  We consider an intermediate category between the category of finite quivers
and a certain category of pseudocompact associative algebras whose objects
include all pointed finite dimensional algebras. We define the completed path
algebra and the Gabriel quiver as functors. We give an explicit quotient of the
category of algebras on which these functors form an adjoint pair. We show that
these functors respect ideals, obtaining in this way an equivalence between
related categories.
