In this easy introduction to higher gauge theory, we describe parallel transport for particles
and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a …

This book presents a guide to the extensive literature on the topic of semirings and includes
a complete bibliography. It serves as a complement to the existing monographs and a point …

We present a framework to systematically investigate higher categorical symmetries in two-
dimensional spin systems. Though exotic, such generalised symmetries have been shown …

The theory of Lie algebras can be categorified starting from a new notion of" 2-vector space",
which we define as an internal category in Vect. There is a 2-category 2Vect having these 2 …

For every tensor category C there is a braided tensor category Z (C), the 'center'of C. It is well
known to be related to Drinfel'd's notion of the quantum double of a finite dimensional Hopf …

Just as gauge theory describes the parallel transport of point particles using connections on
bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (eg …

We propose a notion of weak (n+ k, n)–category, which we call (n+ k, n)–Θ–spaces. The (n+
k, n)–Θ–spaces are precisely the fibrant objects of a certain model category structure on the …

This book is an invitation to discover advanced topics in category theory through concrete,
real-world examples. It aims to give a tour: a gentle, quick introduction to guide later …

arXiv:math/0107188v1 [math.CT] 25 Jul 2001 Page 1 arXiv:math/0107188v1 [math.CT] 25 Jul
2001 A Survey of Definitions of n-Category Tom Leinster Department of Pure Mathematics …

Prediction is hard, especially when it comes to the future, but barring some unforeseen
catastrophe, we can expect the amount of mathematics produced in the 21st century to dwarf …