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タイトル: A generalization of Gabriel's Galois covering functors and derived equivalences
著者: Asashiba, Hideto
掲載誌名: Journal of Algebra
出版者: Elsevier
巻: 334
号: 1
開始ページ: 109
終了ページ: 149
出版日付: 2011-05-15
NDC: 411
抄録: Let G be a group acting on a category C. We give a definition for a functor F : C -> C' to be a G-covering and three constructions of the orbit category C/G, which generalizes the notion of a Galois covering of locally finite-dimensional categories with group G whose action on C is free and locally bonded defined by Gabriel. Here C/G is defined for any category C and we do not require that the action of G is free or locally bounded. We show that a G-covering is a universal "G-invariant" functor and is essentially given by the canonical functor C -> C/G. By using this we improve a covering technique for derived equivalences. Also we prove theorems describing the relationships between smash product construction and the orbit category construction by Cibils and Marcos (2006) without the assumption that the G-action is free. The orbit category construction by a cyclic group generated by an auto-equivalence modulo natural isomorphisms (e.g., the construction of cluster categories) is justified by a notion of the "colimit orbit category". In addition, we give a presentation of the orbit category of a category with a monoid action by a quiver with relations, which enables us to calculate many examples.
ISSN: 00218693 OPAC
出版者DOI: 10.1016/j.jalgebra.2011.03.002   
NII書誌ID: AA00692420 OPAC ciniib
バージョン: author
出現コレクション:04. 雑誌論文・記事(Journal Article, Article, Preprint)

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