Abelian Hearts of Twin Cotorsion Pairs on Extriangulated Categories

Abstract

It was shown recently that the heart of a twin cotorsion pair on an extriangulated category is semi-abelian. In this article, we consider a special class of hearts of twin cotorsion pairs induced by [Formula: see text]-cluster tilting subcategories in extriangulated categories. We give a necessary and sufficient condition for such hearts to be abelian. In particular, we can also see that such hearts are hereditary. As an application, this generalizes the work by Liu in the exact case, thereby providing new insights into the triangulated case.