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Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence / Leonid POSITSELSKI (cop. 2010)
Titre : Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence Type de document : texte imprimé Auteurs : Leonid POSITSELSKI, Auteur Editeur : Providence, R. I. [Etats Unis] : American Mathematical Society Année de publication : cop. 2010 Collection : Memoirs of the American Mathematical Society, ISSN 0065-9266 num. 996 Importance : V-133 p. ISBN/ISSN/EAN : 978-0-8218-5296-5 Langues : Anglais Catégories : 14F10
16S37
16T15
18E30
18G10Mots-clés : catégorie dérivée catégorie triangulé comodule Résumé : The aim of this paper is to construct the derived nonhomogeneous Koszul duality. We consider 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. Note de contenu : bibliogr. Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence [texte imprimé] / Leonid POSITSELSKI, Auteur . - Providence, R. I. (Etats Unis) : American Mathematical Society, cop. 2010 . - V-133 p.. - (Memoirs of the American Mathematical Society, ISSN 0065-9266; 996) .
ISBN : 978-0-8218-5296-5
Langues : Anglais
Catégories : 14F10
16S37
16T15
18E30
18G10Mots-clés : catégorie dérivée catégorie triangulé comodule Résumé : The aim of this paper is to construct the derived nonhomogeneous Koszul duality. We consider 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. Note de contenu : bibliogr. Exemplaires
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