  Let $R$ be a commutative noetherian ring and let $\frak a$ be an ideal of
$R$. In this paper, we study a certain condition, namely $C_{\frak a}$,
introduced by Aghapournahr and Melkersson, on the extension of two
subcategories of $R$-modules. We extend and generalize some of the main results
of Yoshizawa [Y1,Y2]. As an example of extension of subcategories, we study the
weakly Laskerian modules and we find some conditions under which the local
cohomology modules of a weakly Laskerian module lie in an arbitrary Serre
subcategory. Eventually, we investigate the cofiniteness of the local
cohomology modules of weakly Laskerian modules.
