Theorems · Definition · category theory

CategoryTheory.Functor.mapTriangle

{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) →
              [F.CommShift ℤ] →
                CategoryTheory.Functor (CategoryTheory.Pretriangulated.Triangle C)
                  (CategoryTheory.Pretriangulated.Triangle D)

The functor Triangle C ⥤ Triangle D that is induced by a functor F : C ⥤ D which commutes with shift by ℤ.

Defined in

Mathlib.CategoryTheory.Triangulated.Functor

Cited by

87 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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