Theorems · Definition · commutative algebra

IsLocalizedModule.iso

{R : Type u_1} →
  [inst : CommSemiring R] →
    (S : Submonoid R) →
      {M : Type u_2} →
        {M' : Type u_3} →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : AddCommMonoid M'] →
              [inst_3 : Module R M] →
                [inst_4 : Module R M'] → (f : M →ₗ[R] M') → [IsLocalizedModule S f] → LocalizedModule S M ≃ₗ[R] M'

If (M', f : M ⟶ M') satisfies universal property of localized module, then M' is isomorphic to LocalizedModule S M as an R-module.

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

34 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleIsLocalizedModule