Are there famous results that can be stated as "Every functor from category A to concrete category B is representable"? Or at least "Every functor from this class that would a priori seem to be too large is representable"? I don't have any use for such a result, I just want to have more feeling for representability vs nonrepresentability. A more specialized question: the representing object for a representable functor from k-Alg to Grp gets a natural commutative Hopf algebra structure. This can be generalized in two ways: lose representability, and just have a functor, or lose commutativity, and just have a noncommutative Hopf algebra. Has anyone ever seen an example where it was desirable to lose both, somehow? Allen K. ==============================================================================