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Strongly Finitary Monads for Varieties of Quantitative Algebras

Authors Jiří Adámek, Matěj Dostál , Jiří Velebil

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Author Details

Jiří Adámek
  • Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic
  • Institute for Theoretical Computer Science, Technische Universität Braunschweig, Germany
Matěj Dostál
  • Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic
Jiří Velebil
  • Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic

Funding

  • Adámek, Jiří: J. Adámek acknowledges the support by the Grant Agency of the Czech Republic under the grant 22-02964S.
  • Dostál, Matěj: M. Dostál acknowledges the support by the Grant Agency of the Czech Republic under the grant 22-02964S.

Cite AsGet BibTex

Jiří Adámek, Matěj Dostál, and Jiří Velebil. Strongly Finitary Monads for Varieties of Quantitative Algebras. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CALCO.2023.10

Abstract

Quantitative algebras are algebras enriched in the category Met of metric spaces or UMet of ultrametric spaces so that all operations are nonexpanding. Mardare, Plotkin and Panangaden introduced varieties (aka 1-basic varieties) as classes of quantitative algebras presented by quantitative equations. We prove that, when restricted to ultrametrics, varieties bijectively correspond to strongly finitary monads T on UMet. This means that T is the left Kan extension of its restriction to finite discrete spaces. An analogous result holds in the category CUMet of complete ultrametric spaces.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
Keywords
  • quantitative algebras
  • ultra-quantitative algebras
  • strongly finitary monads
  • varieties

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References

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