Categorical representations of categorical groups

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.