Theorems · Theorem · group theory
Submonoid.LocalizationMap.lift_id
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoid N]
(f : S.LocalizationMap N) (x : N), (f.lift ⋯) x = x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 51 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.
Cites11
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
- MonoidHom.idproof · cited by 323
- Submonoid.LocalizationMapstatement and proof · cited by 147
- DFunLike.ext_iffproof · cited by 102
- Submonoid.LocalizationMap.map_unitsstatement · cited by 46
- Submonoid.LocalizationMap.toMonoidHomstatement · cited by 33
- Submonoid.LocalizationMap.liftstatement · cited by 26
- Submonoid.LocalizationMap.lift_of_compproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IsLocalization.lift_idproof · cited by 2
- Submonoid.LocalizationMap.lift_left_inverseproof · cited by 0
- Submonoid.LocalizationMap.map_idproof · cited by 0