Theorems · Theorem · category theory

DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : HasDerivedCategory C] (K : CochainComplex C ℤ) (n : ℤ),
  (DerivedCategory.homologyFunctorFactorsh C n).inv.app ((HomotopyCategory.quotient C (ComplexShape.up ℤ)).obj K) =
    CategoryTheory.CategoryStruct.comp ((HomotopyCategory.homologyFunctorFactors C (ComplexShape.up ℤ) n).hom.app K)
      (CategoryTheory.CategoryStruct.comp ((DerivedCategory.homologyFunctorFactors C n).inv.app K)
        ((DerivedCategory.homologyFunctor C n).map ((DerivedCategory.quotientCompQhIso C).inv.app K)))

Defined in

Mathlib.Algebra.Homology.DerivedCategory.HomologySequence

Cited by

2 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianHasDerivedCategory