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Another look on tense and related operators

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Abstract

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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Acknowledgements

We thank the anonymous referee for the thorough reading and contributions to improve our paper presentation.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Michal Botur

  2. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Jan Paseka & Richard Smolka

Authors
  1. Michal Botur
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  2. Jan Paseka
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  3. Richard Smolka
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Correspondence to Jan Paseka.

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Presented by M. Plošica.

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The research of the first author was supported by the IGA under grant no. PřF 2021 030. The second author acknowledges the support by the Austrian Science Fund (FWF): project I 4579-N and the Czech Science Foundation (GAČR): project 20-09869L, entitled “The many facets of orthomodularity”. Support of the research of the third author by the project “New approaches to aggregation operators in analysis and processing of data”, Nr. 18-06915S by Czech Grant Agency (GAČR) is gratefully acknowledged.

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Botur, M., Paseka, J. & Smolka, R. Another look on tense and related operators. Algebra Univers. 83, 41 (2022). https://doi.org/10.1007/s00012-022-00794-1

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  • DOI: https://doi.org/10.1007/s00012-022-00794-1

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