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Finitary monads on the category of posets

Published online by Cambridge University Press:  26 November 2021

Jiří Adámek
Affiliation:
Department of Mathematics, Czech Technical University Prague, Prague, Czech Republic Institute of Theoretical Computer Science, Technische Universität Braunschweig, Brunswick, Germany
Chase Ford
Affiliation:
Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany
Stefan Milius*
Affiliation:
Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany
Lutz Schröder
Affiliation:
Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany
*
*Corresponding author. Email: stefan.milius@fau.de
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Abstract

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Finitary monads on Pos are characterized as precisely the free-algebra monads of varieties of algebras. These are classes of ordered algebras specified by inequations in context. Analogously, finitary enriched monads on Pos are characterized: here we work with varieties of coherent algebras which means that their operations are monotone.

Type
Paper
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

Supported by the Grant Agency of the Czech Republic under the grant 19-00902S.

Supported by the Deutsche Forschungsgemeinschaft (DFG) within the Research and Training Group 2475 “Cybercrime and Forensic Computing” (393541319/GRK2475/1-2019).

§

Supported by the Deutsche Forschungsgemeinschaft (DFG) under project MI 717/7-1.

Supported by the Deutsche Forschungsgemeinschaft (DFG) under project SCHR 1118/6-2.

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