In this paper, the characterization of right and left quasi-Frobenius
categories, has been given.
Let C be a small preadditive category, C* the dual category of C. It has
shown, that the following conditions are equivalent:
(i) C is right and lef
t quasi-Frobenius;
(ii) All flat C-modules and all flat C*-modules are injective;
(iii) All injective C-modules and all injective C*-modules are projective.
