Addendum to my reply to Yetter's letter: There were other things I meant to say but was short of time yesterday. 1) The work of Brown, Porter, Higgins deals with the non-additive groupoid case. Now I see that they have replied by referring to SLN 72. 2) Andre Joyal has a beautiful proof of the Dold-Kan theorem showing that it is a qualitative version of Isaac Newton's result that a list of data can be recaptured from the first column of iterated differences. I told Dold this while he was visiting Macquarie; he was delighted. 3) The generalisation of Gray's tensor product of 2-categories is performed as follows. Let me write G for the monoidal category 2-Cat with Gray's tensor product. Then G-Cat is the category of categories with homs enriched in G. The category 3-Cat of 3-categories is contained in G-Cat. Let O(I^n) denote the free n-category on the n-cube I^n (as per the work of Iain Aitchison, Mike Johnson, Richard Steiner and myself; in fact, "Parity complexes" has appeared in Cahiers XXXII-4 1991 315-343 and provides a simple model for O(I^n)). Let Q^n denote the 3-category obtained from O(I^n) by forcing all cells of dimension higher than 3 to be identities. Thus we have a full subcategory T of G-Cat consisting of the Q^n; furthermore, T is dense in G-Cat. We certainly know how to multiply cubes: Q^m (tensor) Q^n = Q^(m+n). This tensor product extends from T to G-Cat by Kan extension along the inclusion (Brian Day studied the general process of extending promonoidal structures along dense functors; his convolution structures are about extension along Yoneda). This is the third stage in a clear recursive construction. Regards, Ross ==============================================================================