Algebras over a symmetric fusion category and integrations

TL;DR

This paper explores the structure of $E_n$-algebras within the symmetric monoidal 2-category of finite semisimple module categories over a symmetric fusion category, computing their centers and factorization homology for stratified surfaces.

Contribution

It introduces the study of $E_n$-algebras in this 2-category and explicitly computes their centers and factorization homology for specific cases.

Findings

Computed $E_n$-centers for n=0,1,2.

Calculated factorization homology of stratified surfaces with these algebras.

Provided results under certain anomaly-free conditions.

Abstract

We study the symmetric monoidal 2-category of finite semisimple module categories over a symmetric fusion category. In particular, we study $E_n$-algebras in this 2-category and compute their $E_n$-centers for $n=0,1,2$. We also compute the factorization homology of stratified surfaces with coefficients given by $E_n$-algebras in this 2-category for $n=0,1,2$ satisfying certain anomaly-free conditions.