We have corrected a few errors in TTT and there is new version that can be found on Charles' home page and at ftp.math.mcgill.ca/pub/barr. Thanks to Francisco Marmelejo, Tom Holroyd and Peter Selinger. Peter is responsible for the most substantive change, having noticed that the proof we gave in Chapter one that monics are pullback-stable is incoherent. We welcome all error notices and will eventually correct them. Michael 16-Jan-2002 17:33:19 -0400,2548;000000000000-00000000