Theorems · Theorem · category theory

CochainComplex.mappingCone.inr_f_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 : ℤ),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.inr φ).f p)
      ((CochainComplex.mappingCone.desc φ α β eq).f p) =
    β.f p

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

8 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber