Theorems · Theorem · commutative algebra
IsLocalization.lift_algebraMap_eq_algebraMap
∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) (S : Type u_2) [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] (Rₘ : Type u_4) (Sₘ : Type u_5) [inst_3 : CommSemiring Rₘ] [inst_4 : CommSemiring Sₘ]
[inst_5 : Algebra R Rₘ] [inst_6 : IsLocalization M Rₘ] [inst_7 : Algebra S Sₘ]
[i : IsLocalization (Algebra.algebraMapSubmonoid S M) Sₘ] [inst_8 : Algebra Rₘ Sₘ] [inst_9 : Algebra R Sₘ]
[IsScalarTower R Rₘ Sₘ] [inst_11 : IsScalarTower R S Sₘ], IsLocalization.lift ⋯ = algebraMap Rₘ Sₘ- Defined in
- Mathlib.RingTheory.Localization.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- Algebra.algebraMapSubmonoidstatement and proof · cited by 137
- IsScalarTower.algebraMap_applyproof · cited by 116
- IsLocalization.liftstatement · cited by 27
- IsLocalization.lift_uniqueproof · cited by 3
- IsLocalization.map_units_map_submonoidstatement and proof · cited by 1
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