Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.preadditiveYoneda_shiftMap_apply

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.HasShift C ℤ] [inst_3 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] (B : C)
  {X Y : Cᵒᵖ} (n : ℤ) (f : X ⟶ (CategoryTheory.shiftFunctor Cᵒᵖ n).obj Y) (a a' : ℤ) (h : n + a = a')
  (z : Opposite.unop X ⟶ (CategoryTheory.shiftFunctor C a).obj B),
  (CategoryTheory.ConcreteCategory.hom ((CategoryTheory.preadditiveYoneda.obj B).shiftMap f a a' h)) z =
    ((CategoryTheory.ShiftedHom.opEquiv n).symm f).comp z ⋯

Defined in

Mathlib.CategoryTheory.Triangulated.Yoneda

Cited by

1 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.HasShiftCategoryTheory.Functor.Additive