_mk -> CategoryTheory.Pretriangulated.Triangle.homMk is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle.hom_mk CategoryTheory.Pretriangulated.Triangle.homMkₓ'. -/
 /-- a constructor for morphisms of triangles -/
 @[simps]
@@ -218,10 +215,7 @@ def Triangle.homMk (A B : Triangle C) (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ :
 #align category_theory.pretriangulated.triangle.hom_mk CategoryTheory.Pretriangulated.Triangle.homMk
 
 /- warning: category_theory.pretriangulated.triangle.iso_mk -> CategoryTheory.Pretriangulated.Triangle.isoMk is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle.iso_mk CategoryTheory.Pretriangulated.Triangle.isoMkₓ'. -/
 /-- a constructor for isomorphisms of triangles -/
 @[simps]

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

@@ -143,7 +143,7 @@ restate_axiom triangle_morphism.comm₂'
 
 restate_axiom triangle_morphism.comm₃'
 
-attribute [simp, reassoc.1] triangle_morphism.comm₁ triangle_morphism.comm₂ triangle_morphism.comm₃
+attribute [simp, reassoc] triangle_morphism.comm₁ triangle_morphism.comm₂ triangle_morphism.comm₃
 
 /- warning: category_theory.pretriangulated.triangle_morphism_id -> CategoryTheory.Pretriangulated.triangleMorphismId is a dubious translation:
 lean 3 declaration is

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
 
 ! This file was ported from Lean 3 source module category_theory.triangulated.basic
-! leanprover-community/mathlib commit 6876fa15e3158ff3e4a4e2af1fb6e1945c6e8803
+! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Shift.Basic
 /-!
 # Triangles
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains the definition of triangles in an additive category with an additive shift.
 It also defines morphisms between these triangles.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

@@ -38,6 +38,12 @@ We work in a category `C` equipped with a shift.
 -/
 variable (C : Type u) [Category.{v} C] [HasShift C ℤ]
 
+/- warning: category_theory.pretriangulated.triangle -> CategoryTheory.Pretriangulated.Triangle is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid], Sort.{max (succ u2) (succ u1)}
+but is expected to have type
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt], Sort.{max (succ u2) (succ u1)}
+Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle CategoryTheory.Pretriangulated.Triangleₓ'. -/
 /-- A triangle in `C` is a sextuple `(X,Y,Z,f,g,h)` where `X,Y,Z` are objects of `C`,
 and `f : X ⟶ Y`, `g : Y ⟶ Z`, `h : Z ⟶ X⟦1⟧` are morphisms in `C`.
 See <https://stacks.math.columbia.edu/tag/0144>.
@@ -53,6 +59,12 @@ structure Triangle where mk' ::
 
 variable {C}
 
+/- warning: category_theory.pretriangulated.triangle.mk -> CategoryTheory.Pretriangulated.Triangle.mk is a dubious translation:
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid] {X : C} {Y : C} {Z : C}, (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Z (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.shiftFunctor.{u1, u2, 0} C Int _inst_1 Int.addMonoid _inst_2 (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) X)) -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt] {X : C} {Y : C} {Z : C}, (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Z (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.shiftFunctor.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt _inst_2 (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) X)) -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle.mk CategoryTheory.Pretriangulated.Triangle.mkₓ'. -/
 /-- A triangle `(X,Y,Z,f,g,h)` in `C` is defined by the morphisms `f : X ⟶ Y`, `g : Y ⟶ Z`
 and `h : Z ⟶ X⟦1⟧`.
 -/
@@ -76,6 +88,12 @@ open ZeroObject
 instance : Inhabited (Triangle C) :=
   ⟨⟨0, 0, 0, 0, 0, 0⟩⟩
 
