  Kan extensions provide a natural general framework for a variety of
combinatorial problems. We have developed rewriting procedures for Kan
extensions (over the category of sets) and this enables one program to address
a wide range of problems. Thus it is possible to use the same framework (and
therefore program) to enumerate monoid or group (or category of groupoid)
elements, to enumerate cosets or congruence classes on monoids, calculate
equivariant equivalence relations, induced actions of groups, monoids or
categories and even more. This extended abstract is an outline of "Using
Rewriting Systems to Compute Kan Extensions and Induced Actions of Categories"
by R. Brown and A. Heyworth.
