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Disquisitions on Monoidal Categories and Operads
Ribbon tensor 2-categories and a target for ribbon 2-functors
Ribbon tensor 2-categories and a target for ribbon 2-functors
Organizers
Speaker
Time
Monday, March 23, 2026 4:00 PM - 5:00 PM
Venue
A3-1-301
Online
Zoom 559 700 6085
(BIMSA)
Abstract
Procedures for producing 3d topological invariants from algebraic categorical data are well-known; they now come under the name of "topological quantum field theories" (TQFTs). To lift these techniques to higher-dimensions, one performs a categorification, but this program still faces many unknowns. In particular, the central notion of a modular tensor 2-category is an important 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.