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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 C(R,I)cof is an Abelian subcategory of the category of all R-modules, whenever q(I,R)ï¿½?ï¿½1. 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.
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