On categories with semidirect products
In this paper, necessary and sufficient conditions for a pointed category to admid semidirect products in the sense of \textit{D. Bourn} and \textit{G. Janelidze} [Theory Appl. Categ. 4, 37--46 (1998; Zbl 0890.18003) are given and interpreted in exactness of appropriate split extensions. In the cited reference [loc. cit.], the categorical notion of semidirect product in a category was introduced generalizing the notion of semidirect product of groups. By Theorem 3.4 in [loc. cit.] semi-abelian categories admits semidirect products but semi-abelianess is not a necessary condition for the existence of semidirect productdirectness.
scientific article; zbMATH DE number 6094158