Two Kinds of Derived Categories, Koszul Duality, and Comodule-contramodule Correspondence (Memoirs of the American Mathematical Society) issue 996
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.
سب زمرہ:
سال:
2011
ناشر کتب:
American Mathematical Society
زبان:
english
صفحات:
146
ISBN 10:
0821852965
ISBN 13:
9780821852965
سیریز:
Memoirs of the American Mathematical Society 212
فائل:
PDF, 1.39 MB
IPFS:
,
english, 2011