2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61844This 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.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 manuscriptAlgebraic Topology18D50; 16W30text