Theorems · Theorem · category theory

CochainComplex.mappingCocone.liftCochain_v_snd_v

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {K L : CochainComplex C ℤ} (φ : K ⟶ L) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] {M : CochainComplex C ℤ}
  {n m : ℤ} (α : CochainComplex.HomComplex.Cochain M K n) (β : CochainComplex.HomComplex.Cochain M L m) (h : m + 1 = n)
  (p₁ p₂ p₃ : ℤ) (h₁₂ : p₁ + n = p₂) (h₂₃ : p₂ + -1 = p₃),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCocone.liftCochain φ α β h).v p₁ p₂ h₁₂)
      ((CochainComplex.mappingCocone.snd φ).v p₂ p₃ h₂₃) =
    β.v p₁ p₃ ⋯

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

3 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber