Abelian category of cominimax modules and local cohomology

Let $R$ be a commutative Noetherian ring, $\text{fa}$ an ideal of $R$, $M$ an arbitrary $R$-module and $X$ a finite $R$-module. We prove that the category of $\text{fa}$-cominimax modules is a Melkersson subcategory of $R$-modules whenever $\dim R\le 1$ and is an Abelian subcategory whenever $\dim R\le 2$. We prove a characterization theorem for ${\text{lc}}_{\text{fa}}^i(M)$ and ${\text{lc}}_{\text{fa}}^i(X,M)$ to be $\text{fa}$-cominimax for all $i$, whenever one of the following cases holds: (a) $\text{ara}(\text{fa})\le 1$, (b) $\dim R\mathrm{/}\text{fa}\le 1$ or © $\dim R\le 2$.