  In 2004 and 2005 Enochs et al. characterized the flat and projective
quiver-representations of left rooted quivers. The proofs can be understood as
filtering the classes $\Phi(\operatorname{Add}\mathscr X)$ and
$\Phi(\varinjlim\mathscr X)$ when $\mathscr X$ is the finitely generated
projective modules over a ring. In this paper we generalize the above and show
that $\Phi(\mathscr X)$ can always be filtered for any class $\mathscr X$ in
any AB5-abelian category. With an emphasis on $\Phi(\varinjlim\mathscr X)$ we
investigate the Gorenstein homological situation. Using an abstract version of
Pontryagin duals in abelian categories we give a more general characterization
of the flat representations and end up by describing the Gorenstein flat quiver
representations over right coherent rings.
