Split extensions, semidirect product and holomorph of categorical groups
(2006) Homology, Homotopy and Applications — Vol. 8, n° 1, p. 145-167 (2006)
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- 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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Citations
Kasangian, S., Metere, G., & Vitale, E. (2006). Split extensions, semidirect product and holomorph of categorical groups. Homology, Homotopy and Applications, 8(1), 145-167. https://doi.org/10.4310/HHA.2006.v8.n1.a4 (Original work published 2006)