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

Souheila Hassoun, Amit Shah*

*Corresponding author af dette arbejde

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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.

OriginalsprogEngelsk
TidsskriftCommunications in Algebra
Sider (fra-til)1-21
Antal sider21
ISSN0092-7872
DOI
StatusUdgivet - 2020
Udgivet eksterntJa

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