# Annular Representations of Free Product Categories

## TL;DR

This paper characterizes the annular representation category arising from the free product of two rigid C*-tensor categories, advancing understanding of their structural properties.

## Contribution

It introduces a description of the annular representation category for free product categories, a novel theoretical development in tensor category theory.

## Key findings

- Provides a new framework for annular representations of free product categories
- Establishes structural properties of the annular representation category
- Enhances understanding of free product constructions in tensor categories

## Abstract

We provide a description of the annular representation category of the free product of two rigid C*-tensor categories.