A category internal to itself

Chatting at a conference, the question came up why there is no (non-trivial) category which is "internal to itself" (interpret this in some sensible sense). And over coffee we thought this must be well known, but not to us. Can somene shed some light on the matter? With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]