Theorems · Definition · category theory
ModuleCat.localizedModuleMkLinearMap
{R : Type u} →
[inst : CommRing R] →
[inst_1 : Small.{v, u} R] → (M : ModuleCat R) → (S : Submonoid R) → ↑M →ₗ[R] ↑(M.localizedModule S)The linear map M →ₗ[R] (M.localizedModule S) which
exhibits M.localizedModule S as a localized module of M.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Submonoidstatement and proof · cited by 3,086
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
- ModuleCatstatement and proof · cited by 1,429
- LinearEquiv.toLinearMapproof · cited by 1,171
- ModuleCat.carrierstatement and proof · cited by 997
- Smallstatement and proof · cited by 369
- Localizationstatement · cited by 270
- LocalizedModuleproof · cited by 154
Cited by7
Results whose statement or proof uses this declaration.
- ModuleCat.hasProjectiveDimensionLE_iff_forall_maximalSpectrumproof · cited by 2
- ModuleCat.localizedModuleMapproof · cited by 2
- ModuleCat.localizedModule_hasInjectiveDimensionLEproof · cited by 2
- ModuleCat.localizedModule_hasProjectiveDimensionLEproof · cited by 2
- ModuleCat.hasInjectiveDimensionLE_iff_forall_maximalSpectrumproof · cited by 2
- ModuleCat.localizedModuleFunctor_map_exactproof · cited by 0
- ModuleCat.localizedModuleMap_hom_applystatement · cited by 0