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
Categorie:
Anno:
2011
Casa editrice:
Amer Mathematical Society
Lingua:
english
Pagine:
146
ISBN 10:
0821852965
ISBN 13:
9780821852965
Collana:
Memoirs of the American Mathematical Society 0996
File:
PDF, 1.10 MB
IPFS:
,
english, 2011
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