There's some discussion on the Universal Algebra list at present on operads. I'm not very familiar with them. What I understand from the discussion is they capture single sorted algebraic theories with respect to a symmetric monoidal product ox. For each natural number n an object of n-ary operators O_n is given, and an algebra A has operations O_n ox A^(n) -> A where A^(n) is A ox ... ox A n times. If you do this sort of thing with respect to categorical product, then it already contains the information of the Lawvere theory category (for single-sorted finitary algebraic theories), since hom(m,n) is hom(m,1)^n and you take hom(m,1) to be O_m. But with a monoidal product this doesn't work. It seemed to me that for proper generality the operad ought to have objects O_mn (m, n natural numbers) representing the object of operations from A^(m) to A^(n). Is there a name for that? Steve Vickers Department of Pure Maths Faculty of Maths and Computing The Open University ----------- Tel: 01908-653144 Fax: 01908-652140 Web: http://mcs.open.ac.uk/sjv22