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Title
Japanese: 
English:Codensity Lifting of Monads and its Dual 
Author
Japanese: 勝股 審也, 佐藤 哲也, Tarmo Uustalu.  
English: Shin-ya Katsumata, Tetsuya Sato, Tarmo Uustalu.  
Language English 
Journal/Book name
Japanese: 
English:Logical Methods in Computer Science 
Volume, Number, Page Volume 14    Issue 4   
Published date Oct. 2018 
Publisher
Japanese: 
English: 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
Official URL https://lmcs.episciences.org/4924
 
Abstract We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations which were not supported by its precursor, categorical TT-lifting. After introducing the codensity lifting, we illustrate some examples of codensity liftings of monads along the fibrations from the category of preorders, topological spaces and extended pseudometric spaces to the category of sets, and also the fibration from the category of binary relations between measurable spaces. We also introduce the dual method called density lifting of comonads. We next study the liftings of algebraic operations to the codensity liftings of monads. We also give a characterisation of the class of liftings of monads along posetal fibrations with fibred small meets as a limit of a certain large diagram.

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