Monadic reconstruction of unitary Drinfeld centers and Factorization Homology

TL;DR

This paper establishes a connection between the unitary Drinfeld center of a tensor category and bimodule categories over a W*-algebra, extending known results to non-fusion categories and applying this to factorization homology.

Contribution

It generalizes M"uger's result to non-fusion categories and relates factorization homology to C*-algebraic extensions and quantum group doubles.

Findings

Equivalence of the unitary Drinfeld center to bimodule categories over a W*-algebra.

Expression of factorization homology via C*-algebraic extensions.

Extension of M"uger's result to non-fusion tensor categories.

Abstract

We prove that the unitary Drinfeld center of a unitary tensor category is equivalente to the category of unitary bimodules for the canonical W*-algebra object, generalizing M\"uger's result to the non-fusion case. This is then used to express factorization homology in terms of C*-algebraic extensions of symmetric enveloping algebras and actions of Drinfeld dobules of compact quantum groups.