A module having dual properties with respect to a free module, as enumerated below. 1. Every free module is projective; every cofree module is injective. 2. For every module M, there is a surjective homomorphism from a free module to M; for every module M, there is an injective homomorphism from M to a cofree module. 3. A module is projective iff it can be completed by a direct sum to a free module; a module is injective iff it can be completed by a direct product to a cofree module.