Theorems · Theorem · category theory

CochainComplex.mappingCone.descCocycle_coe

∀ {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.Cocycle G K n) (h : m + 1 = n)
  (eq : CochainComplex.HomComplex.δ m n α = n.negOnePow • (CochainComplex.HomComplex.Cochain.ofHom φ).comp ↑β ⋯),
  ↑(CochainComplex.mappingCone.descCocycle φ α β h eq) = CochainComplex.mappingCone.descCochain φ α (↑β) h

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

6 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber