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 DThe right derived functors of an additive functor.
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
- ComplexShape.upproof · cited by 1,123
- HomotopyCategory.homologyFunctorproof · cited by 36
- CategoryTheory.HasInjectiveResolutionsstatement and proof · cited by 34
- CategoryTheory.Functor.rightDerivedToHomotopyCategoryproof · cited by 12
Cited by25
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.toRightDerivedZerostatement · cited by 10
- CategoryTheory.Functor.rightDerivedZeroIsoSelfstatement · cited by 10
- CategoryTheory.InjectiveResolution.isoRightDerivedObjstatement · cited by 8
- CategoryTheory.NatTrans.rightDerivedstatement · cited by 4
- CategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturalitystatement · cited by 3
- CategoryTheory.NatTrans.rightDerived_compstatement · cited by 1
- CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_idstatement · cited by 1
- CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_appstatement · cited by 1
- CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_idstatement · cited by 1
- CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_appstatement · cited by 1
- CategoryTheory.InjectiveResolution.isoRightDerivedObj_inv_naturalitystatement and proof · cited by 1
- CategoryTheory.NatTrans.rightDerived_comp_assocstatement and proof · cited by 0