# Rank-finiteness for G-crossed braided fusion categories

## TL;DR

This paper proves that the class of G-crossed braided fusion categories has finitely many ranks, extending known results for modular categories and exploring the structure of degenerate categories and their centers.

## Contribution

It generalizes rank-finiteness to G-crossed braided fusion categories and investigates the properties of slightly degenerate categories and their centers.

## Key findings

- Rank-finiteness established for G-crossed braided fusion categories
- Includes analysis of slightly degenerate braided fusion categories
- Provides insights into the structure of centers of these categories

## Abstract

We establish rank-finiteness for the class of $G$-crossed braided fusion categories, generalizing the recent result for modular categories and including the important case of braided fusion categories. This necessitates a study of slightly degenerate braided fusion categories and their centers, which are interesting for their own sake.