Theorems · Theorem · category theory

CochainComplex.mappingCocone.ofHom_desc

∀ {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] {M : CochainComplex C ℤ}
  (α : CochainComplex.HomComplex.Cochain K M 0) (β : CochainComplex.HomComplex.Cocycle L M 1)
  (hαβ : CochainComplex.HomComplex.δ 0 1 α + (CochainComplex.HomComplex.Cochain.ofHom φ).comp ↑β ⋯ = 0),
  CochainComplex.HomComplex.Cochain.ofHom (CochainComplex.mappingCocone.desc φ α β hαβ) =
    CochainComplex.mappingCocone.descCochain φ α (↑β) CochainComplex.mappingCocone.ofHom_desc._proof_2

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber