Theorems · Theorem · category theory

CategoryTheory.InjectiveResolution.toRightDerivedZero_eq

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  [inst_2 : CategoryTheory.Abelian C] [inst_3 : CategoryTheory.HasInjectiveResolutions C]
  [inst_4 : CategoryTheory.Abelian D] {X : C} (I : CategoryTheory.InjectiveResolution X)
  (F : CategoryTheory.Functor C D) [inst_5 : F.Additive],
  F.toRightDerivedZero.app X =
    CategoryTheory.CategoryStruct.comp (I.toRightDerivedZero' F)
      (CategoryTheory.CategoryStruct.comp
        (CochainComplex.isoHomologyπ₀ ((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj I.cocomplex)).hom
        (I.isoRightDerivedObj F 0).inv)

Defined in

Mathlib.CategoryTheory.Abelian.RightDerived

Cited by

0 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasInjectiveResolutionsCategoryTheory.AbelianCategoryTheory.Functor.Additive