Theorems · Theorem · category theory

CochainComplex.mappingCone.lift_f

∀ {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}
  (α : CochainComplex.HomComplex.Cocycle K F 1) (β : CochainComplex.HomComplex.Cochain K G 0)
  (eq : CochainComplex.HomComplex.δ 0 1 β + (↑α).comp (CochainComplex.HomComplex.Cochain.ofHom φ) ⋯ = 0) (p q : ℤ)
  (hpq : p + 1 = q),
  (CochainComplex.mappingCone.lift φ α β eq).f p =
    CategoryTheory.CategoryStruct.comp ((↑α).v p q hpq) ((CochainComplex.mappingCone.inl φ).v q p ⋯) +
      CategoryTheory.CategoryStruct.comp (β.v p p ⋯) ((CochainComplex.mappingCone.inr φ).f p)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber