Semidirect products and extensions in protomodular categories

George Janelidze – 7 January 1998

This is joint work with D.Bourn. Eilenberg - Mac Lane theory of group exnetsions is extended to protomodular categories in the sense of D.Bourn, using J.Beck's theory of torsors. A new syntactical description of protomodular varieties helps to construct various examples and establish the relationship with M.Barr - G.Orzech theory of extensions of omega-groups.