Theorems · Theorem · category theory

CochainComplex.mappingCone.inl_descCochain

∀ {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}
  {n m : ℤ} (α : CochainComplex.HomComplex.Cochain F K m) (β : CochainComplex.HomComplex.Cochain G K n) (h : m + 1 = n),
  (CochainComplex.mappingCone.inl φ).comp (CochainComplex.mappingCone.descCochain φ α β h) ⋯ = α

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber