Theorems · Definition · group theory

Submonoid.LocalizationMap.ofMulEquivOfLocalizations

{M : Type u_1} →
  [inst : CommMonoid M] →
    {S : Submonoid M} →
      {N : Type u_2} →
        [inst_1 : CommMonoid N] →
          {P : Type u_3} → [inst_2 : CommMonoid P] → S.LocalizationMap N → N ≃* P → S.LocalizationMap P

If f : M →* N is a Localization map for a Submonoid S and k : N ≃* P is an isomorphism of CommMonoids, k ∘ f is a Localization map for M at S.

Defined in

Mathlib.GroupTheory.MonoidLocalization.Maps

Cited by

13 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidCommMonoidCommMonoid