Lower bounds for levels of complexes by resolution dimensions

Abstract

Let [Formula: see text] be an abelian category. Denote by [Formula: see text] the bounded derived category of [Formula: see text]. In this paper, we investigate the lower bounds for the levels of objects in [Formula: see text] with respect to a (co)resolving subcategory satisfying a certain condition. As an application, we not only recover the results of Altmann–Grifo–Montaño–Sanders–Vu, and Awadalla–Marley but also extend them to establish lower bounds for levels with respect to some other subcategories in an abelian category.