+/- warning: category_theory.pretriangulated.contractible_triangle -> CategoryTheory.Pretriangulated.contractibleTriangle is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1], C -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1], C -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.contractible_triangle CategoryTheory.Pretriangulated.contractibleTriangleₓ'. -/
 /-- For each object in `C`, there is a triangle of the form `(X,X,0,𝟙 X,0,0)`
 -/
 @[simps]
@@ -85,6 +103,12 @@ def contractibleTriangle (X : C) : Triangle C :=
 
 end
 
+/- warning: category_theory.pretriangulated.triangle_morphism -> CategoryTheory.Pretriangulated.TriangleMorphism is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid], (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2) -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2) -> Type.{u1}
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt], (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2) -> (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2) -> Type.{u1}
+Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle_morphism CategoryTheory.Pretriangulated.TriangleMorphismₓ'. -/
 /-- A morphism of triangles `(X,Y,Z,f,g,h) ⟶ (X',Y',Z',f',g',h')` in `C` is a triple of morphisms
 `a : X ⟶ X'`, `b : Y ⟶ Y'`, `c : Z ⟶ Z'` such that
 `a ≫ f' = f ≫ b`, `b ≫ g' = g ≫ c`, and `a⟦1⟧' ≫ h = h' ≫ c`.
@@ -118,6 +142,12 @@ restate_axiom triangle_morphism.comm₃'
 
 attribute [simp, reassoc.1] triangle_morphism.comm₁ triangle_morphism.comm₂ triangle_morphism.comm₃
 
+/- warning: category_theory.pretriangulated.triangle_morphism_id -> CategoryTheory.Pretriangulated.triangleMorphismId is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid] (T : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2), CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T T
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt] (T : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2), CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T T
+Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle_morphism_id CategoryTheory.Pretriangulated.triangleMorphismIdₓ'. -/
 /-- The identity triangle morphism.
 -/
 @[simps]
@@ -133,6 +163,12 @@ instance (T : Triangle C) : Inhabited (TriangleMorphism T T) :=
 
 variable {T₁ T₂ T₃ : Triangle C}
 
+/- warning: category_theory.pretriangulated.triangle_morphism.comp -> CategoryTheory.Pretriangulated.TriangleMorphism.comp is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid] {T₁ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2} {T₂ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2} {T₃ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2}, (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₁ T₂) -> (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₂ T₃) -> (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₁ T₃)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt] {T₁ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2} {T₂ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2} {T₃ : CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2}, (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₁ T₂) -> (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₂ T₃) -> (CategoryTheory.Pretriangulated.TriangleMorphism.{u1, u2} C _inst_1 _inst_2 T₁ T₃)
+Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle_morphism.comp CategoryTheory.Pretriangulated.TriangleMorphism.compₓ'. -/
 /-- Composition of triangle morphisms gives a triangle morphism.
 -/
 @[simps]
@@ -143,6 +179,12 @@ def TriangleMorphism.comp (f : TriangleMorphism T₁ T₂) (g : TriangleMorphism
   hom₃ := f.hom₃ ≫ g.hom₃
 #align category_theory.pretriangulated.triangle_morphism.comp CategoryTheory.Pretriangulated.TriangleMorphism.comp
 
+/- warning: category_theory.pretriangulated.triangle_category -> CategoryTheory.Pretriangulated.triangleCategory is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.addMonoid], CategoryTheory.Category.{u1, max u2 u1} (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.HasShift.{u1, u2, 0} C Int _inst_1 Int.instAddMonoidInt], CategoryTheory.Category.{u1, max u2 u1} (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle_category CategoryTheory.Pretriangulated.triangleCategoryₓ'. -/
 /-- Triangles with triangle morphisms form a category.
 -/
 @[simps]
@@ -153,6 +195,12 @@ instance triangleCategory : Category (Triangle C)
   comp A B C f g := f.comp g
 #align category_theory.pretriangulated.triangle_category CategoryTheory.Pretriangulated.triangleCategory
 
+/- warning: category_theory.pretriangulated.triangle.hom_mk -> CategoryTheory.Pretriangulated.Triangle.homMk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle.hom_mk CategoryTheory.Pretriangulated.Triangle.homMkₓ'. -/
 /-- a constructor for morphisms of triangles -/
 @[simps]
 def Triangle.homMk (A B : Triangle C) (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ : A.obj₂ ⟶ B.obj₂)
@@ -166,6 +214,12 @@ def Triangle.homMk (A B : Triangle C) (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ :
     comm₃' := comm₃ }
 #align category_theory.pretriangulated.triangle.hom_mk CategoryTheory.Pretriangulated.Triangle.homMk
 
