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LOCALIZATIONS OF THE HEARTS OF COTORSION PAIRS

Part of: Representation theory of rings and algebras Abelian categories

Published online by Cambridge University Press:  03 July 2019

YU LIU
YU LIU*
Affiliation:
School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China e-mail: liuyu86@swjtu.edu.cn
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Abstract

In this article, we study localizations of hearts of cotorsion pairs ($\mathcal{U}, \mathcal{V}$) where $\mathcal{U}$ is rigid on an extriangulated category $\mathcal{B}$ . The hearts of such cotorsion pairs are equivalent to the functor categories over the stable category of $\mathcal{U}$ ( $\bmod \underline{\mathcal{U}}$ ). Inspired by Marsh and Palu (Nagoya Math. J.225(2017), 64–99), we consider the mutation (in the sense of Iyama and Yoshino, Invent. Math.172(1) (2008), 117–168) of $\mathcal{U}$ that induces a cotorsion pair ( $\mathcal{U}^{\prime}, \mathcal{V}^{\prime}$ ). Generally speaking, the hearts of ( $\mathcal{U}, \mathcal{V}$ ) and ( $\mathcal{U}^{\prime}, \mathcal{V}^{\prime}$ ) are not equivalent to each other, but we will give a generalized pseudo-Morita equivalence between certain localizations of their hearts.

MSC classification

Primary: 16G99: None of the above, but in this section
Secondary: 18E99: None of the above, but in this section
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 3 , September 2020 , pp. 564 - 583
Copyright
© Glasgow Mathematical Journal Trust 2019

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