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

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  • Souheila Hassoun, Universite de Sherbrooke
  • ,
  • Amit Shah

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.

Original languageEnglish
JournalCommunications in Algebra
Pages (from-to)1-21
Number of pages21
Publication statusPublished - 2020
Externally publishedYes

Bibliographical 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:
© 2020, © 2020 Taylor & Francis Group, LLC.

Copyright 2020 Elsevier B.V., All rights reserved.

    Research areas

  • Extriangulated category, heart, integral category, localization, quasi-abelian category, twin cotorsion pair

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