+/- warning: category_theory.pretriangulated.triangle.iso_mk -> CategoryTheory.Pretriangulated.Triangle.isoMk is a dubious translation:
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_inst_2 B) iso₃) (CategoryTheory.Pretriangulated.Triangle.mor₃.{u1, u2} C _inst_1 _inst_2 B))) -> (CategoryTheory.Iso.{u1, max u2 u1} (CategoryTheory.Pretriangulated.Triangle.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Pretriangulated.triangleCategory.{u1, u2} C _inst_1 _inst_2) A B)
+Case conversion may be inaccurate. Consider using '#align category_theory.pretriangulated.triangle.iso_mk CategoryTheory.Pretriangulated.Triangle.isoMkₓ'. -/
 /-- a constructor for isomorphisms of triangles -/
 @[simps]
 def Triangle.isoMk (A B : Triangle C) (iso₁ : A.obj₁ ≅ B.obj₁) (iso₂ : A.obj₂ ≅ B.obj₂)

mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
 
 ! This file was ported from Lean 3 source module category_theory.triangulated.basic
-! leanprover-community/mathlib commit f7707875544ef1f81b32cb68c79e0e24e45a0e76
+! leanprover-community/mathlib commit 6876fa15e3158ff3e4a4e2af1fb6e1945c6e8803
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.Int.Basic
-import Mathbin.CategoryTheory.Shift
+import Mathbin.CategoryTheory.Shift.Basic
 
 /-!
 # Triangles
@@ -153,5 +153,39 @@ instance triangleCategory : Category (Triangle C)
   comp A B C f g := f.comp g
 #align category_theory.pretriangulated.triangle_category CategoryTheory.Pretriangulated.triangleCategory
 
+/-- a constructor for morphisms of triangles -/
+@[simps]
+def Triangle.homMk (A B : Triangle C) (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ : A.obj₂ ⟶ B.obj₂)
+    (hom₃ : A.obj₃ ⟶ B.obj₃) (comm₁ : A.mor₁ ≫ hom₂ = hom₁ ≫ B.mor₁)
+    (comm₂ : A.mor₂ ≫ hom₃ = hom₂ ≫ B.mor₂) (comm₃ : A.mor₃ ≫ hom₁⟦1⟧' = hom₃ ≫ B.mor₃) : A ⟶ B :=
+  { hom₁
+    hom₂
+    hom₃
+    comm₁' := comm₁
+    comm₂' := comm₂
+    comm₃' := comm₃ }
+#align category_theory.pretriangulated.triangle.hom_mk CategoryTheory.Pretriangulated.Triangle.homMk
+
+/-- a constructor for isomorphisms of triangles -/
+@[simps]
+def Triangle.isoMk (A B : Triangle C) (iso₁ : A.obj₁ ≅ B.obj₁) (iso₂ : A.obj₂ ≅ B.obj₂)
+    (iso₃ : A.obj₃ ≅ B.obj₃) (comm₁ : A.mor₁ ≫ iso₂.Hom = iso₁.Hom ≫ B.mor₁)
+    (comm₂ : A.mor₂ ≫ iso₃.Hom = iso₂.Hom ≫ B.mor₂)
+    (comm₃ : A.mor₃ ≫ iso₁.Hom⟦1⟧' = iso₃.Hom ≫ B.mor₃) : A ≅ B
+    where
+  Hom := Triangle.homMk _ _ iso₁.Hom iso₂.Hom iso₃.Hom comm₁ comm₂ comm₃
+  inv :=
+    Triangle.homMk _ _ iso₁.inv iso₂.inv iso₃.inv
+      (by
+        simp only [← cancel_mono iso₂.hom, assoc, iso.inv_hom_id, comp_id, comm₁,
+          iso.inv_hom_id_assoc])
+      (by
+        simp only [← cancel_mono iso₃.hom, assoc, iso.inv_hom_id, comp_id, comm₂,
+          iso.inv_hom_id_assoc])
+      (by
+        simp only [← cancel_mono (iso₁.hom⟦(1 : ℤ)⟧'), assoc, ← functor.map_comp, iso.inv_hom_id,
+          CategoryTheory.Functor.map_id, comp_id, comm₃, iso.inv_hom_id_assoc])
+#align category_theory.pretriangulated.triangle.iso_mk CategoryTheory.Pretriangulated.Triangle.isoMk
+
 end CategoryTheory.Pretriangulated
 

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

In this PR, it is shown that in order to show that a pretriangulated category is triangulated category, i.e. in order to check the octahedron axiom, it is possible to replace a given diagram by an isomorphic diagram. This shall be used in #9550 in order to show that the homotopy category of cochain complexes in an additive category is triangulated.

