Theorems · Definition · category theory
ModuleCat.localizedModule
{R : Type u} → [inst : CommRing R] → [Small.{v, u} R] → ModuleCat R → (S : Submonoid R) → ModuleCat (Localization S)Shrink of LocalizedModule S M in category which M belongs.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 52 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.
- CommRingstatement and proof · cited by 17,173
- Submonoidstatement and proof · cited by 3,086
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierproof · cited by 997
- ModuleCat.ofproof · cited by 594
- Smallstatement and proof · cited by 369
- Localizationstatement and proof · cited by 270
- LocalizedModuleproof · cited by 154
- Shrinkproof · cited by 132
Cited by19
Results whose statement or proof uses this declaration.
- ModuleCat.localizedModuleFunctorproof · cited by 8
- ModuleCat.localizedModuleMkLinearMapstatement · cited by 6
- ModuleCat.hasInjectiveDimensionLE_iff_forall_maximalSpectrumstatement and proof · cited by 2
- ModuleCat.hasProjectiveDimensionLE_iff_forall_maximalSpectrumstatement and proof · cited by 2
- ModuleCat.localizedModuleMapstatement · cited by 2
- ModuleCat.localizedModule_hasInjectiveDimensionLEstatement and proof · cited by 2
- ModuleCat.localizedModule_hasProjectiveDimensionLEstatement and proof · cited by 2
- ModuleCat.hasInjectiveDimensionLE_iff_forall_primeSpectrumstatement and proof · cited by 1
- ModuleCat.hasProjectiveDimensionLE_iff_forall_primeSpectrumstatement and proof · cited by 1
- ModuleCat.injectiveDimension_eq_iSup_localizedModule_maximalstatement and proof · cited by 0
- ModuleCat.injectiveDimension_eq_iSup_localizedModule_primestatement and proof · cited by 0
- ModuleCat.injectiveDimension_le_injectiveDimension_of_isLocalizedModulestatement and proof · cited by 0