Bicommutant categories

Bicommutant categories are higher categorical analogs of von Neumann algberas. Examples of bicommutant categories can be constructed from unitary fusion categories, and from conformal nets. We will review these constructions, and present a new result, joint with Dave Penneys: given two Morita equivalent unitary fusion categories, their associated bicommutant categories are equivalent as tensor categories (not just Morita equivalent). We conjecture that, similarly, there exist many non-isomorphic conformal nets whose associated bicommutant categories are equivalent as tensor categories.