Theorems · Theorem · commutative algebra
IsLocalization.lift_comp
∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} {S : Type u_2} [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] {P : Type u_3} [inst_3 : CommSemiring P] [inst_4 : IsLocalization M S] {g : R →+* P}
(hg : ∀ (y : ↥M), IsUnit (g ↑y)), (IsLocalization.lift hg).comp (algebraMap R S) = g- Defined in
- Mathlib.RingTheory.Localization.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsUnitstatement and proof · cited by 1,602
- RingHom.compstatement · cited by 899
- IsLocalizationstatement and proof · cited by 636
- RingHom.extproof · cited by 331
- DFunLike.ext_iffproof · cited by 102
- IsLocalization.toLocalizationMapproof · cited by 69
Cited by5
Results whose statement or proof uses this declaration.
- IsLocalization.map_compproof · cited by 31
- IsLocalization.localization_isScalarTower_of_submonoid_leproof · cited by 4
- IsLocalization.Away.lift_compproof · cited by 2
- RingHom.isIntegral_ofLocalizationSpanproof · cited by 0
- galLift_galRestrict'proof · cited by 0