Theorems · Definition · category theory

CategoryTheory.Triangulated.TStructure.triangleLEGE

{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] →
              CategoryTheory.Triangulated.TStructure C →
                (a b : ℤ) → a + 1 = b → CategoryTheory.Functor C (CategoryTheory.Pretriangulated.Triangle C)

The distinguished triangle (t.truncLE a).obj A ⟶ A ⟶ (t.truncGE b).obj A ⟶ ... as a functor C ⥤ Triangle C when t is a t-structure on a pretriangulated category C and a + 1 = b.

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.TruncLEGT

Cited by

13 results in Mathlib

Foundations

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

Assumes

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