Theorems · Theorem · category theory

CochainComplex.mappingCone.decomp_from

∀ {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] {j : ℤ} {A : C}
  (f : (CochainComplex.mappingCone φ).X j ⟶ A) (i : ℤ) (hij : j + 1 = i),
  ∃ a b,
    f =
      CategoryTheory.CategoryStruct.comp ((↑(CochainComplex.mappingCone.fst φ)).v j i hij) a +
        CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.snd φ).v j j ⋯) b

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

0 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber