Lower bounds for levels of complexes by resolution dimensions

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.