Theorems · Definition · category theory

CategoryTheory.Pretriangulated.invRotCompRot

{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).comp (CategoryTheory.Pretriangulated.rotate C) ≅
            CategoryTheory.Functor.id (CategoryTheory.Pretriangulated.Triangle C)

The counit isomorphism of the auto-equivalence of categories triangleRotation C of Triangle C given by the rotation of triangles.

Defined in

Mathlib.CategoryTheory.Triangulated.Rotate

Cited by

9 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.HasShiftCategoryTheory.Functor.Additive