Homology, Homotopy and Applications

Volume 4 (2002)

Number 1

Extensions of symmetric cat-groups

Pages: 103 – 162

DOI: http://dx.doi.org/10.4310/HHA.2002.v4.n1.a8

Authors

D. Bourn (Laboratoire de Mathématiques, Université du Littoral, Dunkerque, France)

E. M. Vitale (Département de Mathématiques, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

This paper is an attempt to study extensions of symmetric categorical groups from a structural point of view. Using in a systematic way bilimits in the 2-category of symmetric categorical groups, we develop a theory which closely follows the classical theory of abelian group extensions. The basic results are established for any proper class of extensions, and a cohomological classification is obtained for those extensions whose epi part has a categorical section.

Keywords

symmetric categorical groups, extensions, bilimits, homological algebra

2010 Mathematics Subject Classification

18D10, 18Gxx, 20L05

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