Using Rewriting Systems to Compute Left Kan Extensions and Induced Actions of Categories

The aim is to apply string-rewriting methods to compute left Kan extensions, or, equivalently, induced actions of monoids, categories, groups or groupoids. This allows rewriting methods to be applied to a greater range of situations and examples than before. The data for the rewriting is called a Kan extension presentation. The paper has its origins in earlier work by Carmody and Walters who gave an algorithm for computing left Kan extensions based on extending the Todd–Coxeter procedure, an algorithm only applicable when the induced action is finite. The current work, in contrast, gives information even when the induced action is infinite.