I came across the definitions of graded twisted modules while reading about the syzygy theorem. In the meantime I also attended an algebraic geometry course where twisted sheaves occured. For both twisted modules and twisted sheaves I have only seen some introductory examples. I now wonder what the relation between those is. Since they are named similarly I suspect there is some connection.
I think it could be that twisted sheaves could be analyzed in a similar manner as twisted modules with the theory of Hilbert but by using a more modern perspective developed by Grothendieck and so on. I wonder whether and how that could be made a little more precise to get a better intuition on that possible connection. An example would be great as well.
