Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.rotate_distinguished_triangle

∀ {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]
  (T : CategoryTheory.Pretriangulated.Triangle C),
  T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles ↔
    T.rotate ∈ CategoryTheory.Pretriangulated.distinguishedTriangles

a triangle is distinguished iff it is so after rotating it

Defined in

Mathlib.CategoryTheory.Triangulated.Pretriangulated

Cited by

8 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Pretriangulated