Peter Huston (University of Leeds) – Morita-invariant computations in Morita 3-categories of enriched fusion categories

Finding Morita invariants of fusion categories enriched over a fixed modular tensor category is important because, by a form of the cobordism hypothesis, they correspond (2+1)D twice-extended framed TQFTs, and therefore to physical characteristics of topological phases of matter. In this talk, we will introduce the notions of fusion 1- and 2-category and see how they appear naturally in higher linear algebra. We will then see how the Morita 3-category of fusion categories, bimodule categories, bimodule functors, and natural transformations can be equivalently described by concrete Morita invariants, so that choices of representatives of Morita class need not be made.