By way of comment on David Feldman's question. One can trivially produce lots of endofunctors of n-MAN. Since n-MAN had coproducts, so does any functor category targetted in n-MAN, in particular END(n-MAN). Second, note that given any endofunctor and a functor from n-MAN to SET, one can take a copower of the endofunctor by the set-valued functor. (Feldman's "functors of set-type" being an example of this in the case where the endofunctor is the identity, but one could just as easily take say X |----> pi_0(X) x A for a fixed n-manifold, A.) It might be better to stick to connected n-manifolds, in which case I'm not sure how to construct any endofunctors other than the constant ones and the identity. ---David Yetter =========================================================================