# Some remarks on protolocalizations and protoadditive reflections

## TL;DR

This paper explores properties of protolocalizations and protoadditive reflections, revealing their limitations in group categories and linking them to radicals and subvarieties in algebraic structures.

## Contribution

It demonstrates the non-existence of non-trivial protoadditive reflections in groups and connects protolocalizations to Kurosh–Amitsur radicals with multiple operators.

## Key findings

- No non-trivial protoadditive reflections of groups exist.
- Established a link between protolocalizations and Kurosh–Amitsur radicals.
- Connected protolocalizations to subvarieties via semisimple classes.

## Abstract

We investigate additional properties of protolocalizations, introduced and studied by F. Borceux, M. M. Clementino, M. Gran, and L. Sousa, and of protoadditive reflections, introduced and studied by T. Everaert and M. 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.