Some remarks on protolocalizations and protoadditive reflections

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.

12 pages

References in corpus (3)

• A torsion theory in the category of cocommutative Hopf algebras
• Monotone-light factorisation systems and torsion theories
• Split extension classifiers in the category of cocommutative Hopf algebras

Cited by in corpus (1)

• Non-additive derived functors via chain resolutions