shortComplexOfDistTriangleIsoOfIso

English

For a distinguished triangle T, any morphism f from T.obj₂ to an object X with f ≫ T.mor₂ = 0 factors through T.obj₁ via T.mor₁, i.e., f = g ≫ T.mor₁ for some g.

Русский

Для выделенного треугольника T любой морфизм f: T.obj₂ → X с условием f ≫ T.mor₂ = 0 факторизуется через T.obj₁ по T.mor₁: f = g ∘ T.mor₁.

LaTeX

$$yoneda_exact₂$$

Lean4

/-- The isomorphism between the short complex attached to
two isomorphic distinguished triangles. -/
@[simps!]
def shortComplexOfDistTriangleIsoOfIso {T T' : Triangle C} (e : T ≅ T') (hT : T ∈ distTriang C) :
    shortComplexOfDistTriangle T hT ≅ shortComplexOfDistTriangle T' (isomorphic_distinguished _ hT _ e.symm) :=
  ShortComplex.isoMk (Triangle.π₁.mapIso e) (Triangle.π₂.mapIso e) (Triangle.π₃.mapIso e)

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