Vaughan's question and Mike's reply arrived here today. The question is a bit vague, but I shall indicate a general technique which can be modified as desired. One useful candidate for a tensor product on the category P of omega categories can be obtained as follows. A glob is a free-living n-cell. Regard these as very simple examples of parity complexes and consider the collection C of finite products of them (here parity complex and product are as per my widely circulated Macquarie Report 1987; or was it Jan 88). Make the members of C into omega categories using my big script O construction. This gives a dense full subcategory G of P on which we have a "product" defined. Extend to P by left Kan extension to obtain a tensor product on P. Greetings, Ross Street