There seems some confusion as to whether Left Kan extensions are right Kan extensions and conversely, and it seems different authors use different conventions. What do people think of using a terminology analogous to limits and colimits, i.e. Kan extensions and Kan coextensions? In particular, what Carmody and Walters call left Kan extensions would here be Kan coextensions, which can be constructed as coends (as in Mac Lane, CFTWM). This point has come from Anne Heyworth, where left Kan extensions use right rewriting, if you write composition in a category in the algebraic rather than functional way. Any other ideas? Ronnie 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