Split extensions, semidirect product and holomorph of categorical groups
- Autori: Kasangian, S.; Metere, G.; Vitale, E.
- Anno di pubblicazione: 2006
- Tipologia: Articolo in rivista (Articolo in rivista)
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.