On categories with semidirect products. (English) Zbl 1264.18004
In this paper, necessary and sufficient conditions for a pointed category to admid semidirect products in the sense of D. Bourn and 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.
Reviewer: Osman Mucuk (Kayseri)
Citations:
Zbl 0890.18003References:
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