Theorems · Theorem · category theory

CochainComplex.mappingCocone.inr_v_descCochain_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 K M m) (β : CochainComplex.HomComplex.Cochain L M n) (h : m + 1 = n)
  (p q : ℤ) (hpq : p + 1 = q) (r : ℤ) (hr : q + m = r),
  CategoryTheory.CategoryStruct.comp ((↑(CochainComplex.mappingCocone.inr φ)).v p q hpq)
      ((CochainComplex.mappingCocone.descCochain φ α β h).v q r hr) =
    β.v p r ⋯

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

3 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber