LOCALIZATIONS OF THE HEARTS OF COTORSION PAIRS. (3rd September 2020)

• Record Type: Journal Article
• Authors: LIU, YU
• Is Part Of: Glasgow mathematical journal. Volume 62:Part 3(2020)
• Page Start: 564
• Page End: 583
• Publication Date: 2020-09-03
• Subjects: 16G99, -- 18E99; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0017089519000284
• Languages: English
• ISSNs: 0017-0895

Abstract

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.