Cofree coalgebras over operads

This paper explicitely constructs cofree coalgebras over operads in the category of DG-modules. Special cases are considered in which the general expression simplifies (such as the pointed, irreducible case). It is shown that the existence of an operad-action on a coalgebra implies a ``generalized coassociativity'' that facilitates the construction. Some areas of application are discussed.Comment: A revised version of this paper will appear in the journal Topology and its Applications (communicated by Paul Goerss). The revision involves editorial changes to the manuscrip