Two Kinds Of Derived Categories Koszul Duality And Comodulecontramodule Correspondence Memoirs Of The American Mathematical Society Issue 996 Leonid Positselski by Leonid Positselski 9780821852965, 0821852965 instant download after payment.

The aim of this paper is to construct the derived nonhomogeneous Koszul duality. The author considers the derived categories of DG-modules, DG-comodules, and DG-contramodules, the coderived and contraderived categories of CDG-modules, the coderived category of CDG-comodules, and the contraderived category of CDG-contramodules. The equivalence between the latter two categories (the comodule-contramodule correspondence) is established. Nonhomogeneous Koszul duality or “triality” (an equivalence between exotic derived categories corresponding to Koszul dual (C)DG-algebra and CDG-coalgebra) is obtained in the conilpotent and nonconilpotent versions. Various A-infinity structures are considered, and a number of model category structures are described. Homogeneous Koszul duality and D-$Omega$ duality are discussed in the appendices.