Dear Paul,
(I believe that there was a development of "locally internal" instead of "locally small" categories by some French categorists in the 1970s -- Burroni again maybe?.)
I must mention that it is not me, but Jacques Penon who has worked on "locally internal" notions. I would like to add (to my yesterday mail) some indications on what I have called "small categories theory". In fact, this theory begins to exist. It is, for instance, what is called the "higher dimensionnal words problem", but also a developpement on higher automata theory (I have made many talks on this subjet, but not published --- I can send a manuscript to anybody interested). I have for example proved that finite and finitary Lawvere theory are finitely presentable 2-monoïds (it is my motivation for introducing the notion of polygraphs, previously introduced by Ross Street under the name of computads). It is perhaps not well-known by the categorists because it is published in a computer sciences revue : http://people.math.jussieu.fr/~burroni/mapage/highwordpb.pdf Best, Albert [For admin and other information see: http://www.mta.ca/~cat-dist/ ]