文章基本信息

标题：Powerset-Like Monads Weakly Distribute over Themselves in Toposes and Compact Hausdorff Spaces
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作者：Goy, Alexandre ; Petrişan, Daniela ; Aiguier, Marc 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：198
DOI：10.4230/LIPIcs.ICALP.2021.132
语种：English
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The powerset monad on the category of sets does not distribute over itself. Nevertheless a weaker form of distributive law of the powerset monad over itself exists and it essentially stems from the canonical Egli-Milner extension of the powerset to the category of relations. On the other hand, any regular category yields a category of relations, and some regular categories also possess a powerset-like monad, as is the Vietoris monad on compact Hausdorff spaces. We derive the Egli-Milner extension in three different frameworks : sets, toposes, and compact Hausdorff spaces. We prove that it corresponds to a monotone weak distributive law in each case by showing that the multiplication extends to relations but the unit does not. We provide an application to coalgebraic determinization of alternating automata.
关键词：Egli-Milner relation;weak extension;weak distributive law;weak lifting;powerset monad;Vietoris monad;topos;alternating automaton;generalized determinization