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

摘要

It was shown recently that the heart (H) over bar of a twin cotorsion pair ((S,T), (U,V)) 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 T = U, then we show that the Gabriel-Zisman localization of (H) over bar at the class of its regular morphisms is equivalent to the heart of the single twin cotorsion pair (S,T). This generalizes and improves the known result for triangulated categories, thereby providing new insights in the exact setting.