| eBook ISBN: | 978-1-4704-0613-4 |
| Product Code: | MEMO/212/996.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $45.00 |
| eBook ISBN: | 978-1-4704-0613-4 |
| Product Code: | MEMO/212/996.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $45.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 212; 2011; 133 ppMSC: Primary 18; 16; 14; Secondary 17; 58
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.
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Table of Contents
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Chapters
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Introduction
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1. Derived Category of DG-Modules
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2. Derived Categories of DG-Comodules and DG-Contramodules
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3. Coderived and Contraderived Categories of CDG-Modules
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4. Coderived Category of CDG-Comodules and Contraderived Category of CDG-Contramodules
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5. Comodule-Contramodule Correspondence
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6. Koszul Duality: Conilpotent and Nonconilpotent Cases
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7. $\mathrm {A}_\infty $-Algebras and Curved $\mathrm {A}_\infty $-Coalgebras
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8. Model Categories of DG-Modules, CDG-Comodules, and CDG-Contramodules
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9. Model Categories of DG-Algebras and CDG-Coalgebras
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Appendix A. Homogeneous Koszul Duality
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Appendix B. $\mathcal {D}$–$\Omega $ Duality
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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.
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Chapters
-
Introduction
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1. Derived Category of DG-Modules
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2. Derived Categories of DG-Comodules and DG-Contramodules
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3. Coderived and Contraderived Categories of CDG-Modules
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4. Coderived Category of CDG-Comodules and Contraderived Category of CDG-Contramodules
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5. Comodule-Contramodule Correspondence
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6. Koszul Duality: Conilpotent and Nonconilpotent Cases
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7. $\mathrm {A}_\infty $-Algebras and Curved $\mathrm {A}_\infty $-Coalgebras
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8. Model Categories of DG-Modules, CDG-Comodules, and CDG-Contramodules
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9. Model Categories of DG-Algebras and CDG-Coalgebras
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Appendix A. Homogeneous Koszul Duality
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Appendix B. $\mathcal {D}$–$\Omega $ Duality
