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Can cartesian product of several (not necessarily binary) relations be described in categorical terms?

Don't propose me direct product in the category Set, as it does not preserve the structure of relations.

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You know there's a category $\textbf{Rel}$, right? – Zhen Lin May 3 '12 at 20:40
@Zhen Lin: <strong>Rel</strong> is for binary relations but my relations are of arbitrary arity. – porton May 4 '12 at 1:28

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