Theorems · Theorem · category theory

CochainComplex.mappingCone.d_snd_v

∀ {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] (i j : ℤ) (hij : i + 1 = j),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone φ).d i j)
      ((CochainComplex.mappingCone.snd φ).v j j ⋯) =
    CategoryTheory.CategoryStruct.comp ((↑(CochainComplex.mappingCone.fst φ)).v i j hij) (φ.f j) +
      CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.snd φ).v i i ⋯) (G.d i j)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

5 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber