Theorems · Theorem · category theory

CategoryTheory.ShiftedHom.opEquiv_symm_add

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ] {X Y : C}
  [inst_2 : CategoryTheory.Preadditive C] [∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] {n : ℤ}
  (x y : CategoryTheory.ShiftedHom (Opposite.op Y) (Opposite.op X) n),
  (CategoryTheory.ShiftedHom.opEquiv n).symm (x + y) =
    (CategoryTheory.ShiftedHom.opEquiv n).symm x + (CategoryTheory.ShiftedHom.opEquiv n).symm y

Defined in

Mathlib.CategoryTheory.Shift.ShiftedHomOpposite

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.Additive