Theorems · Definition · category theory

HomotopyCategory.Pretriangulated.distinguishedTriangles

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

A triangle in HomotopyCategory C (ComplexShape.up ℤ) is distinguished if it is isomorphic to the triangle CochainComplex.mappingCone.triangleh φ for some morphism of cochain complexes φ.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated

Cited by

8 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts