Abstract
This note is devoted to the study of cotorsion theory in the category of quiver representations. Let [Formula: see text] be a quiver, Ο be a class of representations, and let VΟ denote the class of all modules each of which appears in a vertex of an element of Ο. If the pair (â„VΟ, VΟ) (respectively, (VΟ, VΟâ„)) is a cotorsion theory, we investigate conditions under which the pair (â„Ο, Ο) (respectively, (Ο, Οâ„)) is a cotorsion theory and vice versa. We show that in certain cases, completeness can be transferred between these cotorsion theories.
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