Allow me please to muse on Peter Freyd's two postings concerning observations of Peter Selinger and himself on the category of topological spaces and local homeomorphisms. Is the product of X_1 and X_2 identical to the etale space of the sheaf that associates to an open set U of X_1 all the local homeomorphisms from U to X_2? Of course if this is right, then the roles of X_1 and X_2 can be reversed. Indeed, both etale spaces consist of germs of homeomorphisms between X_1 and X_2. The advantage of taking this point of view, besides that fact that perhaps the sheaf is easier to thing about than its etale space, is that it suggests persuing a more general construction. In a sense that I don't yet know how to make precise, X_1 x X_2 is a schizophrenic object because it lives in both toposes of sheaves, over X_1 and X_2, and it is in some sense the universal such schizophrenic object. So my question is, can this be made precise so that one could ask for a universal schizophrenic given any two toposes. My guess is that the analogous construction given the topos of M_1-sets and M_2-sets, M_1 and M_2 being monoids, would be to construct the free product M_1 * M_2, which also lives naturally in both categories. Moreover all M_1 * M_2-sets live in both categories, just as all sheaves over X_1 x X_2 induce sheaves over X_1 and over X_2. I don't know much about toposes. Is there already some well-known construction that fits the bill? David Feldman University of New Hampshire