Homology, Homotopy and Applications
Volume 8 (2006)
Split extensions, semidirect product and holomorph of categorical groups
Pages: 145 – 167
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.
categorical groups, semidirect product, split extensions, holomorph
2010 Mathematics Subject Classification
18D05, 18D10, 18D35, 18G50