@@ -331,4 +331,36 @@ lemma productTriangle.zero₃₁ [HasZeroMorphisms C]
 
 end
 
+namespace Triangle
+
+/-- The first projection `Triangle C ⥤ C`. -/
+@[simps]
+def π₁ : Triangle C ⥤ C where
+  obj T := T.obj₁
+  map f := f.hom₁
+
+/-- The second projection `Triangle C ⥤ C`. -/
+@[simps]
+def π₂ : Triangle C ⥤ C where
+  obj T := T.obj₂
+  map f := f.hom₂
+
+/-- The third projection `Triangle C ⥤ C`. -/
+@[simps]
+def π₃ : Triangle C ⥤ C where
+  obj T := T.obj₃
+  map f := f.hom₃
+
+section
+
+variable {A B : Triangle C} (φ : A ⟶ B) [IsIso φ]
+
+instance : IsIso φ.hom₁ := (inferInstance : IsIso (π₁.map φ))
+instance : IsIso φ.hom₂ := (inferInstance : IsIso (π₂.map φ))
+instance : IsIso φ.hom₃ := (inferInstance : IsIso (π₃.map φ))
+
+end
+
+end Triangle
+
 end CategoryTheory.Pretriangulated

This PR adds various small prerequisites for the construction of the triangulated structure on the homotopy category of cochain complexes.

@@ -162,6 +162,23 @@ lemma Triangle.hom_ext {A B : Triangle C} (f g : A ⟶ B)
     (h₁ : f.hom₁ = g.hom₁) (h₂ : f.hom₂ = g.hom₂) (h₃ : f.hom₃ = g.hom₃) : f = g :=
   TriangleMorphism.ext _ _ h₁ h₂ h₃
 
+@[simp]
+lemma id_hom₁ (A : Triangle C) : TriangleMorphism.hom₁ (𝟙 A) = 𝟙 _ := rfl
+@[simp]
+lemma id_hom₂ (A : Triangle C) : TriangleMorphism.hom₂ (𝟙 A) = 𝟙 _ := rfl
+@[simp]
+lemma id_hom₃ (A : Triangle C) : TriangleMorphism.hom₃ (𝟙 A) = 𝟙 _ := rfl
+
+@[simp, reassoc]
+lemma comp_hom₁ {X Y Z : Triangle C} (f : X ⟶ Y) (g : Y ⟶ Z) :
+    (f ≫ g).hom₁ = f.hom₁ ≫ g.hom₁ := rfl
+@[simp, reassoc]
+lemma comp_hom₂ {X Y Z : Triangle C} (f : X ⟶ Y) (g : Y ⟶ Z) :
+    (f ≫ g).hom₂ = f.hom₂ ≫ g.hom₂ := rfl
+@[simp, reassoc]
+lemma comp_hom₃ {X Y Z : Triangle C} (f : X ⟶ Y) (g : Y ⟶ Z) :
+    (f ≫ g).hom₃ = f.hom₃ ≫ g.hom₃ := rfl
+
 @[simps]
 def Triangle.homMk (A B : Triangle C)
     (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ : A.obj₂ ⟶ B.obj₂) (hom₃ : A.obj₃ ⟶ B.obj₃)
@@ -200,6 +217,26 @@ lemma Triangle.isIso_of_isIsos {A B : Triangle C} (f : A ⟶ B)
     (by simp) (by simp) (by simp)
   exact (inferInstance : IsIso e.hom)
 
