Greetings, fellow categorists. I'm wondering, if anybody has ever described the following monoidal structure on the category of oriented multigraphs, what MacLane calls graphs, the most common kind of graph in category theory (but not everywhere) : Given mgs X, Y, the set |X-oY| of vertices on X-oY is the set of mg morphisms X --> Y. Given f,g : X --> Y the set of arrows f-->g is the set of pairs (p_0,p_1) of functions such that forall x in |X|, p_0(x) : f-->g forall k: x-->y in X, p_1(k) : f(x)-->g(y) This co-contra bifunctor has a tensor left adjoint, which is symmetric and monoidal. I would be quite surprised if this structure had never been seen before. Enriched universal algebra in there has applications in computer science. Thanks, Francois Lamarche