Theorems · Definition · group theory
Submonoid.LocalizationMap.toMonoidHom
{M : Type u_1} →
[inst : CommMonoid M] → {S : Submonoid M} → {N : Type u_2} → [inst_1 : CommMonoid N] → S.LocalizationMap N → M →* NA localization map between monoids automatically preserves 1 and therefore is a monoid homomorphism.
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- CommMonoidCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidHomstatement · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- Submonoid.LocalizationMapstatement and proof · cited by 147
- MulHom.toFunproof · cited by 36
- Submonoid.LocalizationMap.toMulHomproof · cited by 2
Cited by37
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.mk'proof · cited by 49
- Submonoid.LocalizationMap.ofMulEquivOfLocalizationsproof · cited by 13
- IsLocalization.map_underproof · cited by 12
- Submonoid.LocalizationMap.ofMulEquivOfDomproof · cited by 6
- Submonoid.LocalizationMap.mk'_eq_iff_eqproof · cited by 5
- Submonoid.LocalizationMap.mk'_secproof · cited by 5
- Submonoid.LocalizationMap.mk'_specproof · cited by 5
- Submonoid.LocalizationMap.lift_compstatement · cited by 5
- Localization.mk_eq_monoidOf_mk'_applyproof · cited by 4
- Submonoid.LocalizationMap.mk'_self'proof · cited by 3
- Submonoid.LocalizationMap.lift_idstatement · cited by 3
- Submonoid.LocalizationMap.lift_of_compstatement and proof · cited by 3