File: Mathlib/Algebra/Homology/DerivedCategory/ShortExact.lean

full_name: DerivedCategory.triangleOfSESδ
code: /-- The connecting homomorphism `Q.obj (S.X₃) ⟶ (Q.obj S.X₁)⟦(1 : ℤ)⟧`
in the derived category when `S` is a short exact short complex of
cochain complexes in an abelian category. -/
noncomputable def triangleOfSESδ :
  Q.obj (S.X₃) ⟶ (Q.obj S.X₁)⟦(1 : ℤ)⟧ 
goal: DerivedCategory.Q.obj S.X₃ ⟶ (CategoryTheory.shiftFunctor (DerivedCategory C) 1).obj (DerivedCategory.Q.obj S.X₁)

full_name: DerivedCategory.triangleOfSES_obj₃
code: /-- The distinguished triangle in the derived category associated to a short
exact sequence of cochain complexes. -/
@[simps!]
noncomputable def triangleOfSES : Triangle (DerivedCategory C) 
goal: (DerivedCategory.triangleOfSES hS).obj₃ = DerivedCategory.Q.obj S.X₃

full_name: DerivedCategory.triangleOfSES_mor₃
code: /-- The distinguished triangle in the derived category associated to a short
exact sequence of cochain complexes. -/
@[simps!]
noncomputable def triangleOfSES : Triangle (DerivedCategory C) 
goal: (DerivedCategory.triangleOfSES hS).mor₃ = DerivedCategory.triangleOfSESδ hS

full_name: DerivedCategory.triangleOfSES_mor₂
code: /-- The distinguished triangle in the derived category associated to a short
exact sequence of cochain complexes. -/
@[simps!]
noncomputable def triangleOfSES : Triangle (DerivedCategory C) 
goal: (DerivedCategory.triangleOfSES hS).mor₂ = DerivedCategory.Q.map S.g

full_name: DerivedCategory.triangleOfSES_obj₁
code: /-- The distinguished triangle in the derived category associated to a short
exact sequence of cochain complexes. -/
@[simps!]
noncomputable def triangleOfSES : Triangle (DerivedCategory C) 
goal: (DerivedCategory.triangleOfSES hS).obj₁ = DerivedCategory.Q.obj S.X₁

full_name: DerivedCategory.triangleOfSES_mor₁
code: /-- The distinguished triangle in the derived category associated to a short
exact sequence of cochain complexes. -/
@[simps!]
noncomputable def triangleOfSES : Triangle (DerivedCategory C) 
goal: (DerivedCategory.triangleOfSES hS).mor₁ = DerivedCategory.Q.map S.f

full_name: DerivedCategory.triangleOfSES
code: /-- The distinguished triangle in the derived category associated to a short
exact sequence of cochain complexes. -/
@[simps!]
noncomputable def triangleOfSES : Triangle (DerivedCategory C) 
goal: CategoryTheory.Pretriangulated.Triangle (DerivedCategory C)

full_name: DerivedCategory.triangleOfSES_obj₂
code: /-- The distinguished triangle in the derived category associated to a short
exact sequence of cochain complexes. -/
@[simps!]
noncomputable def triangleOfSES : Triangle (DerivedCategory C) 
goal: (DerivedCategory.triangleOfSES hS).obj₂ = DerivedCategory.Q.obj S.X₂

full_name: DerivedCategory.triangleOfSESIso
code: /-- The triangle `triangleOfSES` attached to a short exact sequence `S` of cochain
complexes is isomorphism to the standard distinguished triangle associated to
the morphism `S.f`. -/
noncomputable def triangleOfSESIso :
    triangleOfSES hS ≅ Q.mapTriangle.obj (CochainComplex.mappingCone.triangle S.f) 
goal: DerivedCategory.triangleOfSES hS ≅ DerivedCategory.Q.mapTriangle.obj (CochainComplex.mappingCone.triangle S.f)

full_name: DerivedCategory.triangleOfSES_distinguished
code: lemma triangleOfSES_distinguished :
    triangleOfSES hS ∈ distTriang (DerivedCategory C) 
goal: DerivedCategory.triangleOfSES hS ∈ CategoryTheory.Pretriangulated.distinguishedTriangles