Publication: Balanced pairs, cotorsion triplets and quiver representations
Authors
Estrada, Sergio ; PĂ©rez, Marco A. ; Zhu, Haiyan
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Publisher
Cambridge University Press
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DOI
https://doi.org/10.1017/S0013091519000270
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info:eu-repo/semantics/article
Description
©2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
This document is the Accepted version of a Published Work that appeared in final form in Proceedings of the Edinburgh Mathematical Society. To access the final edited and published work seehttps://doi.org/10.1017/S0013091519000270
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.
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Citation
Estrada S, PĂ©rez MA, Zhu H. Balanced pairs, cotorsion triplets and quiver representations. Proceedings of the Edinburgh Mathematical Society. 2020;63(1):67-90.
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