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The notion of locality semigroups was recently introduced with motivationfrom locality in convex geometry and quantum field theory. We show that thereis a natural correspondence between locality sets and quivers which leads to aconcrete class of locality semigroups given by the paths of quivers. Furtherthese path semigroups from paths are precisely the free objects in the categoryof locality semigroups with a rigid condition. This characterization gives auniversal property of path algebras and at the same time a combinatorialrealization of free rigid locality semigroups.

Quivers and path semigroups characterized by locality conditions