Split extensions, semidirect product and holomorph of categorical groups
- Authors: Kasangian, S.; Metere, G.; Vitale, E.
- Publication year: 2006
- Type: Articolo in rivista (Articolo in rivista)
- OA Link: http://hdl.handle.net/10447/74828
Working in the context of categorical groups, we show that the semidirect product provides a biequivalence between actions and points. From this biequivalence, we deduce a two-dimensional classification of split extensions of categorical groups, as well as the universal property of the holomorph of a categorical group. We also discuss the link between the holomorph and inner autoequivalences.