Theorems · Inductive type · group theory
AddSubmonoid.IsLocalizationMap
{M : Type u_1} → [inst : AddCommMonoid M] → {N : Type u_2} → [AddCommMonoid N] → AddSubmonoid M → (M → N) → PropA predicate characterizing homomorphisms between additive monoids M and N that form a
commutative triangle with the canonical map from M to its localization at S and
some isomorphism between N and the localization.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- AddCommMonoidAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement · cited by 12,281
- AddSubmonoidstatement · cited by 1,178
Cited by25
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.isLocalizationMapstatement · cited by 5
- AddSubmonoid.IsLocalizationMap.exists_of_eqstatement and proof · cited by 5
- AddSubmonoid.IsLocalizationMap.surjstatement and proof · cited by 5
- AddSubmonoid.IsLocalizationMap.map_addUnitsstatement and proof · cited by 4
- AddSubmonoid.LocalizationMap.casesOnstatement and proof · cited by 1
- AddSubmonoid.isLocalizationMap_iff_bijectivestatement and proof · cited by 1
- AddSubmonoid.isLocalizationMap_nat_intstatement · cited by 1
- AddSubmonoid.isLocalizationMap_of_addGroupstatement · cited by 1
- AddSubmonoid.LocalizationMap.toAddMonoidHom_injectiveproof · cited by 1
- AddSubmonoid.IsLocalizationMap.casesOnstatement and proof · cited by 1
- AddSubmonoid.IsLocalizationMap.map_zerostatement and proof · cited by 1
- AddSubmonoid.LocalizationMap.mk.injstatement and proof · cited by 1