-

Ribbon tensor 2-categories and a target for ribbon 2-functors

组织者

斯拉瓦·皮缅诺夫 , 安吉尔·托莱多

演讲者

陈群皓

时间

2026年03月23日 16:00 至 17:00

地点

A3-1-301

线上

Zoom 559 700 6085 (BIMSA)

摘要

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.