Categorical representations of categorical groups

John W. Barrett and Marco Mackaay

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.

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