Some remarks on protolocalizations and protoadditive reflections

Abstract

We investigate additional properties of protolocalizations, introduced and studied by Borceux, Clementino, Gran, and Sousa, and of protoadditive reflections, introduced and studied by Everaert and Gran. Among other things, we show that there are no non-trivial (protolocalizations and) protoadditive reflections of the category of groups, and establish a connection between protolocalizations and Kurosh–Amitsur radicals of groups with multiple operators whose semisimple classes form subvarieties.