Theorems · Theorem · group theory
Localization.mulEquivOfQuotient_apply
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoid N]
{f : S.LocalizationMap N} (x : Localization S),
(Localization.mulEquivOfQuotient f) x = ((Localization.monoidOf S).lift ⋯) x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MonoidHomstatement · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- MulEquivstatement · cited by 1,142
- Localizationstatement and proof · cited by 270
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Submonoid.LocalizationMap.map_unitsstatement · cited by 46
- Submonoid.LocalizationMap.toMonoidHomstatement · cited by 33
- Submonoid.LocalizationMap.liftstatement · cited by 26
- Localization.monoidOfstatement · cited by 17
- Localization.mulEquivOfQuotientstatement · cited by 7
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