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Theorems · Inductive type · category theory

CategoryTheory.HasInjectiveResolutions

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.Limits.HasZeroObject C] → [CategoryTheory.Limits.HasZeroMorphisms C] → Prop

You will rarely use this typeclass directly: it is implied by the combination [EnoughInjectives C] and [Abelian C].

Defined in
Mathlib.CategoryTheory.Preadditive.Injective.Resolution
Cited by
34 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

CategoryTheory.Functor.rightDerived · cited by 21Functor.rightDerivedCategoryTheory.Functor.rightDerivedToHomotopyCategory · cited by 12Functor.rightDerivedToHom…CategoryTheory.Functor.toRightDerivedZero · cited by 10Functor.toRightDerivedZeroCategoryTheory.Functor.rightDerivedZeroIsoSelf · cited by 10Functor.rightDerivedZeroI…CategoryTheory.InjectiveResolution.isoRightDerivedObj · cited by 8InjectiveResolution.isoRi…CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj · cited by 8InjectiveResolution.isoRi…CategoryTheory.InjectiveResolution.iso · cited by 7InjectiveResolution.isoCategoryTheory.injectiveResolutions · cited by 6CategoryTheory.injectiveR…CategoryTheory.NatTrans.rightDerivedToHomotopyCategory · cited by 5NatTrans.rightDerivedToHo…CategoryTheory.NatTrans.rightDerived · cited by 4NatTrans.rightDerivedCategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturality · cited by 3InjectiveResolution.isoRi…CategoryTheory.InjectiveResolution.iso_hom_naturality · cited by 3InjectiveResolution.iso_h…CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality · cited by 2InjectiveResolution.isoRi…CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_comp · cited by 1NatTrans.rightDerivedToHo…CategoryTheory.NatTrans.rightDerived_comp · cited by 1NatTrans.rightDerived_compCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectCategoryTheory.HasInjectiveRe…CITED BYCITES

Cites3

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

Cited by46

Results whose statement or proof uses this declaration.