Theorems · Definition · category theory

CategoryTheory.Functor.mapTriangleInvRotateIso

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        [inst_2 : CategoryTheory.HasShift C ℤ] →
          [inst_3 : CategoryTheory.HasShift D ℤ] →
            (F : CategoryTheory.Functor C D) →
              [inst_4 : F.CommShift ℤ] →
                [inst_5 : CategoryTheory.Preadditive C] →
                  [inst_6 : CategoryTheory.Preadditive D] →
                    [F.Additive] →
                      F.mapTriangle.comp (CategoryTheory.Pretriangulated.invRotate D) ≅
                        (CategoryTheory.Pretriangulated.invRotate C).comp F.mapTriangle

F.mapTriangle commutes with the inverse of the rotation of triangles.

Defined in

Mathlib.CategoryTheory.Triangulated.Functor

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.PreadditiveCategoryTheory.PreadditiveCategoryTheory.Functor.Additive