On 19/10/2011, at 12:27 AM, Urs Schreiber quoted Dmitry Roytenberg:
Finally, to my astonishment I have not been able to find an abstract description of any of the cubical sites, in the spirit of the simplex category being the category of non-empty finite ordinals.
Dear Urs and Dmitry Perhaps the example I learned from Dominic Verity that I gave in my CT 1995 Halifax talk will suffice for this. Using strings, we derive a model for the free monoidal category containing a cointerval. Cubical sets are functors from this to Set. See pages 7, 8, 9 of http://www.mta.ca/~cat-dist/ct95.html or http://www.maths.mq.edu.au/~street/LowDTop.pdf Apologies if this model was already mentioned. Best wishes, Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]