Theorems · Definition · category theory

CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.HasShift C ℤ] →
      (n : ℤ) →
        (CategoryTheory.shiftFunctor Cᵒᵖᵒᵖ n).comp (CategoryTheory.unopUnop C) ≅
          (CategoryTheory.unopUnop C).comp (CategoryTheory.shiftFunctor C n)

The isomorphism expressing the commutation of the functor unopUnop C : Cᵒᵖᵒᵖ ⥤ C with the shift by n : ℤ.

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.OpOp

Cited by

4 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift