Theorems · Definition · category theory

CategoryTheory.Functor.mapTriangleCompIso

{C : Type u_1} →
  {D : Type u_2} →
    {E : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} E] →
            [inst_3 : CategoryTheory.HasShift C ℤ] →
              [inst_4 : CategoryTheory.HasShift D ℤ] →
                [inst_5 : CategoryTheory.HasShift E ℤ] →
                  (F : CategoryTheory.Functor C D) →
                    [inst_6 : F.CommShift ℤ] →
                      (G : CategoryTheory.Functor D E) →
                        [inst_7 : G.CommShift ℤ] → (F.comp G).mapTriangle ≅ F.mapTriangle.comp G.mapTriangle

The canonical isomorphism (F ⋙ G).mapTriangle ≅ F.mapTriangle ⋙ G.mapTriangle.

Defined in

Mathlib.CategoryTheory.Triangulated.Functor

Cited by

9 results in Mathlib

Foundations

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

Assumes

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