+@[reassoc (attr := simp)]
+lemma _root_.CategoryTheory.Iso.hom_inv_id_triangle_hom₁ {A B : Triangle C} (e : A ≅ B) :
+    e.hom.hom₁ ≫ e.inv.hom₁ = 𝟙 _ := by rw [← comp_hom₁, e.hom_inv_id, id_hom₁]
+@[reassoc (attr := simp)]
+lemma _root_.CategoryTheory.Iso.hom_inv_id_triangle_hom₂ {A B : Triangle C} (e : A ≅ B) :
+    e.hom.hom₂ ≫ e.inv.hom₂ = 𝟙 _ := by rw [← comp_hom₂, e.hom_inv_id, id_hom₂]
+@[reassoc (attr := simp)]
+lemma _root_.CategoryTheory.Iso.hom_inv_id_triangle_hom₃ {A B : Triangle C} (e : A ≅ B) :
+    e.hom.hom₃ ≫ e.inv.hom₃ = 𝟙 _ := by rw [← comp_hom₃, e.hom_inv_id, id_hom₃]
+
+@[reassoc (attr := simp)]
+lemma _root_.CategoryTheory.Iso.inv_hom_id_triangle_hom₁ {A B : Triangle C} (e : A ≅ B) :
+    e.inv.hom₁ ≫ e.hom.hom₁ = 𝟙 _ := by rw [← comp_hom₁, e.inv_hom_id, id_hom₁]
+@[reassoc (attr := simp)]
+lemma _root_.CategoryTheory.Iso.inv_hom_id_triangle_hom₂ {A B : Triangle C} (e : A ≅ B) :
+    e.inv.hom₂ ≫ e.hom.hom₂ = 𝟙 _ := by rw [← comp_hom₂, e.inv_hom_id, id_hom₂]
+@[reassoc (attr := simp)]
+lemma _root_.CategoryTheory.Iso.inv_hom_id_triangle_hom₃ {A B : Triangle C} (e : A ≅ B) :
+    e.inv.hom₃ ≫ e.hom.hom₃ = 𝟙 _ := by rw [← comp_hom₃, e.inv_hom_id, id_hom₃]
+
 lemma Triangle.eqToHom_hom₁ {A B : Triangle C} (h : A = B) :
     (eqToHom h).hom₁ = eqToHom (by subst h; rfl) := by subst h; rfl
 lemma Triangle.eqToHom_hom₂ {A B : Triangle C} (h : A = B) :

@@ -3,7 +3,8 @@ Copyright (c) 2021 Luke Kershaw. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
 -/
-import Mathlib.Data.Int.Basic
+import Mathlib.CategoryTheory.Adjunction.Limits
+import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
 import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
 import Mathlib.CategoryTheory.Shift.Basic
 
@@ -193,6 +194,12 @@ def Triangle.isoMk (A B : Triangle C)
       Functor.map_id, Category.comp_id])
 #align category_theory.pretriangulated.triangle.iso_mk CategoryTheory.Pretriangulated.Triangle.isoMk
 
+lemma Triangle.isIso_of_isIsos {A B : Triangle C} (f : A ⟶ B)
+    (h₁ : IsIso f.hom₁) (h₂ : IsIso f.hom₂) (h₃ : IsIso f.hom₃) : IsIso f := by
+  let e := Triangle.isoMk A B (asIso f.hom₁) (asIso f.hom₂) (asIso f.hom₃)
+    (by simp) (by simp) (by simp)
+  exact (inferInstance : IsIso e.hom)
+
 lemma Triangle.eqToHom_hom₁ {A B : Triangle C} (h : A = B) :
     (eqToHom h).hom₁ = eqToHom (by subst h; rfl) := by subst h; rfl
 lemma Triangle.eqToHom_hom₂ {A B : Triangle C} (h : A = B) :
@@ -221,4 +228,70 @@ def binaryProductTriangleIsoBinaryBiproductTriangle
   Triangle.isoMk _ _ (Iso.refl _) (biprod.isoProd X₁ X₂).symm (Iso.refl _)
     (by aesop_cat) (by aesop_cat) (by aesop_cat)
 
