Dear all, Categories can be defined by extending directed multi graphs with identities and composition. The underlying directed multi graph of a small category C is given by the sets C_Mor, C_Obj and the source and target maps src^C,trg^C:C_Mor -> C_Obj. Has it ever been investigated what structures arise when we try, instead, to extend directed multi hypergraphs by identities and composition? A "directed multi hypergraph" H is thereby given by a set H_E of edges, a set H_V of vertices and two maps src^H,trg^H:H_E -> Pow(H_V) from H_E into the power set Pow(H_V) of H_V. I'm aware of monoidal categories and I would like to know if there is something else around. Any comment or reference is welcome Uwe Wolter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]