Theorems · Theorem · commutative algebra
LocalizedModule.map_surjective
∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M : Type u_2} [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] {N : Type u_3} [inst_3 : AddCommMonoid N] [inst_4 : Module R N] (l : M →ₗ[R] N),
Function.Surjective ⇑l → Function.Surjective ⇑((LocalizedModule.map S) l)- Defined in
- Mathlib.RingTheory.Localization.Module
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- Submonoidstatement and proof · cited by 3,086
- Localizationstatement · cited by 270
- LocalizedModulestatement · cited by 154
- LocalizedModule.mkLinearMapproof · cited by 76
- LocalizedModule.mapstatement · cited by 29
- IsLocalizedModule.map_surjectiveproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Module.projective_of_localization_maximalproof · cited by 3
- Module.bijective_of_surjective_of_rankAtStalk_eqproof · cited by 1