Another look on tense and related operators

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Authors

BOTUR Michal PASEKA Jan SMOLKA Richard

Year of publication 2022
Type Article in Periodical
Magazine / Source Algebra Universalis
MU Faculty or unit

Faculty of Science

Citation
Web
Doi http://dx.doi.org/10.1007/s00012-022-00794-1
Keywords Tense operator; Sup-semilattice; Frame; Poset; Nucleus; Prenucleus
Description Motivated by the classical work of Halmos on functional monadic Boolean algebras, we derive three basic sup-semilattice constructions, among other things, the so-called powersets and powerset operators. Such constructions are extremely useful and can be found in almost all branches of modern mathematics, including algebra, logic, and topology. Our three constructions give rise to four covariant and two contravariant functors and constitute three adjoint situations we illustrate in simple examples.
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