Biography

The main area of research of G. Janelidze is category theory and its applications in pure mathematics, especially in algebra and topology. This includes: (a) his Galois theory in general categories with various special cases (classical Galois theory, Galois theory of commutative rings in sense of ChaseHarrisonRosenberg and Magid – with earlier publications unrelated to the categorical context, Grothendieck Galois theory, several geometric/topological/simplicial theories of covering maps, and theory of generalized central extensions he developed in joint work with G. M. Kelly); (b) Grothendieck descent theory in algebra and topology (mostly joint work with W. Tholen, and later also with M. Sobral); (c) new links with homological and universal algebra via central extensions, Huq-Smith-Pedicchio commutator theory, protomodular and semi-abelian categories, internal actions and semidirect products, internal categories and crossed modules, and Ursini theory of ideals and ideal determined categories; (d) the so-called Kurosh-Amitsur radical theory; (e) several other topics of research in algebra and general and algebraic topology with one or two publications devoted to each of them.