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RESEARCH PRODUCT

Split extensions, semidirect product and holomorph of categorical groups

Giuseppe MetereEnrico VitaleStefano Kasangian

subject

Semidirect product18D05categorical groupsGroup (mathematics)split extensionssplit extension18D10Context (language use)18G5018D35AlgebraMathematics (miscellaneous)HolomorphMathematics::Category TheoryholomorphUniversal propertysemidirect productcategorical groupLink (knot theory)Categorical variableMathematics

description

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.

yearjournalcountryeditionlanguage
2006-01-01
http://projecteuclid.org/euclid.hha/1140012468