Dear Mike and everbody The converse result , as stated by Mac Lane, was what needed to be said in 1950, especially since it began to bring out that category theory has content. What it's converse to, namely that when maps can be added then the cartesian product has the mapping property now called coproduct, had already been folklore for years... or if it hadn't been, how else to explain the widespread terminological ambiguity concerning "direct sums"? Perhaps a much older reference needs to be adduced. Thanks for bringing this up. Best regards Bill ******************************************************************************* F. William Lawvere Mathematics Dept. SUNY wlawvere@acsu.buffalo.edu 106 Diefendorf Hall 716-829-2144 ext. 117 Buffalo, N.Y. 14214, USA ******************************************************************************* On Fri, 30 Oct 1998, Michael Barr wrote:

I have checked Mac Lane's 1950 paper and I cannot find any such result. The converse, that a category in which finite sums are equivalent to products then the category takes homs in commutative monoids is sort of there, but the one I asked is not, or at least I didn't find it. However, CWM is a likely source and I will check that out. I just need some reference in any case.

Michael