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By a graphic we will mean any finite category each of whose endomorphism monoids satisfies the identity xyx = xy ; in particular, a graphic monoid is a graphic category with one object.
By an application of a graphic category we will mean any right action of it on finite sets (i.e. any contravariant finite-set- valued functor on it).
-- Lawvere, The Hegelian "Taco", 1989.

I think social networking satisfies this requirement, e.g. Make Use Make = Make Use (a user to Make a new user).

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