Modules and Morita theorem for operads

Associative rings A, B are called Morita equivalent when the categories of left modules over them are equivalent. We call two classical linear operads P, Q Morita equivalent if the categories of algebras over them are equival ent. We transport a part of Morita theory to the operadic context by studyi ng modules over operads. As an application of this philosophy, we consider an operadic version of the sheaf of linear differential operators on a (sup er)manifold M and give a comparison theorem between algebras over this shea f on M and M-red.