+section
+
+variable {J : Type*} (T : J → Triangle C)
+  [HasProduct (fun j => (T j).obj₁)] [HasProduct (fun j => (T j).obj₂)]
+  [HasProduct (fun j => (T j).obj₃)] [HasProduct (fun j => (T j).obj₁⟦(1 : ℤ)⟧)]
+
+/-- The product of a family of triangles. -/
+@[simps!]
+def productTriangle : Triangle C :=
+  Triangle.mk (Pi.map (fun j => (T j).mor₁))
+    (Pi.map (fun j => (T j).mor₂))
+    (Pi.map (fun j => (T j).mor₃) ≫ inv (piComparison _ _))
+
+/-- A projection from the product of a family of triangles. -/
+@[simps]
+def productTriangle.π (j : J) :
+    productTriangle T ⟶ T j where
+  hom₁ := Pi.π _ j
+  hom₂ := Pi.π _ j
+  hom₃ := Pi.π _ j
+  comm₃ := by
+    dsimp
+    rw [← piComparison_comp_π, assoc, IsIso.inv_hom_id_assoc]
+    simp only [limMap_π, Discrete.natTrans_app]
+
+/-- The fan given by `productTriangle T`. -/
+@[simp]
+def productTriangle.fan : Fan T := Fan.mk (productTriangle T) (productTriangle.π T)
+
+/-- A family of morphisms `T' ⟶ T j` lifts to a morphism `T' ⟶ productTriangle T`. -/
+@[simps]
+def productTriangle.lift {T' : Triangle C} (φ : ∀ j, T' ⟶ T j) :
+    T' ⟶ productTriangle T where
+  hom₁ := Pi.lift (fun j => (φ j).hom₁)
+  hom₂ := Pi.lift (fun j => (φ j).hom₂)
+  hom₃ := Pi.lift (fun j => (φ j).hom₃)
+  comm₃ := by
+    dsimp
+    rw [← cancel_mono (piComparison _ _), assoc, assoc, assoc, IsIso.inv_hom_id, comp_id]
+    aesop_cat
+
+/-- The triangle `productTriangle T` satisfies the universal property of the categorical
+product of the triangles `T`. -/
+def productTriangle.isLimitFan : IsLimit (productTriangle.fan T) :=
+  mkFanLimit _ (fun s => productTriangle.lift T s.proj) (fun s j => by aesop_cat) (by
+    intro s m hm
+    ext1
+    all_goals
+      exact Pi.hom_ext _ _ (fun j => (by simp [← hm])))
+
+lemma productTriangle.zero₃₁ [HasZeroMorphisms C]
+    (h : ∀ j, (T j).mor₃ ≫ (T j).mor₁⟦(1 : ℤ)⟧' = 0) :
+    (productTriangle T).mor₃ ≫ (productTriangle T).mor₁⟦1⟧' = 0 := by
+  have : HasProduct (fun j => (T j).obj₂⟦(1 : ℤ)⟧) :=
+    ⟨_, isLimitFanMkObjOfIsLimit (shiftFunctor C (1 : ℤ)) _ _
+      (productIsProduct (fun j => (T j).obj₂))⟩
+  dsimp
+  change _ ≫ (Pi.lift (fun j => Pi.π _ j ≫ (T j).mor₁))⟦(1 : ℤ)⟧' = 0
+  rw [assoc, ← cancel_mono (piComparison _ _), zero_comp, assoc, assoc]
+  ext j
+  simp only [map_lift_piComparison, assoc, limit.lift_π, Fan.mk_π_app, zero_comp,
+    Functor.map_comp, ← piComparison_comp_π_assoc, IsIso.inv_hom_id_assoc,
+    limMap_π_assoc, Discrete.natTrans_app, h j, comp_zero]
+
+end
+
 end CategoryTheory.Pretriangulated

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
 -/
 import Mathlib.Data.Int.Basic
+import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
 import Mathlib.CategoryTheory.Shift.Basic
 
 #align_import category_theory.triangulated.basic from "leanprover-community/mathlib"@"6876fa15e3158ff3e4a4e2af1fb6e1945c6e8803"
@@ -199,4 +200,25 @@ lemma Triangle.eqToHom_hom₂ {A B : Triangle C} (h : A = B) :
 lemma Triangle.eqToHom_hom₃ {A B : Triangle C} (h : A = B) :
     (eqToHom h).hom₃ = eqToHom (by subst h; rfl) := by subst h; rfl
 
