Theorems · Theorem · category theory

CochainComplex.mappingCone.inr_snd_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {F G : CochainComplex C ℤ} (φ : F ⟶ G) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] {K : CochainComplex C ℤ}
  {d e : ℤ} (γ : CochainComplex.HomComplex.Cochain G K d) (he : 0 + d = e),
  (CochainComplex.HomComplex.Cochain.ofHom (CochainComplex.mappingCone.inr φ)).comp
      ((CochainComplex.mappingCone.snd φ).comp γ he) ⋯ =
    γ

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

3 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber