Theorems · Inductive type · category theory
CategoryTheory.HasInjectiveResolutions
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[CategoryTheory.Limits.HasZeroObject C] → [CategoryTheory.Limits.HasZeroMorphisms C] → PropYou will rarely use this typeclass directly: it is implied by the combination
[EnoughInjectives C] and [Abelian C].
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Limits.HasZeroMorphismsstatement · cited by 3,275
- CategoryTheory.Limits.HasZeroObjectstatement · cited by 1,298
Cited by46
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.rightDerivedstatement and proof · cited by 21
- CategoryTheory.Functor.rightDerivedToHomotopyCategorystatement and proof · cited by 12
- CategoryTheory.Functor.toRightDerivedZerostatement and proof · cited by 10
- CategoryTheory.Functor.rightDerivedZeroIsoSelfstatement and proof · cited by 10
- CategoryTheory.InjectiveResolution.isoRightDerivedObjstatement and proof · cited by 8
- CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObjstatement and proof · cited by 8
- CategoryTheory.InjectiveResolution.isostatement and proof · cited by 7
- CategoryTheory.injectiveResolutionsstatement and proof · cited by 6
- CategoryTheory.NatTrans.rightDerivedToHomotopyCategorystatement and proof · cited by 5
- CategoryTheory.NatTrans.rightDerivedstatement and proof · cited by 4
- CategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturalitystatement and proof · cited by 3
- CategoryTheory.InjectiveResolution.iso_hom_naturalitystatement and proof · cited by 3