Theorems · Definition · category theory

CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp

{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] →
                (T : CategoryTheory.Pretriangulated.Triangle C) →
                  (CategoryTheory.Pretriangulated.triangleOpEquivalence D).functor.obj
                      (Opposite.op (F.mapTriangle.obj T)) ≅
                    F.op.mapTriangle.obj
                      ((CategoryTheory.Pretriangulated.triangleOpEquivalence C).functor.obj (Opposite.op T))

If F : C ⥤ D commutes with shifts, this expresses the compatibility of F.mapTriangle with the equivalences Pretriangulated.triangleOpEquivalence on C and D.

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Functor

Cited by

6 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShift