Theorems · Definition · group theory

Submonoid.LocalizationMap.ofMulEquivOfDom

{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} → {k : P ≃* M} → Submonoid.map k.toMonoidHom T = S → T.LocalizationMap N

Given CommMonoids M, P and Submonoids S ⊆ M, T ⊆ P, if f : M →* N is a Localization map for S and k : P ≃* M is an isomorphism of CommMonoids such that k(T) = S, f ∘ k is a Localization map for T.

Defined in

Mathlib.GroupTheory.MonoidLocalization.Maps

Cited by

6 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

CommMonoidCommMonoidCommMonoid