Theorems · Definition · category theory

CochainComplex.mappingCone.triangleh

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [CategoryTheory.Limits.HasBinaryBiproducts C] →
        {K L : CochainComplex C ℤ} →
          (K ⟶ L) → CategoryTheory.Pretriangulated.Triangle (HomotopyCategory C (ComplexShape.up ℤ))

The (distinguished) triangle in the homotopy category that is associated to a morphism φ : K ⟶ L in the category CochainComplex C ℤ.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated

Cited by

14 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts