The notion of an enriched category and that of a graded category are both similar in the sense that they both endow the usual morphisms of a category with additional structure.
A natural question is thus: Are these notions related in some way? For instance, for every category $C$ enriched over $V$, is there a graded category $(D,F)$ with ``essentially the same structure''? (presumably, this should be some form of categorical equivalence) What about the converse question?
Have these sorts of questions even been considered in the literature? The whole notion of a graded category seems to be a relatively obscure one, and there isn't even an n-cat lab article on the subject, so I've had a hard time looking through the literature to try to find answers, and thus would appreciate any insights into this matter.