A Prehistory of n-Categorical Physics

TL;DR

This paper reviews the historical development of categorical and n-categorical frameworks in physics, highlighting their increasing importance in theories from relativity to quantum gravity and topological quantum field theory.

Contribution

It provides a comprehensive chronology of how categorical concepts have evolved and been applied in physics up to the early 2000s, illustrating their foundational role.

Findings

Categories underpin relativity and quantum theories

n-Categories connect to Feynman diagrams and string theory

Categorification advances in quantum groups and TQFTs

Abstract

This paper traces the growing role of categories and n-categories in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts which manifest themselves in Feynman diagrams, spin networks, string theory, loop quantum gravity, and topological quantum field theory. Our chronology ends around 2000, with just a taste of later developments such as open-closed topological string theory, the categorification of quantum groups, Khovanov homology, and Lurie's work on the classification of topological quantum field theories.