Okay, let's make sure I'm on the same page with those who know homological algebra.

What is **Koszul duality** in general?

What does it mean that *categories* are Koszul dual (I guess representations of Koszul dual algebras are the examples?) What are examples of "categories which seem to a priori have no good reason to be Koszul dual actually are" [Koszul dual] other than (g, R)-admissible modules?