Download E-books Two Kinds of Derived Categories, Koszul Duality, and Comodule-Contramodule Correspondence (Memoirs of the American Mathematical Society) PDF

By Leonid Positselski

The purpose of this paper is to build the derived nonhomogeneous Koszul duality. the writer considers the derived different types of DG-modules, DG-comodules, and DG-contramodules, the coderived and contraderived different types of CDG-modules, the coderived class of CDG-comodules, and the contraderived classification of CDG-contramodules. The equivalence among the latter different types (the comodule-contramodule correspondence) is tested. Nonhomogeneous Koszul duality or "triality" (an equivalence among unique derived different types such as Koszul twin (C)DG-algebra and CDG-coalgebra) is acquired within the conilpotent and nonconilpotent models. a variety of A-infinity buildings are thought of, and a couple of version class buildings are defined. Homogeneous Koszul duality and D-$\Omega$ duality are mentioned within the appendices.

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