University of Sussex
Browse
Binder1.pdf (592.65 kB)

Combining semilattices and semimodules

Download (592.65 kB)
conference contribution
posted on 2023-06-10, 06:24 authored by Filippp Bonchi, Alessio Santamaria
We 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 .

History

Publication status

  • Published

File Version

  • Published version

Journal

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ISSN

0302-9743

Publisher

Springer International Publishing

Volume

12650

Page range

102-123

Event name

24th International Conference on Foundations of Software Science and Computation Structures

Event location

Online

Event type

conference

Event date

27th March - 1st April, 2021

ISBN

9783030719944

Department affiliated with

  • Informatics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2023-03-03

First Open Access (FOA) Date

2023-03-03

First Compliant Deposit (FCD) Date

2023-03-03

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC