Theorems · Definition · group theory

Submonoid.LocalizationMap.mulEquivOfMulEquiv

{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 →
                {T : Submonoid P} →
                  {Q : Type u_4} →
                    [inst_3 : CommMonoid Q] →
                      T.LocalizationMap Q → {j : M ≃* P} → Submonoid.map j.toMonoidHom S = T → N ≃* Q

Given Localization maps f : M →* N, k : P →* U for Submonoids S, T respectively, an isomorphism j : M ≃* P such that j(S) = T induces an isomorphism of localizations N ≃* U.

Defined in

Mathlib.GroupTheory.MonoidLocalization.Maps

Cited by

6 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidCommMonoidCommMonoidCommMonoid