Theorems · Definition · category theory

CategoryTheory.Pretriangulated.Opposite.commShiftFunctorOpInt

{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] → F.op.CommShift ℤ

If F commutes with shifts, so does F.op, for the shifts chosen on Cᵒᵖ in CategoryTheory.Triangulated.Opposite.Basic.

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Functor

Cited by

27 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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