Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.exists_triangle

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.HasShift C ℤ]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
  (t : CategoryTheory.Triangulated.TStructure C) (A : C) (n₀ n₁ : ℤ),
  n₀ + 1 = n₁ →
    ∃ X Y,
      ∃ (_ : t.le n₀ X) (_ : t.ge n₁ Y),
        ∃ f g h,
          CategoryTheory.Pretriangulated.Triangle.mk f g h ∈ CategoryTheory.Pretriangulated.distinguishedTriangles

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.Basic

Cited by

0 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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