I regret that my recent posting on Pratt's construction should not have been sent to categories. He sent me privately a construction showing that A -o A has at least 2^K dinatural endomorphisms (that is the diagonalization of the functor that takes A,B to A -o B) in chu(Set,K) and I mistakenly thought it had come off the categories bulletin board. But it had been sent to me privately. In any case, the claim is correct and my description for K = 2 is too. Sorry for the mixup. Michael