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In the first part of this paper, we prove the existence of torsion free covers in the category of representations of quivers, , 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 -modules is injective. In the second part, we prove the existence of -covers and -envelopes for any quiver and any ring with unity, where is the class of all "componentwise" flat representations of .