Shah, A orcid.org/0000-0002-6623-8228 (2019) Quasi-abelian hearts of twin cotorsion pairs on triangulated categories. Journal of Algebra, 534. pp. 313-338. ISSN 0021-8693
Abstract
We prove that, under a mild assumption, the heart H of a twin cotorsion pair ((S,T),(U,V)) on a triangulated category C is a quasi-abelian category. If C is also Krull-Schmidt and T=U, we show that the heart of the cotorsion pair (S,T) is equivalent to the Gabriel-Zisman localisation of H at the class of its regular morphisms.
In particular, suppose C is a cluster category with a rigid object R and [X_R] the ideal of morphisms factoring through X_R=Ker(Hom(R,-)), then applications of our results show that C/[X_R] is a quasi-abelian category. We also obtain a new proof of an equivalence between the localisation of this category at its class of regular morphisms and a certain subfactor category of C.
Metadata
Item Type: | Article |
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Authors/Creators: | |
Copyright, Publisher and Additional Information: | © 2019 Elsevier Inc. All rights reserved. Copyright (c) 2018 Elsevier B. V. All rights reserved. This is an author produced version of a paper published in Journal of Algebra. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | math.CT; math.CT; math.RT; 18E30, 16G20, 18E05, 18E35, 18E40; Triangulated category; Twin cotorsion pair; Heart; Quasi-abelian category; Localisation; Cluster category |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Jul 2019 09:09 |
Last Modified: | 21 Jun 2020 00:38 |
Status: | Published |
Publisher: | Elsevier Inc. |
Identification Number: | 10.1016/j.jalgebra.2019.06.011 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:148095 |