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On the representations of 2-groups in Baez-Crans 2-vector spaces

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Benjamin A. Heredia and Josep Elgueta

We study the theory of representations of a 2-group G in Baez-Crans
2-vector spaces over a field k of arbitrary characteristic, and the
corresponding 2-vector spaces of intertwiners. We also characterize the
irreducible and indecomposable representations. Finally, it is shown that
when the 2-group is finite and the base field k is of characteristic zero
or coprime to the orders of the homotopy groups of G, the theory
essentially reduces to the theory of k-linear representations of the first
homotopy group of G, the remaining homotopy invariants of G playing no
role.

Keywords:
2-groups (categorical groups); 2-vector spaces; Representations; 2-categories

2010 MSC:
18D05, 18D10, 20L05

*Theory and Applications of Categories,*
Vol. 31, 2016,
No. 32, pp 907-927.

Published 2016-10-06.

http://www.tac.mta.ca/tac/volumes/31/32/31-32.pdf

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