Shin-ya Katsumata ; Tetsuya Sato ; Tarmo Uustalu - Codensity Lifting of Monads and its Dual

lmcs:4899 - Logical Methods in Computer Science, October 29, 2018, Volume 14, Issue 4 -
Codensity Lifting of Monads and its Dual

Authors: Shin-ya Katsumata ; Tetsuya Sato ORCID-iD; Tarmo Uustalu

    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.

    Volume: Volume 14, Issue 4
    Published on: October 29, 2018
    Accepted on: October 24, 2018
    Submitted on: October 19, 2018
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory,18C15, 18D30

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    Source : ScholeXplorer HasVersion DOI 10.48550/arxiv.1810.07972
    • 10.48550/arxiv.1810.07972
    Codensity Lifting of Monads and its Dual
    Katsumata, Shin-ya ; Sato, Tetsuya ; Uustalu, Tarmo ;

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