Dear categorician (or categorist, I do not know the word in English), I posted the following question some days ago in sci.math.research. Maybe this list is more appropirated : I would need to understand a proof of the following proposition : There is only one functor up to isomorphism TENS : omega-Cat x omega-Cat -> omega-Cat for which C TENS - and - TENS C have right adjoint for every omega-category C and which satisfies I^p TENS I^q = I^{p+q} where I^p is the omega-category canonically associated to the p-cube, (using for example the set of composable sub pasting schemes of the pasting scheme associated to the p-cube). I have a paper from Crans ("Pasting schemes for the monoidal biclosed structure on omega-Cat") which proves explicitely the proposition. I do not understand the construction, which is very technical (*). Is there a less complicated way to prove this proposition ? I do not need an explicit construction. Any help is welcome. pg. (*) What is a pasting presentation for example ? I know the definition of pasting scheme, realization of pasting schemes, but I do not know the one of "pasting presentation". Another question : if f, g are morphisms in C and h, k morphisms in D, is there in C TENS D elements corresponding to f TENS h and g TENS k, and if the answer is yes, is it true that (f TENS h) o_p (g TENS k) = (f o_p g) TENS (h o_p k) ? I suppose that it is false : if it should be true, why the construction of this monoidal structure is so complicated ?