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Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories

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Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories. / Hassoun, Souheila; Shah, Amit.

I: Communications in Algebra, 2020, s. 1-21.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Hassoun, Souheila ; Shah, Amit. / Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories. I: Communications in Algebra. 2020 ; s. 1-21.

Bibtex

@article{34afabbabeb64496a5c28beee546efc3,
title = "Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories",
abstract = "It was shown recently that the heart (Formula presented.) of a twin cotorsion pair (Formula presented.) on an extriangulated category is semi-abelian. We provide a sufficient condition for the heart to be integral and another for the heart to be quasi-abelian. This unifies and improves the corresponding results for exact and triangulated categories. Furthermore, if (Formula presented.) then we show that the Gabriel-Zisman localization of (Formula presented.) at the class of its regular morphisms is equivalent to the heart of the single twin cotorsion pair (Formula presented.) This generalizes and improves the known result for triangulated categories, thereby providing new insights in the exact setting.",
keywords = "Extriangulated category, heart, integral category, localization, quasi-abelian category, twin cotorsion pair",
author = "Souheila Hassoun and Amit Shah",
note = "Funding Information: The first author is supported by a ?th?sards ?toiles? scholarship of the ISM, Bishop?s University and Universit? de Sherbrooke. The second author is grateful for financial support from the EPSRC grant EP/P016014/1 ?Higher Dimensional Homological Algebra?. He also gratefully acknowledges financial support from the London Mathematical Society for his visit to Universit? de Sherbrooke. This study is also supported by Natural Sciences and Engineering Research Council of Canada. Some of this work was carried out during the second author?s Ph.D. at the University of Leeds. The authors would like to thank Thomas Br?stle and Robert J. Marsh for their support and guidance. This work began while the second author was visiting Sherbrooke, and he thanks the algebra group at Universit? de Sherbrooke for their hospitality and financial help. The authors are grateful to Dixy Msapato for spotting a typo in a previous version. The authors also thank the referee for comments and suggestions on an earlier version of the paper. Publisher Copyright: {\textcopyright} 2020, {\textcopyright} 2020 Taylor & Francis Group, LLC. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
doi = "10.1080/00927872.2020.1779737",
language = "English",
pages = "1--21",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor & Francis Inc.",

}

RIS

TY - JOUR

T1 - Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories

AU - Hassoun, Souheila

AU - Shah, Amit

N1 - Funding Information: The first author is supported by a ?th?sards ?toiles? scholarship of the ISM, Bishop?s University and Universit? de Sherbrooke. The second author is grateful for financial support from the EPSRC grant EP/P016014/1 ?Higher Dimensional Homological Algebra?. He also gratefully acknowledges financial support from the London Mathematical Society for his visit to Universit? de Sherbrooke. This study is also supported by Natural Sciences and Engineering Research Council of Canada. Some of this work was carried out during the second author?s Ph.D. at the University of Leeds. The authors would like to thank Thomas Br?stle and Robert J. Marsh for their support and guidance. This work began while the second author was visiting Sherbrooke, and he thanks the algebra group at Universit? de Sherbrooke for their hospitality and financial help. The authors are grateful to Dixy Msapato for spotting a typo in a previous version. The authors also thank the referee for comments and suggestions on an earlier version of the paper. Publisher Copyright: © 2020, © 2020 Taylor & Francis Group, LLC. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - It was shown recently that the heart (Formula presented.) of a twin cotorsion pair (Formula presented.) on an extriangulated category is semi-abelian. We provide a sufficient condition for the heart to be integral and another for the heart to be quasi-abelian. This unifies and improves the corresponding results for exact and triangulated categories. Furthermore, if (Formula presented.) then we show that the Gabriel-Zisman localization of (Formula presented.) at the class of its regular morphisms is equivalent to the heart of the single twin cotorsion pair (Formula presented.) This generalizes and improves the known result for triangulated categories, thereby providing new insights in the exact setting.

AB - It was shown recently that the heart (Formula presented.) of a twin cotorsion pair (Formula presented.) on an extriangulated category is semi-abelian. We provide a sufficient condition for the heart to be integral and another for the heart to be quasi-abelian. This unifies and improves the corresponding results for exact and triangulated categories. Furthermore, if (Formula presented.) then we show that the Gabriel-Zisman localization of (Formula presented.) at the class of its regular morphisms is equivalent to the heart of the single twin cotorsion pair (Formula presented.) This generalizes and improves the known result for triangulated categories, thereby providing new insights in the exact setting.

KW - Extriangulated category

KW - heart

KW - integral category

KW - localization

KW - quasi-abelian category

KW - twin cotorsion pair

UR - http://www.scopus.com/inward/record.url?scp=85087834268&partnerID=8YFLogxK

U2 - 10.1080/00927872.2020.1779737

DO - 10.1080/00927872.2020.1779737

M3 - Journal article

AN - SCOPUS:85087834268

SP - 1

EP - 21

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

ER -