Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories
Hassoun, S. & Shah, A. 
ORCID: 0000-0002-6623-8228 (2020).
Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories.
Communications in Algebra, 48(12),
pp. 5142-5162.
doi: 10.1080/00927872.2020.1779737
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.
| Publication Type: | Article |
|---|---|
| Additional Information: | This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 09 Jul 2020 available at: https://doi.org/10.1080/00927872.2020.1779737 |
| Publisher Keywords: | Extriangulated category, heart, integral category, localization, quasi-abelian category, twin cotorsion pair |
| Subjects: | Q Science > QA Mathematics |
| Departments: | School of Science & Technology School of Science & Technology > Department of Mathematics |
| SWORD Depositor: |
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