Theorems · Theorem · group theory
Submonoid.LocalizationMap.map_units
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoid N]
(f : S.LocalizationMap N) (y : ↥S), IsUnit (f ↑y)- Cited by
- 46 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, 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.
- DFunLike.coestatement · cited by 62,936
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- IsUnitstatement · cited by 1,602
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Submonoid.IsLocalizationMap.map_unitsproof · cited by 5
- Submonoid.LocalizationMap.isLocalizationMapproof · cited by 5
Cited by48
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.mk'proof · cited by 49
- IsLocalization.map_underproof · cited by 12
- Submonoid.LocalizationMap.eq_iff_existsproof · cited by 9
- Submonoid.LocalizationMap.mulEquivOfLocalizationsproof · cited by 8
- Submonoid.LocalizationMap.mk'_eq_iff_eqproof · cited by 5
- Submonoid.LocalizationMap.mk'_secproof · cited by 5
- Submonoid.LocalizationMap.mk'_specproof · cited by 5
- Localization.mk_eq_monoidOf_mk'_applyproof · cited by 4
- Submonoid.LocalizationMap.eq_mk'_iff_mul_eqproof · cited by 4
- Submonoid.LocalizationMap.mk'_self'proof · cited by 3
- Submonoid.LocalizationMap.lift_idstatement · cited by 3
- Submonoid.LocalizationMap.map_right_cancelproof · cited by 2