Theorems · Definition · group theory

AddSubmonoid.LocalizationMap.addEquivOfAddEquiv

{M : Type u_1} →
  [inst : AddCommMonoid M] →
    {S : AddSubmonoid M} →
      {N : Type u_2} →
        [inst_1 : AddCommMonoid N] →
          {P : Type u_3} →
            [inst_2 : AddCommMonoid P] →
              S.LocalizationMap N →
                {T : AddSubmonoid P} →
                  {Q : Type u_4} →
                    [inst_3 : AddCommMonoid Q] →
                      T.LocalizationMap Q → {j : M ≃+ P} → AddSubmonoid.map j.toAddMonoidHom 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

AddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoid