Theorems · Definition · category theory

CategoryTheory.Pretriangulated.opShiftFunctorEquivalence

(C : Type u_1) → [inst : CategoryTheory.Category.{v_1, u_1} C] → [CategoryTheory.HasShift C ℤ] → ℤ → (Cᵒᵖ ≌ Cᵒᵖ)

The autoequivalence Cᵒᵖ ≌ Cᵒᵖ whose functor is shiftFunctor Cᵒᵖ n and whose inverse functor is (shiftFunctor C n).op. In most cases, it is not necessary to unfold the definitions of the unit and counit isomorphisms: the compatibilities they satisfy are stated as separate lemmas.

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Basic

Cited by

61 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift