Vetenskap & teknik
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Two Kinds of Derived Categories, Koszul Duality, and Comodule-Contramodule Correspondence
Leonid Positselski
1349:-
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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.
- Format: Pocket/Paperback
- ISBN: 9780821852965
- Språk: Engelska
- Antal sidor: 133
- Utgivningsdatum: 2011-06-30
- Förlag: American Mathematical Society