Two Kinds of Derived Categories, Koszul Duality, and Comodule-Contramodule Correspondence
Leonid Positselski
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.
الفئات:
عام:
2011
الناشر:
Amer Mathematical Society
اللغة:
english
الصفحات:
133
ISBN 10:
0821852965
ISBN 13:
9780821852965
سلسلة الكتب:
Memoirs of the American Mathematical Society
ملف:
PDF, 3.11 MB
IPFS:
,
english, 2011
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