Using rewriting systems to compute left Kan extensions and induced actionsof categories

The aim is to apply string-rewriting methods to compute left Kan extensions , or: equivalently, induced actions of monoids, categories, groups or group oids. This allows rewriting methods to be applied to a greater range of sit uations and examples than before. The data for the rewriting is called a Ka n extension presentation. The paper has its origins in earlier work by Carm ody and Waiters who gave an algorithm for computing left Kan extensions bas ed on extending the Todd-Coxeter procedure, an algorithm only applicable wh en the induced action is finite. The current work, in contrast, gives infor mation even when the induced action is infinite. (C) 2000 Academic Press.