On the reflectiveness of special homogeneous surjections of monoids

Abstract

We prove that the so-called special homogeneous surjections are reflective amongst surjective homomorphisms of monoids. To do so, we use a general result in categorical Galois theory, and the recent result that the special homogeneous surjections are the normal (= central) extensions with respect to the admissible Galois structure Γ_Mon determined by the Grothendieck group adjunction together with the classes of surjective homomorphisms.