Theorems · Inductive type · group theory
AddSubmonoid.LocalizationMap
{M : Type u_1} → [inst : AddCommMonoid M] → AddSubmonoid M → (N : Type u_2) → [AddCommMonoid N] → Type (max u_1 u_2)The type of AddMonoid homomorphisms satisfying the characteristic predicate: if f : M →+ N
satisfies this predicate, then N is isomorphic to the localization of M at S.
- Cited by
- 119 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 27 definitions · 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 by141
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.mk'statement and proof · cited by 44
- AddSubmonoid.LocalizationMap.map_addUnitsstatement and proof · cited by 36
- AddSubmonoid.LocalizationMap.toAddMonoidHomstatement and proof · cited by 29
- AddSubmonoid.LocalizationMap.liftstatement and proof · cited by 23
- AddSubmonoid.LocalizationMap.secstatement and proof · cited by 20
- AddSubmonoid.LocalizationMap.mapstatement and proof · cited by 15
- AddLocalization.addMonoidOfstatement · cited by 13
- AddSubmonoid.LocalizationMap.ofAddEquivOfLocalizationsstatement and proof · cited by 13
- AddSubmonoid.LocalizationMap.addEquivOfLocalizationsstatement and proof · cited by 8
- AddSubmonoid.LocalizationMap.eq_iff_existsstatement and proof · cited by 8
- AddSubmonoid.LocalizationMap.lift_eqstatement and proof · cited by 8
- AddLocalization.addEquivOfQuotientstatement and proof · cited by 7