Koszul duality and equivalences of categories
arXiv:math/0012264 · doi:10.1090/S0002-9947-05-04035-3
Abstract
Let A and A! be dual Koszul algebras. By Positselski a filtered algebra U with gr U = A is Koszul dual to differential graded algebra (A!,d). We relate the module categories of this dual pair by a tensor-Hom adjunction. This descends to give an equivalence of suitable quotient categories and generalizes work of Beilinson, Ginzburg and Soergel.
AMSLatex, 29 pages. Slimmed and trimmed version. Also generalized to the setting of differential graded Koszul algebras