A representation theory for (strict) categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these bicategories contain representations which are indecomposable but not irreducible. A simple example is computed in explicit detail.
Keywords: categorical group, categorical representations, monoidal 2-categories
2000 MSC: 18D05
Theory and Applications of Categories,
Vol. 16, 2006,
No. 20, pp 529-557.
http://www.tac.mta.ca/tac/volumes/16/20/16-20.dvi
http://www.tac.mta.ca/tac/volumes/16/20/16-20.ps
http://www.tac.mta.ca/tac/volumes/16/20/16-20.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/20/16-20.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/20/16-20.ps