Models for 2-Hilb and 3-Hilb as target categories for Functorial Field Theories

Abstract: We introduce W*-Cat, the bicategory of complete W*‐categories, functors and natural transformations and discuss its equivalence with the Morita category of von Neumann algebras (vN2). We highlight some analogies of W*‐categories with Hilbert spaces pointing towards W*-Cat being a model for 2-Hilb (based on arxiv.org/abs/2411.01678). We also introduce a categorified analogue of von Neumann algebras, motivating definition of a Bicommutant Category such that the Morita category of bicommutant categories would model 3-Hilb. This is work in progress.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home