Theorems · Theorem · category theory

CochainComplex.mappingCone.desc_f

∀ {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.Cochain F K (-1)) (β : G ⟶ K)
  (eq :
    CochainComplex.HomComplex.δ (-1) 0 α =
      CochainComplex.HomComplex.Cochain.ofHom (CategoryTheory.CategoryStruct.comp φ β))
  (p q : ℤ) (hpq : p + 1 = q),
  (CochainComplex.mappingCone.desc φ α β eq).f p =
    CategoryTheory.CategoryStruct.comp ((↑(CochainComplex.mappingCone.fst φ)).v p q hpq) (α.v q p ⋯) +
      CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.snd φ).v p p ⋯) (β.f p)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

1 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber