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Supported Sets - A New Foundation for Nominal Sets and Automata Wißmann, Thorsten Nominal Sets Monads LFP-Category Supported Sets Coalgebra The present work proposes and discusses the category of supported sets which provides a uniform foundation for nominal sets of various kinds, such as those for equality symmetry, for the order symmetry, and renaming sets. We show that all these differently flavoured categories of nominal sets are monadic over supported sets. Thus, supported sets provide a canonical finite way to represent nominal sets and the automata therein, e.g. register automata and coalgebras in general. Name binding in supported sets is modelled by a functor following the idea of de Bruijn indices. This functor lifts to the well-known abstraction functor in nominal sets. Together with the monadicity result, this gives rise to a transformation process from finite coalgebras in supported sets to orbit-finite coalgebras in nominal sets. One instance of this process transforms the finite representation of a register automaton in supported sets into its configuration automaton in nominal sets. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thorsten Wißmann 2023 Is Part Of LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2023.38 urn:nbn:de:0030-drops-174992 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.38 eng https://creativecommons.org/licenses/by/4.0/legalcode