Subject: categories: higher gauge theory

From: "John Baez" <[email-masked]>
Date: Mon, 28 Nov 2005 23:11:40 -0800 (PST)

Dear Categorists -

Here's a new paper:

  http://math.ucr.edu/home/baez/higher.pdf
  http://math.ucr.edu/home/baez/higher.ps

  John Baez and Urs Schreiber
  Higher Gauge Theory

  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 (e.g.
  strings) using 2-connections on 2-bundles.  A 2-bundle is a
  categorified version of a bundle: that is, one where the fiber
  is not a manifold but a category with a suitable smooth structure.
  Where gauge theory uses Lie groups and Lie algebras, higher gauge
  theory uses their categorified analogues: Lie 2-groups and Lie
  2-algebras.  We describe a theory of 2-connections on principal
  2-bundles and explain how this is related to Breen and Messing's
  theory of connections on nonabelian gerbes.  The distinctive
  feature of our theory is that a 2-connection allows parallel
  transport along paths and surfaces in a parametrization-independent
  way.  In terms of Breen and Messing's framework, this requires
  that the `fake curvature' must vanish.  In this paper we summarize
  the main results of our theory without proofs.

Fans of Lie groupoids may enjoy the "smooth 2-groupoid" used in this
paper.

Best,
jb