Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence / Leonid Positselski.

Format:

Book

Author/Creator:

Positselski, Leonid, 1973- author.

Series:

Memoirs of the American Mathematical Society ; Volume 212, Number 996.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 212, Number 996

Language:

English

Subjects (All):

Derived categories (Mathematics).

Triangulated categories.

Comodules.

Koszul algebras.

Physical Description:

1 online resource (133 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2010.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""Introduction""; ""1. Derived Category of DG-Modules""; ""2. Derived Categories of DG-Comodules and DG-Contramodules""; ""3. Coderived and Contraderived Categories of CDG-Modules""; ""4. Coderived Category of CDG-Comodules and Contraderived Category of CDG-Contramodules""; ""5. Comodule-Contramodule Correspondence""; ""6. Koszul Duality: Conilpotent and Nonconilpotent Cases""; ""7. A-Algebras and Curved A-Coalgebras""; ""8. Model Categories of DG-Modules, CDG-Comodules, and CDG-Contramodules""; ""9. Model Categories of DG-Algebras and CDG-Coalgebras""

""Appendix A. Homogeneous Koszul Duality""""Appendix B. D� Duality""; ""Bibliography""

Notes:

"Volume 212, Number 996 (first of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0613-6