Cotorsion theory in the category of quiver representations

Abstract

This note is devoted to the study of cotorsion theory in the category of quiver representations. Let Q be a quiver, x be a class of representations, and let Vx denote the class of all modules each of which appears in a vertex of an element of x. If the pair (⊥Vx, V x) (respectively, (Vx, Vx⊥)) is a cotorsion theory, we investigate conditions under which the pair ( ⊥x, x) (respectively, (x, x⊥)) is a cotorsion theory and vice versa. We show that in certain cases, completeness can be transferred between these cotorsion theories. © 2013 World Scientific Publishing Company.