Another look on tense and related operators

• 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

Web

• https://arxiv.org/pdf/2207.05453.pdf
• https://link.springer.com/article/10.1007/s00012-022-00794-1

• 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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