Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.isomorphic_distinguished

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {inst_1 : CategoryTheory.Limits.HasZeroObject C}
  {inst_2 : CategoryTheory.HasShift C ℤ} {inst_3 : CategoryTheory.Preadditive C}
  {inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive} [self : CategoryTheory.Pretriangulated C],
  ∀ T₁ ∈ CategoryTheory.Pretriangulated.distinguishedTriangles,
    ∀ (T₂ : CategoryTheory.Pretriangulated.Triangle C) (x : T₂ ≅ T₁),
      T₂ ∈ CategoryTheory.Pretriangulated.distinguishedTriangles

a triangle that is isomorphic to a distinguished triangle is distinguished

Defined in

Mathlib.CategoryTheory.Triangulated.Pretriangulated

Cited by

47 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Pretriangulated