Theorems · Theorem · category theory

HomotopyCategory.Pretriangulated.contractible_distinguished

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] [inst_3 : CategoryTheory.Limits.HasZeroObject C]
  (X : HomotopyCategory C (ComplexShape.up ℤ)),
  CategoryTheory.Pretriangulated.contractibleTriangle X ∈ HomotopyCategory.Pretriangulated.distinguishedTriangles C

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproductsCategoryTheory.Limits.HasZeroObject