Theorems · Definition · category theory

CochainComplex.mappingCocone.triangle

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

Given a morphism φ : K ⟶ L of cochain complexes, this is the triangle mappingCocone φ ⟶ K ⟶ L ⟶ ....

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

6 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts