## Quantum Gravity Seminar - Spring 2002

#### John Baez

This is the continuation of my lectures on categorified
gauge theory, which I began in Winter 2002.
This quarter's lectures explain the classification
of bundles using Cech cohomology in a way that is easy to generalize
to "2-bundles". These are a "categorified"
version of bundles in which the fiber is not a set but a
*category*,
transition functions are replaced by transition *functors*,
and the usual equation satisifed by the transition
functions now holds only up to a specified
*natural isomorphism*, which satisfies an equation of
of its own.
If you're the sort of mathematician who is fond of
"stacks", you'll be pleased
to know that just as an ordinary bundle has a sheaf of sections,
a 2-bundle has a stack of sections.

If you're more interested
in physics, you should think of 2-bundles as permitting a generalization
of gauge theory that describes not the parallel transport of point
particles but of 1-dimensional extended objects - open strings, or
spin network edges.
The most familiar example is 2-form electromagnetism, which I explained
in detail in the Winter 2002 notes.

To get a general overview of these ideas,
you should start by peeking at the slides of this talk:

- Categorified
Gauge Theory,
lecture at the 2002 Joint Spring Meeting of the Pacific Northwest
Geometry Seminar and Cascade Topology Seminar.

There are also a lot of links to papers here.
The course notes below were taken by
Alissa Crans,
who has kindly scanned them in and made PDF files out
of them:

Eventually I will try to give descriptive titles
for the notes from each class, but right now I only have
them listed by date.

Enjoy!

baez@math.removethis.ucr.andthis.edu

© 2002 John Baez and Alissa Crans