Singular extensions and the second cohomology categorical group

We give a classification of the 2-groupoid of singular extensions of categorical groups by means of a second cohomology categorical group, whose definition uses the notion of nerve of a categorical group. This second cohomology is, then, shown to be involved in a five term 2-exact sequence a ` la Ho...

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Bibliographic Details
Published in:Journal of homotopy and related structures 2017-06, Vol.12 (2), p.447-485
Main Author: Garzón, A. R.
Format: Article
Language:English
Subjects:
Algebra
Algebraic Topology
Functional Analysis
Homology
Homomorphisms
Mathematics
Mathematics and Statistics
Number Theory
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Summary:We give a classification of the 2-groupoid of singular extensions of categorical groups by means of a second cohomology categorical group, whose definition uses the notion of nerve of a categorical group. This second cohomology is, then, shown to be involved in a five term 2-exact sequence a ` la Hochschild–Serre which is associated with any essentially surjective homomorphism of categorical groups.
ISSN:2193-8407
1512-2891
DOI:10.1007/s40062-016-0135-1