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.
Kasangian, S., Metere, G., Vitale, E. (2006). Split extensions, semidirect product and holomorph of categorical groups. HOMOLOGY, HOMOTOPY AND APPLICATIONS, 8(1), 145-167.
Split extensions, semidirect product and holomorph of categorical groups
METERE, Giuseppe;
2006-01-01
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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