Weighted colimits of 2-representations and star algebras

TL;DR

This paper uses weighted bicategorical colimits to classify simple transitive birepresentations of a specific bicategory, confirming a prior conjecture and advancing understanding of 2-representations in bicategory theory.

Contribution

It applies weighted bicategorical colimits to classify simple transitive birepresentations, providing a complete solution to a conjecture in the field.

Findings

Confirmed a conjecture on simple transitive birepresentations

Provided a classification of birepresentations for a specific bicategory

Advanced the theory of weighted bicategorical colimits

Abstract

We apply the theory of weighted bicategorical colimits to study the problem of existence and computation of such colimits of birepresentations of finitary bicategories. The main application of our results is the complete classification of simple transitive birepresentations of a bicategory studied in arXiv:1805.05724, which confirms a conjecture made therein.