Theorems · Definition · category theory

CategoryTheory.Pretriangulated.shortComplexOfDistTriangle

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] →
      [inst_2 : CategoryTheory.HasShift C ℤ] →
        [inst_3 : CategoryTheory.Preadditive C] →
          [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
            [hC : CategoryTheory.Pretriangulated C] →
              (T : CategoryTheory.Pretriangulated.Triangle C) →
                T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles → CategoryTheory.ShortComplex C

The short complex T.obj₁ ⟶ T.obj₂ ⟶ T.obj₃ attached to a distinguished triangle.

Defined in

Mathlib.CategoryTheory.Triangulated.Pretriangulated

Cited by

17 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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