Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
著者
書誌事項
Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
（Memoirs of the American Mathematical Society, no. 996）
American Mathematical Society, c2010
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注記
"Volume 212, number 996 (first of 4 numbers)."
Includes bibliographical references (p. 131-133)
内容説明・目次
内容説明
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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