# The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory

## TL;DR

This paper explicitly computes the center of a monoidal 2-category related to 3+1D Dijkgraaf-Witten Topological Quantum Field Theory, providing a detailed mathematical description of topological defects.

## Contribution

It offers a concrete calculation of the center of the monoidal 2-category for twisted G-graded categories, advancing the mathematical understanding of 3+1D Dijkgraaf-Witten TQFT.

## Key findings

- The center is a braided monoidal 2-category.
- The sylleptic center of this category is trivial.
- Provides a mathematical framework for topological defects in 3+1D TQFT.

## Abstract

In this work, for a finite group $G$ and a 4-cocycle $\omega \in Z^4(G, \mathbf{k}^\times)$, we compute explicitly the center of the monoidal 2-category $\operatorname{2Vec}_G^{\omega}$ of $\omega$-twisted $G$-graded 1-categories of finite dimensional $\mathbf{k}$-vector spaces. This center gives a precise mathematical description of the topological defects in the associated 3+1D Dijkgraaf-Witten TQFT. We prove that this center is a braided monoidal 2-category with a trivial sylleptic center.