  The notion of locality semigroups was recently introduced with motivation
from locality in convex geometry and quantum field theory. We show that there
is a natural correspondence between locality sets and quivers which leads to a
concrete class of locality semigroups given by the paths of quivers. Further
these path semigroups from paths are precisely the free objects in the category
of locality semigroups with a rigid condition. This characterization gives a
universal property of path algebras and at the same time a combinatorial
realization of free rigid locality semigroups.
