Theorems · Definition · category theory

CategoryTheory.Pretriangulated.shiftFunctorOpIso

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.HasShift C ℤ] →
      (n m : ℤ) → n + m = 0 → (CategoryTheory.shiftFunctor Cᵒᵖ n ≅ (CategoryTheory.shiftFunctor C m).op)

The shift functor on the opposite category identifies to the opposite functor of a shift functor on the original category.

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Basic

Cited by

45 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift