Hi Reinhard, when I entered category theory I must have gotten on the nerves of a student of logic who found it necessary to point out to me that universality is as good as one knows the ambient universe. That remark came around to bite me once more when I recently pontificated that under the same assumptions on a category S, under which NNO's in S imply that the category of categories in S is monadic over the category of directed graphs in S, the converse would be true. Dietmar (Schumacher) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]