Completeness of the induced cotorsion pairs in categories of quiver representations
Completeness of the induced cotorsion pairs in categories of quiver representations
复制标题
DOI：
10.1016/j.jpaa.2019.02.003
复制
发表时间：
2017-11
影响因子：
0.8
通讯作者：
Sinem Odabaşı
中科院分区：
文献类型：
--
作者：
Sinem Odabaşı
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 (Φ (A), Φ (A)⊥) and (Ψ⊥(B), Ψ (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 (Φ (A), Φ (A)⊥) is complete, and if Q is right rooted, then the cotorsion pair (Ψ⊥(B), Ψ (B)) is complete. Besides, we work on the infinite line quiver A∞∞, which is neither left rooted nor right rooted. We prove that these cotorsion pairs in Rep (A∞∞, R) are complete, as well.
