Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.preadditiveYoneda_map_distinguished

∀ {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 : CategoryTheory.Limits.HasZeroObject C]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
  (T : CategoryTheory.Pretriangulated.Triangle C) (hT : T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles)
  (B : C),
  ((CategoryTheory.Pretriangulated.shortComplexOfDistTriangle T hT).op.map
      (CategoryTheory.preadditiveYoneda.obj B)).Exact

Defined in

Mathlib.CategoryTheory.Triangulated.Yoneda

Cited by

0 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.HasShiftCategoryTheory.Limits.HasZeroObjectCategoryTheory.Functor.AdditiveCategoryTheory.Pretriangulated