+/-- The obvious triangle `X₁ ⟶ X₁ ⊞ X₂ ⟶ X₂ ⟶ X₁⟦1⟧`. -/
+@[simps!]
+def binaryBiproductTriangle (X₁ X₂ : C) [HasZeroMorphisms C] [HasBinaryBiproduct X₁ X₂] :
+    Triangle C :=
+  Triangle.mk biprod.inl (Limits.biprod.snd : X₁ ⊞ X₂ ⟶ _) 0
+
+/-- The obvious triangle `X₁ ⟶ X₁ ⨯ X₂ ⟶ X₂ ⟶ X₁⟦1⟧`. -/
+@[simps!]
+def binaryProductTriangle (X₁ X₂ : C) [HasZeroMorphisms C] [HasBinaryProduct X₁ X₂] :
+    Triangle C :=
+  Triangle.mk ((Limits.prod.lift (𝟙 X₁) 0)) (Limits.prod.snd : X₁ ⨯ X₂ ⟶ _) 0
+
+/-- The canonical isomorphism of triangles
+`binaryProductTriangle X₁ X₂ ≅ binaryBiproductTriangle X₁ X₂`. -/
+@[simps!]
+def binaryProductTriangleIsoBinaryBiproductTriangle
+    (X₁ X₂ : C) [HasZeroMorphisms C] [HasBinaryBiproduct X₁ X₂] :
+    binaryProductTriangle X₁ X₂ ≅ binaryBiproductTriangle X₁ X₂ :=
+  Triangle.isoMk _ _ (Iso.refl _) (biprod.isoProd X₁ X₂).symm (Iso.refl _)
+    (by aesop_cat) (by aesop_cat) (by aesop_cat)
+
 end CategoryTheory.Pretriangulated

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

@@ -157,7 +157,7 @@ instance triangleCategory : Category (Triangle C)
 
 @[ext]
 lemma Triangle.hom_ext {A B : Triangle C} (f g : A ⟶ B)
-  (h₁ : f.hom₁ = g.hom₁) (h₂ : f.hom₂ = g.hom₂) (h₃ : f.hom₃ = g.hom₃) : f = g :=
+    (h₁ : f.hom₁ = g.hom₁) (h₂ : f.hom₂ = g.hom₂) (h₃ : f.hom₃ = g.hom₃) : f = g :=
   TriangleMorphism.ext _ _ h₁ h₂ h₃
 
 @[simps]

If a preadditive category C is equipped with a shift by the integers, then the category of triangles in C is also equipped with a shift.

@@ -192,4 +192,11 @@ def Triangle.isoMk (A B : Triangle C)
       Functor.map_id, Category.comp_id])
 #align category_theory.pretriangulated.triangle.iso_mk CategoryTheory.Pretriangulated.Triangle.isoMk
 
+lemma Triangle.eqToHom_hom₁ {A B : Triangle C} (h : A = B) :
+    (eqToHom h).hom₁ = eqToHom (by subst h; rfl) := by subst h; rfl
+lemma Triangle.eqToHom_hom₂ {A B : Triangle C} (h : A = B) :
+    (eqToHom h).hom₂ = eqToHom (by subst h; rfl) := by subst h; rfl
+lemma Triangle.eqToHom_hom₃ {A B : Triangle C} (h : A = B) :
+    (eqToHom h).hom₃ = eqToHom (by subst h; rfl) := by subst h; rfl
+
 end CategoryTheory.Pretriangulated

• 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 Luke Kershaw. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
-
-! This file was ported from Lean 3 source module category_theory.triangulated.basic
-! leanprover-community/mathlib commit 6876fa15e3158ff3e4a4e2af1fb6e1945c6e8803
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Int.Basic
 import Mathlib.CategoryTheory.Shift.Basic
 
+#align_import category_theory.triangulated.basic from "leanprover-community/mathlib"@"6876fa15e3158ff3e4a4e2af1fb6e1945c6e8803"
+
 /-!
 # Triangles
 

Clean up of automation in the category theory library. Leaving out unnecessary proof steps, or fields done by aesop_cat, and making more use of available autoparameters.

