Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.exists_triangle_zero_one

∀ {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]
  (self : CategoryTheory.Triangulated.TStructure C) (A : C),
  ∃ X Y,
    ∃ (_ : self.le 0 X) (_ : self.ge 1 Y),
      ∃ f g h, CategoryTheory.Pretriangulated.Triangle.mk f g h ∈ CategoryTheory.Pretriangulated.distinguishedTriangles

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.Basic

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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