Theorems · Definition · category theory

CategoryTheory.Pretriangulated.invRotateIsoRotateRotateShiftFunctorNegOne

(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.invRotate C ≅
            (CategoryTheory.Pretriangulated.rotate C).comp
              ((CategoryTheory.Pretriangulated.rotate C).comp
                (CategoryTheory.Pretriangulated.Triangle.shiftFunctor C (-1)))

The inverse of the rotation of triangles can be expressed using a double rotation and the shift by -1.

Defined in

Mathlib.CategoryTheory.Triangulated.TriangleShift

Cited by

1 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.HasShiftCategoryTheory.Functor.Additive