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

@@ -23,9 +23,7 @@ TODO: generalise this to n-angles in n-angulated categories as in https://arxiv.
 
 noncomputable section
 
-open CategoryTheory
-
-open CategoryTheory.Limits
+open CategoryTheory Limits
 
 universe v v₀ v₁ v₂ u u₀ u₁ u₂
 
@@ -168,8 +166,9 @@ lemma Triangle.hom_ext {A B : Triangle C} (f g : A ⟶ B)
 @[simps]
 def Triangle.homMk (A B : Triangle C)
     (hom₁ : A.obj₁ ⟶ B.obj₁) (hom₂ : A.obj₂ ⟶ B.obj₂) (hom₃ : A.obj₃ ⟶ B.obj₃)
-    (comm₁ : A.mor₁ ≫ hom₂ = hom₁ ≫ B.mor₁) (comm₂ : A.mor₂ ≫ hom₃ = hom₂ ≫ B.mor₂)
-    (comm₃ : A.mor₃ ≫ hom₁⟦1⟧' = hom₃ ≫ B.mor₃) :
+    (comm₁ : A.mor₁ ≫ hom₂ = hom₁ ≫ B.mor₁ := by aesop_cat)
+    (comm₂ : A.mor₂ ≫ hom₃ = hom₂ ≫ B.mor₂ := by aesop_cat)
+    (comm₃ : A.mor₃ ≫ hom₁⟦1⟧' = hom₃ ≫ B.mor₃ := by aesop_cat) :
     A ⟶ B where
   hom₁ := hom₁
   hom₂ := hom₂
@@ -182,9 +181,9 @@ def Triangle.homMk (A B : Triangle C)
 @[simps]
 def Triangle.isoMk (A B : Triangle C)
     (iso₁ : A.obj₁ ≅ B.obj₁) (iso₂ : A.obj₂ ≅ B.obj₂) (iso₃ : A.obj₃ ≅ B.obj₃)
-    (comm₁ : A.mor₁ ≫ iso₂.hom = iso₁.hom ≫ B.mor₁)
-    (comm₂ : A.mor₂ ≫ iso₃.hom = iso₂.hom ≫ B.mor₂)
-    (comm₃ : A.mor₃ ≫ iso₁.hom⟦1⟧' = iso₃.hom ≫ B.mor₃) : A ≅ B where
+    (comm₁ : A.mor₁ ≫ iso₂.hom = iso₁.hom ≫ B.mor₁ := by aesop_cat)
+    (comm₂ : A.mor₂ ≫ iso₃.hom = iso₂.hom ≫ B.mor₂ := by aesop_cat)
+    (comm₃ : A.mor₃ ≫ iso₁.hom⟦1⟧' = iso₃.hom ≫ B.mor₃ := by aesop_cat) : A ≅ B where
   hom := Triangle.homMk _ _ iso₁.hom iso₂.hom iso₃.hom comm₁ comm₂ comm₃
   inv := Triangle.homMk _ _ iso₁.inv iso₂.inv iso₃.inv
     (by simp only [← cancel_mono iso₂.hom, assoc, Iso.inv_hom_id, comp_id,

Also actually corrects the SHA that was incorrectly corrected in #3346; the stupid example was in CategoryTheory.Triangulated.Rotate and not CategoryTheory.Triangulated.Basic.

Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Chris Hughes <chrishughes24@gmail.com> Co-authored-by: Jon Eugster <eugster.jon@gmail.com> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: qawbecrdtey <qawbecrdtey@kaist.ac.kr> Co-authored-by: Jeremy Tan Jie Rui <e0191785@u.nus.edu> Co-authored-by: Sebastian Zivota <loewenheim@mailbox.org> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
 
 ! This file was ported from Lean 3 source module category_theory.triangulated.basic
-! leanprover-community/mathlib commit 94d4e70e97c36c896cb70fb42821acfed040de60
+! leanprover-community/mathlib commit 6876fa15e3158ff3e4a4e2af1fb6e1945c6e8803
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

The stupid example (https://github.com/leanprover-community/mathlib/pull/18701) wasn't ported and thus doesn't need to be removed.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Luke Kershaw
 
 ! This file was ported from Lean 3 source module category_theory.triangulated.basic
-! leanprover-community/mathlib commit 6876fa15e3158ff3e4a4e2af1fb6e1945c6e8803
+! leanprover-community/mathlib commit 94d4e70e97c36c896cb70fb42821acfed040de60
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: adamtopaz <github@adamtopaz.com> Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>