Category of MRR-groups over a ring R

The category of exponential MRR-groups for an associative ring RR with unity is defined in [1]. The present paper is devoted to the study of partial exponential MRR-groups which are isomorphically embedded in their tensor completion over the ring RR. The key to its understanding is the notion of tensor completion introduced in [1]. As a consequence, the description of free MRR-groups in the language of group constructions is obtained.