Category : gradings and translation functors

In this article we consider a graded version of category . We reprove some results of [Beilinson et al., J. Amer. Math. Soc. 9 (1996) 473–527] using a different approach. Furthermore, we define a graded version of translation functors and duality. This provides the construction of various graded modules. On the other hand, we describe how to get modules which are not ‘gradable.’