The following is available on the xxx archive. http://xxx.soton.ac.uk/abs/math.CO/9903032 Title: Using Rewriting Systems to Compute Kan Extensions and Induced Actions of Categories Authors: Ronald Brown, Anne Heyworth (University Of Wales, Bangor) Comments: 31 pages, LaTeX2e, (submitted to JSC) Subj-class: Combinatorics MSC-class: 68Q42 18A40 68Q40 The basic method of rewriting for words in a free monoid given a monoid presentation is extended to rewriting for paths in a free category given a `Kan extension presentation'. This is related to work of Carmody-Walters on the Todd-Coxeter procedure for Kan extensions, but allows for the output data to be infinite, described by a language. The result also allows rewrite methods to be applied in a greater range of situations and examples, in terms of induced actions of monoids, categories, groups or groupoids. (28kb) Prof R. Brown, School of Mathematics, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382475 fax: +44 1248 383663 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ New article: Higher dimensional group theory Symbolic Sculpture and Mathematics: http://www.bangor.ac.uk/SculMath/ Mathematics and Knots: http://www.bangor.ac.uk/ma/CPM/exhibit/welcome.htm Dr Anne Heyworth, School of Mathematics, University of Wales, Bangor home page: http://www.bangor.ac.uk/~map130/welcome.html