Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.Opposite.distinguished_cocone_triangle

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
  {X Y : Cᵒᵖ} (f : X ⟶ Y),
  ∃ Z g h,
    CategoryTheory.Pretriangulated.Triangle.mk f g h ∈ CategoryTheory.Pretriangulated.Opposite.distinguishedTriangles C

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated

Cited by

0 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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