Toposes and abelian categories are striking for the number of elementary properties they have in common (monic+epi = iso, mono/epi is a unique factorization system, etc. etc.) and the paucity of their common models, namely just the final category. This observation prompts the following questions. 1. Are there any other pairs of large and/or useful classes of categories whose respective theories have so much in common yet whose models have so little in common? 2. What can be said of the class of those categories having all the elementary properties common to toposes and abelian categories? In particular does it contain anything other than toposes and abelian categories? And if so, does this outcome change when the language is extended to say second order logic? To the extent that both toposes and abelian categories share much pleasant structure, the models of the intersection of their theories, for a suitable choice of language, would seem to be a nice class in its own right. Vaughan Pratt