Categories with hyperedges?

[Uwe Egbert Wolter <Uwe.Wolter@uib.no>]

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


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