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 
,
there is a surjective homomorphism from a free module to 
; for every module 
, there is an injective homomorphism from 
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.
Every cofree module over a unit ring 
is isomorphic to a direct product
 |
indexed on some set 
.
