Theorems · Theorem · category theory

CochainComplex.mappingCone.inl_v_descCochain_v

∀ {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)
  (p₁ p₂ p₃ : ℤ) (h₁₂ : p₁ + -1 = p₂) (h₂₃ : p₂ + n = p₃),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.inl φ).v p₁ p₂ h₁₂)
      ((CochainComplex.mappingCone.descCochain φ α β h).v p₂ p₃ h₂₃) =
    α.v p₁ p₃ ⋯

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber