Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology
Quantum Algebra
2025-09-16 v1 Category Theory
Representation Theory
Abstract
These lecture notes are the product of a week-long learning workshop on the work of Johnson-Freyd and Reutter on the problem of the existence of minimal nondegenerate extensions of braided fusion categories (arXiv:2105.15167). They recount the mathematical arguments of the original paper from an expository angle, with background material covering the algebra and homotopy theory required to understand the statement and follow the proof. The notes are aimed at newcomers to the field of (braided) fusion 1- and 2-categories.
Keywords
Cite
@article{arxiv.2509.10636,
title = {Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology},
author = {Diogo Andrade and Julia Bierent and Jennifer Brown and Tudor Caba and Matthew Cellot and Jonathan Davies and Adrien DeLazzer Meunier and Jannik Gröne and Benjamin Haïoun and Alea Hofstetter and Theo Johnson-Freyd and David Jordan and Tessa Kammermeier and Patrick Kinnear and Cameron Krulewski and Theodoros Lagiotis and Leon Liu and Adrià Marín Salvador and Nivedita and David Reutter and Lorenzo Riva and Iordanis Romaidis and Jack Romo and Sean Sanford and Michail Tagaris and Daniel Teixeira and Jackson van Dyke and Matthias Vancraeynest and Chetan Vuppulury and Matthew Yu and Markus Zetto},
journal= {arXiv preprint arXiv:2509.10636},
year = {2025}
}