Hi -
First, let me say I have avoided contributing to this thread because I don't understand what Vaughan is asking.
He asked if dualities categorify. I guess he meant something like this: There are lots of interesting examples of a pair of categories C,D together with an object c in C and an object d in D such that hom(-,c): C -> D and hom(-,d): D -> C are part of an equivalence of categories. In the nicest examples, c and d are in some sense the same mathematical entity regarded as living in two different categories - a "schizophrenic object", in the words of Harold Simmons. So, can we find equally nice examples where C and D are instead 2-categories? In particular, can we find examples where C and D are 2-categorical generalizations of the 1-categorical examples we already know? In particular, he suggested taking the example where C is the category of finite distributive lattices and finding an analogous example where C is the 2-category of (maybe finite, in some sense?) distributive categories. For more on "schizophrenic objects", Peter Johnstone's review of Clark and Davies' "Natural dualities for the working algebraist" makes good reading: http://north.ecc.edu/alsani/ct99-00(8-12)/msg00116.html