Pratt slices

Just a thought about Vaughan's original question: the class of toposes (and that of pretoposes) is stable under slicing, as are all the `exactness properties' that they share with abelian categories. Slices of abelian categories aren't abelian; but, thanks to Aurelio Carboni, we know how to characterize them. So we ought surely to be looking for a common generalization, not of toposes and abelian categories, but of (pre)toposes and affine categories in Aurelio's sense. How about it, Peter? Peter J.