A note on separable functors and monads with an application to equivariant derived categories

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• 作者：Xiao-Wu Chen (1)
  
  1. Key Laboratory of Wu Wen-Tsun Mathematics ; Chinese Academy of Sciences ; School of Mathematical Sciences ; University of Science and Technology of China ; No. 96 Jinzhai Road ; Hefei ; 230026 ; Anhui Province ; People鈥檚 Republic of China
  
• 关键词：Separable functor ; Separable monad ; Monadic adjoint pair ; Equivariant object ; 16G70 ; 16G10 ; 13D07
• 刊名：Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：85
• 期：1
• 页码：43-52
• 全文大小：170 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Topological Groups and Lie Groups
  Number Theory
  Topology
  Convex and Discrete Geometry
  Differential Geometry
  
• 出版者：Springer Berlin Heidelberg
• ISSN：1865-8784

文摘

For an adjoint pair \((F, U)\) of functors, we prove that \(U\) is a separable functor if and only if the defined monad is separable and the associated comparison functor is an equivalence up to retracts. In this case, under an idempotent completeness condition, the adjoint pair \((F, U)\) is monadic. This applies to the comparison between the derived category of the category of equivariant objects in an abelian category and the category of equivariant objects in the derived category of the abelian category.