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.
Split extensions, semidirect product and holomorph of categorical groups / S. Kasangian, G. Metere, E.M. Vitale. - In: HOMOLOGY, HOMOTOPY AND APPLICATIONS. - ISSN 1532-0073. - 8:1(2006), pp. 145-167. [10.4310/HHA.2006.v8.n1.a4]
Split extensions, semidirect product and holomorph of categorical groups
S. KasangianPrimo
;G. MetereSecondo
;
2006
Abstract
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.
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