Completeness of the induced cotorsion pairs in categories of quiver representations

Given a complete hereditary cotorsion pair (A, B) in an abelian category C satisfying certain conditions, we study the completeness of the induced cotorsion pairs (Phi(A), Phi(A)(perpendicular to)) and ((perpendicular to)Psi(B), Psi(B)) in the category Rep (Q, C) of C-valued representations of a given quiver Q. We show that if Q is left rooted, then the cotorsion pair (Phi(A), Phi(A)(perpendicular to)) is complete, and if Q is right rooted, then the cotorsion pair ((perpendicular to)Psi(B), Psi(B)) is complete. Besides, we work on the infinite line quiver A(infinity)(infinity), which is neither left rooted nor right rooted. We prove that these cotorsion pairs in Rep(A(infinity)(infinity), R) are complete, as well. (C) 2019 Elsevier B.V. All rights reserved.