Theorems · Theorem · commutative algebra
LocalizedModule.map_mk
∀ {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] (f : M →ₗ[R] N) (x : M)
(y : ↥S), ((LocalizedModule.map S) f) (LocalizedModule.mk x y) = LocalizedModule.mk (f x) y- Defined in
- Mathlib.RingTheory.Localization.Module
- Cited by
- 5 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.
Cites15
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 and proof · cited by 154
- LocalizedModule.mkLinearMapproof · cited by 76
- LocalizedModule.mkstatement and proof · cited by 73
- IsLocalizedModule.mk'proof · cited by 54
Cited by5
Results whose statement or proof uses this declaration.
- exists_bijective_map_powersproof · cited by 3
- LocalizedModule.restrictScalars_map_eqproof · cited by 2
- IsLocalizedModule.exists_isLocalizedModule_powers_of_finitePresentationproof · cited by 1
- LinearMap.split_surjective_of_localization_maximalproof · cited by 1
- Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModuleproof · cited by 1