  In the first part of this paper, we prove the existence of torsion free
covers in the category of representations of quivers, $(Q,R-Mod)$, for a wide
class of quivers included in the class of the so-called source injective
representation quivers provided that any direct sum of torsion free and
injective $R$-modules is injective. In the second part, we prove the existence
of $\mathscr{F}_{cw}$-covers and $\mathscr{F}_{cw}^{\perp}$-envelopes for any
quiver $Q$ and any ring $R$ with unity, where $\mathscr{F}_{cw}$ is the class
of all "componentwise" flat representations of $Q$.
