Many thanks for all the replies to my question about what to call a class of arrows closed under composition with isomorphisms. I now think a class of arrows "closed under isomorphism" or "isomorphism closed" is a good terminology. As for what good is it, it is true that if X is closed under isomorphism, the image FX under a functor F is not necessarily closed under isomorphism, but certainly FX generates such an isomorphism-closed class. And, if F and F' are naturally isomorphic, then FX and F'X generate the same isomorphism-closed class. This is very elementary, but I like it. Bill Rowan ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: European Colloquium Category Theory -ECCT- Note from moderator: The following was posted on the Usenet Newsgroup sci.math.research yesterday. It is presumably of interest to subscribers to this list. ++++++++++++++++++++++++++++++++++++++++++++