Author: Peter Webb
email: webb@math.umn.edu
Address:
School of Mathematics,
University of Minnesota,
Minneapolis MN 55455

Title:
An introduction to the representations and cohomology of categories

Abstract:
We survey the basic aspects of the representations of categories, 
focusing attention on the formalism of the category algebra, the properties
of induction and restriction to full subcategories, the parametrization of 
the simple and projective representations, the role of the constant functor
and the properties of the derived functors of the limit and colimit functors.
In the last sections we interpret the low dimensional (co)homology of a
category in a similar way to what is done in group cohomology, including
a description of extension theory.

To appear in proceedings of the Bernoulli Institute program on representation
theory, January - June 2005.

Preprint: February 2006.