Bicommutant categories from fusion categories

Abstract

Bicommutant categories are higher categorical analogs of von Neumann algebras that were recently introduced by the first author. In this article, we prove that every unitary fusion category gives an example of a bicommutant category. This theorem categorifies the well-known result according to which a finite dimensional ∗ -algebra that can be faithfully represented on a Hilbert space is in fact a von Neumann algebra.