Theorems · Theorem · category theory

CochainComplex.mappingCocone.id_X

∀ {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] (p q : ℤ)
  (hpq : p + -1 = q),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCocone.fst φ).f p)
        ((CochainComplex.mappingCocone.inl φ).v p p ⋯) +
      CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCocone.snd φ).v p q hpq)
        ((↑(CochainComplex.mappingCocone.inr φ)).v q p ⋯) =
    CategoryTheory.CategoryStruct.id ((CochainComplex.mappingCocone φ).X p)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber