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Codensity Liftings of Monads

Authors Shin-ya Katsumata, Tetsuya Sato



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LIPIcs.CALCO.2015.156.pdf
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Shin-ya Katsumata
Tetsuya Sato

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Shin-ya Katsumata and Tetsuya Sato. Codensity Liftings of Monads. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 156-170, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)
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.
Keywords
  • Monads
  • Lifting
  • Fibration
  • Giry Monad

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