Theorems · Theorem · category theory

CategoryTheory.ShiftedHom.opEquiv_symm_apply

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ] {X Y : C} {n : ℤ}
  (f : CategoryTheory.ShiftedHom (Opposite.op Y) (Opposite.op X) n),
  (CategoryTheory.ShiftedHom.opEquiv n).symm f =
    CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Pretriangulated.opShiftFunctorEquivalence C n).unitIso.inv.app (Opposite.op X)).unop
      ((CategoryTheory.shiftFunctor C n).map (Quiver.Hom.unop f))

Defined in

Mathlib.CategoryTheory.Shift.ShiftedHomOpposite

Cited by

3 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift