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Title
Japanese:Codensity liftings of monads 
English:Codensity liftings of monads 
Author
Japanese: 勝股 審也, 佐藤哲也.  
English: Shin-ya Katsumata, Tetsuya Sato.  
Language English 
Journal/Book name
Japanese:Leibniz International Proceedings in Informatics, LIPIcs 
English:Leibniz International Proceedings in Informatics, LIPIcs 
Volume, Number, Page Volume 35        pp. 156-170
Published date Oct. 28, 2015 
Publisher
Japanese: 
English:Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik 
Conference name
Japanese: 
English:6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015) 
Conference site
Japanese: 
English:Nijmegen 
Official URL https://drops.dagstuhl.de/opus/volltexte/2015/5532/
 
DOI https://doi.org/10.4230/LIPIcs.CALCO.2015.156
Abstract We introduce a method to lift monads on the base category of a fibration to its total category using codensity monads. This method, called codensity lifting, is applicable to various fibrations which were not supported by the categorical >>-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 psuedometric spaces to the category of sets, and also the fibration from the category of binary relations between measurable spaces. We next study the liftings of algebraic operations to the codensity-lifted monads. We also give a characterisation of the class of liftings (along posetal fibrations with fibred small limits) as a limit of a certain large diagram.

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