Lower bounds for levels of complexes by resolution dimensions

Abstract

Let $\mathcal{A}$ be an abelian category. Denote by ${\mathrm{D}}^b(\mathcal{A})$ the bounded derived category of $\mathcal{A}$. In this paper, we investigate the lower bounds for the levels of objects in ${\mathrm{D}}^b(\mathcal{A})$ 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.

19 pages