For an associative ring (possibly without identity) various subcategories of the category of all (right) -modules MOD- are considered, in particular: canonically}, canonically}.
Every Morita context between and with epimorphic pairings induces the equivalences and . The converse of this fact is proved under hypotheses weaker than the surjectivity of pairings. Namely, for every Morita context the following conditions are equivalent: (1) and are inverse category equivalences between the categories CMOD- and CMOD-; (2) and are inverse category equivalences between the categories -DMOD and -DMOD; (3) the given context is left acceptable, i.e. such that , such that .
An example is given of a ring such that CMOD- is not equivalent to DMOD-.