Quasi-abelian hearts of twin cotorsion pairs on triangulated categories
Shah, A. ORCID: 0000-0002-6623-8228 (2019).
Quasi-abelian hearts of twin cotorsion pairs on triangulated categories.
Journal of Algebra, 534,
pp. 313-338.
doi: 10.1016/j.jalgebra.2019.06.011
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<inf>R</inf>] the ideal of morphisms factoring through X<inf>R</inf>=Ker(Hom<inf>C</inf>(R,−)), then applications of our results show that C/[X<inf>R</inf>] 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.
Publication Type: | Article |
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Additional Information: | © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/ |
Publisher Keywords: | Triangulated category, Twin cotorsion pair, Heart, Quasi-abelian category, Localisation, Cluster category |
Subjects: | Q Science > QA Mathematics |
Departments: | School of Science & Technology School of Science & Technology > Department of Mathematics |
SWORD Depositor: |
Available under License Creative Commons Attribution Non-commercial No Derivatives.
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