Balanced pairs, cotorsion triplets and quiver representations. Issue 1 (13th February 2020)

• Record Type: Journal Article
• Authors: Estrada, Sergio; Pérez, Marco A.; Zhu, Haiyan
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 63:Issue 1(2020)
• Page Start: 67
• Page End: 90
• Publication Date: 2020-02-13
• Subjects: balanced pair, -- cotorsion triplet, -- quiver representation, -- flat balance; 18G25, -- 16G20, -- 18E10, -- 18C15; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091519000270
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: Balanced pairs appear naturally in the realm of relative homological algebra associated with the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural source of such pairs. In this paper, we study the connection between balanced pairs and cotorsion triplets by using recent quiver representation techniques. In doing so, we find a new characterization of abelian categories that have enough projectives and injectives in terms of the existence of complete hereditary cotorsion triplets. We also provide a short proof of the lack of balance for derived functors of Hom computed using flat resolutions, which extends the one given by Enochs in the commutative case.