Given a finite quiver, the path algebra construction generates an algebra as freely as possible given the constraints imposed by the quiver. This construction is functorial. Given a finite dimensional algebra, there is a construction going in the other direction: the Gabriel quiver. As the path algebra is a free construction, it seems natural to suppose that it should be a left adjoint, with the Gabriel quiver as an excellent candidate for the corresponding right adjoint. We make precise to what extent this is true. Joint work with Kostiantyn Iusenko (University of Sao Paulo).