Theorems · Theorem · group theory

Submonoid.LocalizationMap.map_surjective_of_surjective

∀ {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] (f : S.LocalizationMap N) {g : M →* P} {Q : Type u_4} [inst_3 : CommMonoid Q],
  Function.Surjective ⇑g → ∀ (k : (Submonoid.map g S).LocalizationMap Q), Function.Surjective ⇑(f.map ⋯ k)

Given a surjective CommMonoid homomorphism g : M →* P, and a submonoid S ⊆ M, the induced monoid homomorphism from the localization of M at S to the localization of P at g S, is surjective.

Defined in

Mathlib.GroupTheory.MonoidLocalization.Maps

Cited by

1 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidCommMonoidCommMonoidCommMonoid