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?