Theorems · Definition · category theory

CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso

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

The isomorphism expressing the commutation of the functor opOp C : C ⥤ Cᵒᵖᵒᵖ 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