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Combining semilattices and semimodules
conference contribution
posted on 2023-06-10, 06:24 authored by Filippp Bonchi, Alessio SantamariaWe describe the canonical weak distributive law d: SP ? PS of the powerset monad P over the S-left-semimodule monad S, for a class of semirings S. We show that the composition of P with S by means of such d yields almost the monad of convex subsets previously introduced by Jacobs: the only difference consists in the absence in Jacobs’s monad of the empty convex set. We provide a handy characterisation of the canonical weak lifting of P to EM(S) as well as an algebraic theory for the resulting composed monad. Finally, we restrict the composed monad to finitely generated convex subsets and we show that it is presented by an algebraic theory combining semimodules and semilattices with bottom, which are the algebras for the finite powerset monad Pf .
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Publication status
- Published
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- Published version
Journal
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)ISSN
0302-9743Publisher
Springer International PublishingExternal DOI
Volume
12650Page range
102-123Event name
24th International Conference on Foundations of Software Science and Computation StructuresEvent location
OnlineEvent type
conferenceEvent date
27th March - 1st April, 2021ISBN
9783030719944Department affiliated with
- Informatics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2023-03-03First Open Access (FOA) Date
2023-03-03First Compliant Deposit (FCD) Date
2023-03-03Usage metrics
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