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

lmcs:4899 - Logical Methods in Computer Science, October 29, 2018, Volume 14, Issue 4 - https://doi.org/10.23638/LMCS-14(4:6)2018
Codensity Lifting of Monads and its Dual

Authors: Katsumata, Shin-ya and Sato, Tetsuya and Uustalu, Tarmo

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
Submitted on: October 19, 2018
Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory,18C15, 18D30


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