Osofsky’s classical result characterizing semisimple rings by injectivity of cyclic modules was extended by her and Smith for modules in the early 1990s that a cyclic module is a finite direct sum of uniform modules if every cyclic submodule is completely extending.
In this paper the authors formulate the above cited result of Osofsky and Smith in the language of Grothendieck categories and derive several interesting consequences. By this process they obtain that a finitely generated Grothendieck category with a family of completely injective finitely generated generators is semisimple. Again, categorical language is a good tool for the authors making important applications to torsion theories, specializing to certain full and faithful subcategories of module categories. Some open questions are suggested for further research.