Categorified gauge theory

John Baez (UC Riverside)

Categorification is the process of taking concepts defined using sets, functions and equations and generalizing them to concepts defined using categories, functors, and natural transformations.  If we apply this process to gauge theory we obtain a theory of "2-connections," which allow parallel transport not only along paths in the base manifold, but also paths of paths.  These arise naturally from the differential geometry of gerbes, which has recently begun to play a role in string theory.  However, there are also many other examples.  After an overview of these ideas we describe a categorified version of the Yang-Mills equations.

Spring 2002 CTS/PNGS meeting