Theorems · Theorem · category theory

CochainComplex.mappingCone.id

∀ {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],
  (↑(CochainComplex.mappingCone.fst φ)).comp (CochainComplex.mappingCone.inl φ) ⋯ +
      (CochainComplex.mappingCone.snd φ).comp
        (CochainComplex.HomComplex.Cochain.ofHom (CochainComplex.mappingCone.inr φ)) ⋯ =
    CochainComplex.HomComplex.Cochain.ofHom (CategoryTheory.CategoryStruct.id (CochainComplex.mappingCone φ))

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber