Completeness of the induced cotorsion pairs in categories of quiver representations

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Odabasi, Sinem¹ 

[1] Univ Austral Chile, Inst Ciencias Fis & Matemat, Valdivia, Chile

关键词: Cotorsion pairs;    Quiver representations;    Abelian categories;   

DOI  :  10.1016/j.jpaa.2019.02.003

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free