Sketches

Abstract

Abstract This chapter (rather like Chapter A3) is something of a digression from our main line of development: we shall not make any essential use of sketches in anything we wish to do with categorical logic, but, since they are extensively used by others in this context, it seems a good idea to give an account of what they are and how they relate to the line that we are following. Sketches were first introduced by C. Ehresmann [332] and were extensively developed by his pupils, notably L. Coppey and C. Lair [658]; for many years they were regarded as the ‘exclusive property’ of the French school of category-theorists (of which Ehresmann was the founder), but since the publication of the books by Barr and Wells [87, 88], and even more since the work of Makkai and Paré [787], their use has become much more widespread. In this account, we shall largely follow the conventions of Barr and Wells regarding terminology and notation.