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 (eng) | Catégories : | 14F10 16S37 16T15 18E30 18G10
| Mots-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 . - 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 ( eng) Catégories : | 14F10 16S37 16T15 18E30 18G10
| Mots-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. |
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