  A relative derived category for the category of modules over a presheaf of
algebras is constructed to identify the relative Yoneda and Hochschild
cohomologies with its homomorphism groups. The properties of a functor between
this category and the relative derived category of modules over the algebra
associated to the presheaf are studied. We obtain a generalization of the
$Special$ $ Cohomology$ $Comparison$ $Theorem$ of M. Gerstenhaber and S. D.
Schack.
