Rewriting Procedures Generalise to Kan Extensions of Actions of Categories

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.