products of sites

Does the category of sites have products? By a morphism X-->Y of sites, one means a functor Y-->X whose composition with any sheaf of sets on X is a sheaf of sets on Y. I found some stuff in Johnstone's book Topos Theory which says that products exist in the category of Grothendieck toposes. So it is natural to wonder if this extends to sites. Allan Adler ara@altdorf.ai.mit.edu P.S. Please reply to me directly since I haven't yet figured out how to subscribe to this list. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++