Theorems · Definition · category theory

CategoryTheory.Pretriangulated.triangleRotation

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.HasShift C ℤ] →
        [∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
          CategoryTheory.Pretriangulated.Triangle C ≌ CategoryTheory.Pretriangulated.Triangle C

Rotating triangles gives an auto-equivalence on the category of triangles in C.

Defined in

Mathlib.CategoryTheory.Triangulated.Rotate

Cited by

7 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.HasShiftCategoryTheory.Functor.Additive