Just to add one more reference to John's answer. There is a paper Balteanu C., Fiedorowicz Z., Schw\"{a}nzl R., Vogt R., Iterated Monoidal Categories, preprint, (1998), 1-55, where interchange laws and their interplay in all dimensions are considered. They are, however, not invertible morphisms. This noninvertibility makes this theory interesting. The main result of the paper is: the categories with n (strict) monoidal structures and interchange laws between them satisfying some natural coherence conditions model n-fold loop spaces. If $n=2$ and interchange law is isomorphism the theory collapses to the theory of braided monoidal categories. If $n>2$ but interchanges laws are still isomorphisms we get symmetric monoidal categories. It is also possible to define an n-categorical analogue of this theory, in such a way that one object, one arrow , one 2-arrow ,..., one (n-1)-arrow n-category in this sense is exactly n-fold monoidal category of BFSV. This is different from weak n-category but helps a lot in understanding of higher dimensional structures. I hope to finish a paper about it soon. Michael. 19-Jul-2002 14:32:55 -0300,3321;000000000000-0000001f