2026-07-20T07:45:19Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:22835 2025-10-02T13:35:01Z ddc:004 open_access

Monotone Weak Distributive Laws over the Lifted Powerset Monad in Categories of Algebras Aristote, Quentin weak distributive law weak extension weak lifting iterated distributive law Yang-Baxter equation powerset monad Vietoris monad Radon monad Eilenberg-Moore category regular category relational extension In both the category of sets and the category of compact Hausdorff spaces, there is a monotone weak distributive law that combines two layers of non-determinism. Noticing the similarity between these two laws, we study whether the latter can be obtained automatically as a weak lifting of the former. This holds partially, but does not generalize to other categories of algebras. We then characterize when exactly monotone weak distributive laws over powerset monads in categories of algebras exist, on the one hand exhibiting a law combining probabilities and non-determinism in compact Hausdorff spaces and showing on the other hand that such laws do not exist in a lot of other cases. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Quentin Aristote 2025 Is Part Of LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2025.10 urn:nbn:de:0030-drops-228356 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.10 eng https://creativecommons.org/licenses/by/4.0/legalcode