Theorems · Theorem · category theory

CochainComplex.mappingCone.ofHom_lift

∀ {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}
  (α : CochainComplex.HomComplex.Cocycle K F 1) (β : CochainComplex.HomComplex.Cochain K G 0)
  (eq : CochainComplex.HomComplex.δ 0 1 β + (↑α).comp (CochainComplex.HomComplex.Cochain.ofHom φ) ⋯ = 0),
  CochainComplex.HomComplex.Cochain.ofHom (CochainComplex.mappingCone.lift φ α β eq) =
    CochainComplex.mappingCone.liftCochain φ (↑α) β ⋯

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

2 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber