Theorems · Theorem · group theory

Submonoid.LocalizationMap.lift_surjective_iff

∀ {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} (hg : ∀ (y : ↥S), IsUnit (g ↑y)),
  Function.Surjective ⇑(f.lift hg) ↔ ∀ (v : P), ∃ x, v * g ↑x.2 = g x.1

Defined in

Mathlib.GroupTheory.MonoidLocalization.Maps

Cited by

1 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidCommMonoidCommMonoid