Theorems · Definition · group theory
Localization.mulEquivOfQuotient
{M : Type u_1} →
[inst : CommMonoid M] →
{S : Submonoid M} → {N : Type u_2} → [inst_1 : CommMonoid N] → S.LocalizationMap N → Localization S ≃* NGiven a Localization map f : M →* N for a Submonoid S, we get an isomorphism between
the Localization of M at S as a quotient type and N.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- MulEquivstatement · cited by 1,142
- Localizationstatement · cited by 270
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Localization.monoidOfproof · cited by 17
- Submonoid.LocalizationMap.mulEquivOfLocalizationsproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- Localization.mulEquivOfQuotient_mk'statement · cited by 1
- Localization.mulEquivOfQuotient_symm_mk'statement · cited by 1
- Localization.mulEquivOfQuotient_applystatement · cited by 0
- Localization.mulEquivOfQuotient_mkstatement and proof · cited by 0
- Localization.mulEquivOfQuotient_monoidOfstatement · cited by 0
- Localization.mulEquivOfQuotient_symm_mkstatement and proof · cited by 0
- Localization.mulEquivOfQuotient_symm_monoidOfstatement · cited by 0
- Localization.Away.mulEquivOfQuotientproof · cited by 0