  Let $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$. In this
article we answer affirmatively a question raised by the present author in
\cite{B2}. Also, as an immediate consequence of this result it is shown that
the category of all $I$-cofinite $R$-modules $\mathscr{C}(R, I)_{cof}$ is an
Abelian subcategory of the category of all $R$-modules, whenever $q(I,R)\leq
1$. These assertions answer affirmatively a question raised by R. Hartshorne in
[{\it Affine duality and cofiniteness}, Invent. Math. {\bf9}(1970), 145-164],
in some special cases.
