Abstract
For any categorical group H, we introduce the categorical group O ut(H) and then the well-known group exact sequence 1→Z(H)→H→Aut(H)→Out(H)→1 is raised to a categorical group level by using a suitable notion of exactness. Breen's Schreier theory for extensions of categorical groups is codified in terms of homomorphism to O ut(H) and then we develop a sort of Eilenberg–Mac Lane obstruction theory that solves the general problem of the classification of all categorical group extensions of a group G by a categorical group H, in terms of ordinary group cohomology.
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Carrasco, P., Garzón, A.R. Obstruction Theory for Extensions of Categorical Groups. Applied Categorical Structures 12, 35–61 (2004). https://doi.org/10.1023/B:APCS.0000013810.93405.c8
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DOI: https://doi.org/10.1023/B:APCS.0000013810.93405.c8