A few brief thoughts on Dusko's discussion: First, almost all definitions in mathematics when done from the ground up are hopelessly complex. Ask your skeptical friends to define a continuous real-valued function on a topological space from first principles (for them, I suppose, from axiomatic set-theory alone). The only reason real numbers (pairs of subsets of the set of equivalence classes of formal ratios of formal differences of things satisfying the Peano axioms, modulo... and satisfying.... ) don't give the same impression is that we are used to them and have consequently forgotten the formal definition and the proceed to use only the properties. One way of making progress in mathematical understanding, indeed the way most congenial to categorists, is to get the definitions right so that one can forget the morass of quantifiers in the definition, and use only the essential properties of the objects under consideration. (Deep results, though, usually come from doing this, then briefly returning to the less abstract level to pull out an unexpected relation between the more abstract and the more concrete: e.g. the Atiyah-Singer Index Theorem, or Shum's freeness result for framed tangles.) It has been a persistent problem for category theory that we are interested in foundational questions (which most mathematicians abhor), and have not made it generally understood that we are really doing a kind of algebra (albeit a kind of algebra so potent that it can be applied to foundations). You might therefore turn aside much criticism by pointing out that category theory is no longer abstract in the sense of having no really interesting concrete examples: the work of Joyal/Street, Freyd/Yetter, Shum, Turaev, Reshtikhin, Majid, Lyubashenko, (the physicists) Moore/Seiberg, Kapranov/Voevodsky, and Fisher (to name but a few) are full of remarkable categories (with additional structure requiring yet more complex definitions!) with intimate connections to low-dimensional topology and Hopf algebra theory. Similarly, coming from the more foundational uses of category theory, the realizability topos is surely one of the most beautiful objects anywhere. (Indeed, topoi in general are quite beautiful.) --David Yetter