  We study the monoid of so called projection functors $\p{S}$ attached to
simple modules $S$ of a finite dimensional algebra, which appear naturally in
the study of torsion pairs. We determine defining relations in special cases of
path algebras. For the linearly oriented Dynkin quiver of Type $A$, we get an
isomorphism to the monoid of non-decreasing parking functions. Moreover we give
an explicit isomorphism between the monoid algebra of non-decreasing parking
functions and a certain incidence algebra independent of the field.
