I am very interested in seeing the paper of Paul Glenn, but in the meantime, perhaps relevant is Conjecture 5.3 of my "The algebra of oriented simplexes" JPAA 49 (1987) 283-335. This is a slightly more explicit form of a conjecture ( pre 1978 ) of John E. Roberts who motivated my work. Dominic Verity has proved this conjecture (it was announced in Bangor early this year and at the MSRI Conference last July). Verity's preprint on this will be available very soon. This work characterizes n-categories as simplicial sets with certain elements at each dimension distinguished (and called "hollow" in loc cit, but now we call them "thin" in accord with the Welsh School). The kinds of operations Barr and Glenn hint at are expressed as UNIQUE horn filler conditions. Regards, Ross ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++