Theorems · Theorem · category theory

DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj_assoc

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

Defined in

Mathlib.Algebra.Homology.DerivedCategory.HomologySequence

Cited by

0 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianHasDerivedCategory