Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ] (n : ℤ)
  {X Y : Cᵒᵖ} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp f
      ((CategoryTheory.Pretriangulated.opShiftFunctorEquivalence C n).unitIso.hom.app Y) =
    CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Pretriangulated.opShiftFunctorEquivalence C n).unitIso.hom.app X)
      ((CategoryTheory.shiftFunctor C n).map ((CategoryTheory.shiftFunctor Cᵒᵖ n).map f).unop).op

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift