Theorems · Theorem · category theory

CochainComplex.mappingCone.decomp_to

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

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

1 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber