A target for ribbon 2-functors
Organizers
Speaker
Time
Wednesday, November 12, 2025 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
Procedures for producing 3d topological invariants from algebraic categorical data are well-known; they now come under the name of (3d) "topological quantum field theories" (TQFTs). To lift them to higher-dimensions, one performs a categorification, but many unknowns still plague us. In particular, the key notion of a ribbon tensor 2-category is a central topic of recent research. In this talk, I will introduce an approach to this problem inspired from derived higher-gauge theory in 4-dimensions. The strategy is to systematically examine the various structures induced on the 2-category of 2-representations of a so-called "cobraided dagger Hopf category". By walking through the interaction of the braiding with the different levels of duality, we can algebraically and geometrically tease out properties of the 2-ribbon structure necessary for describing framed invariants of knots and surfaces in 4-space. This is based on my recent work arxiv:2501.08041.