Theorems · Inductive type · group theory
Submonoid.LocalizationMap
{M : Type u_1} → [inst : CommMonoid M] → Submonoid M → (N : Type u_2) → [CommMonoid N] → Type (max u_1 u_2)The type of monoid 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
- 147 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 27 definitions · uses no axioms
- Assumes
- CommMonoidCommMonoid
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.
- Submonoidstatement · cited by 3,086
- CommMonoidstatement · cited by 2,264
Cited by173
Results whose statement or proof uses this declaration.
- IsLocalization.toLocalizationMapstatement · cited by 69
- Submonoid.LocalizationMap.mk'statement and proof · cited by 49
- Submonoid.LocalizationMap.map_unitsstatement and proof · cited by 46
- Submonoid.LocalizationMap.toMonoidHomstatement and proof · cited by 33
- Submonoid.LocalizationMap.liftstatement and proof · cited by 26
- Submonoid.LocalizationMap.secstatement and proof · cited by 26
- Localization.monoidOfstatement · cited by 17
- Submonoid.LocalizationMap.mapstatement and proof · cited by 16
- Submonoid.LocalizationMap.surjstatement and proof · cited by 15
- Submonoid.LocalizationMap.ofMulEquivOfLocalizationsstatement and proof · cited by 13
- Submonoid.LocalizationMap.lift_eqstatement and proof · cited by 11
- Submonoid.LocalizationMap.eq_iff_existsstatement and proof · cited by 9