Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Functor.rightDerived

{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] →
          [CategoryTheory.HasInjectiveResolutions C] →
            [inst_4 : CategoryTheory.Abelian D] →
              (F : CategoryTheory.Functor C D) → [F.Additive] → ℕ → CategoryTheory.Functor C D

The right derived functors of an additive functor.

Defined in
Mathlib.CategoryTheory.Abelian.RightDerived
Cited by
21 results in Mathlib
Foundations
Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasInjectiveResolutionsCategoryTheory.AbelianCategoryTheory.Functor.Additive

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Functor.toRightDerivedZero · cited by 10Functor.toRightDerivedZeroCategoryTheory.Functor.rightDerivedZeroIsoSelf · cited by 10Functor.rightDerivedZeroI…CategoryTheory.InjectiveResolution.isoRightDerivedObj · cited by 8InjectiveResolution.isoRi…CategoryTheory.NatTrans.rightDerived · cited by 4NatTrans.rightDerivedCategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturality · cited by 3InjectiveResolution.isoRi…CategoryTheory.NatTrans.rightDerived_comp · cited by 1NatTrans.rightDerived_compCategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id · cited by 1Functor.rightDerivedZeroI…CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app · cited by 1Functor.rightDerivedZeroI…CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id · cited by 1Functor.rightDerivedZeroI…CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app · cited by 1Functor.rightDerivedZeroI…CategoryTheory.InjectiveResolution.isoRightDerivedObj_inv_naturality · cited by 1InjectiveResolution.isoRi…CategoryTheory.NatTrans.rightDerived_comp_assoc · cited by 0NatTrans.rightDerived_com…CategoryTheory.NatTrans.rightDerived_id · cited by 0NatTrans.rightDerived_idCategoryTheory.InjectiveResolution.rightDerived_app_eq · cited by 0InjectiveResolution.right…CategoryTheory.InjectiveResolution.toRightDerivedZero_eq · cited by 0InjectiveResolution.toRig…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianCategoryTheory.Functor.Additive · cited by 1179Functor.AdditiveComplexShape.up · cited by 1123ComplexShape.upHomotopyCategory.homologyFunctor · cited by 36HomotopyCategory.homology…CategoryTheory.HasInjectiveResolutions · cited by 34CategoryTheory.HasInjecti…CategoryTheory.Functor.rightDerivedToHomotopyCategory · cited by 12Functor.rightDerivedToHom…Functor.rightDerivedCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by25

Results whose statement or proof uses this declaration.