Theorems · Theorem · category theory

CochainComplex.mappingCocone.inr_v_snd_v

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {K L : CochainComplex C ℤ} (φ : K ⟶ L) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] (p q : ℤ) (hpq : p + 1 = q),
  CategoryTheory.CategoryStruct.comp ((↑(CochainComplex.mappingCocone.inr φ)).v p q hpq)
      ((CochainComplex.mappingCocone.snd φ).v q p ⋯) =
    CategoryTheory.CategoryStruct.id (L.X p)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber