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--Monta\~{ n}o--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.
Categories: math.AC math.RT