Categorical representations of categorical groups
John W. Barrett, Marco Mackaay

TL;DR
This paper develops a representation theory for categorical groups, constructing a monoidal bicategory of representations that includes indecomposable but not irreducible objects, with an explicit example.
Contribution
It introduces a new framework for representing categorical groups using monoidal bicategories, expanding understanding of their structure.
Findings
Constructed a monoidal bicategory of representations for categorical groups
Identified representations that are indecomposable but not irreducible
Provided a detailed explicit example of such representations
Abstract
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A simple example is computed in explicit detail.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Logic
