2 Search Results for "Velebil, Jiri"

Document
DOI: 10.4230/LIPIcs.CALCO.2023.10
Strongly Finitary Monads for Varieties of Quantitative Algebras

Authors: Jiří Adámek, Matěj Dostál, and Jiří Velebil

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

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.
Cite as

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)

Copy BibTex To Clipboard

@InProceedings{adamek_et_al:LIPIcs.CALCO.2023.10,
  author =	{Ad\'{a}mek, Ji\v{r}{\'\i} and Dost\'{a}l, Mat\v{e}j and Velebil, Ji\v{r}{\'\i}},
  title =	{{Strongly Finitary Monads for Varieties of Quantitative Algebras}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.10},
  URN =		{urn:nbn:de:0030-drops-188078},
  doi =		{10.4230/LIPIcs.CALCO.2023.10},
  annote =	{Keywords: quantitative algebras, ultra-quantitative algebras, strongly finitary monads, varieties}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2015.17
Extensions of Functors From Set to V-cat

Authors: Adriana Balan, Alexander Kurz, and Jiri Velebil

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract
We show that for a commutative quantale V every functor from Set to V-cat has an enriched left-Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric.
Cite as

Adriana Balan, Alexander Kurz, and Jiri Velebil. Extensions of Functors From Set to V-cat. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 17-34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{balan_et_al:LIPIcs.CALCO.2015.17,
  author =	{Balan, Adriana and Kurz, Alexander and Velebil, Jiri},
  title =	{{Extensions of Functors From Set to V-cat}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{17--34},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.17},
  URN =		{urn:nbn:de:0030-drops-55244},
  doi =		{10.4230/LIPIcs.CALCO.2015.17},
  annote =	{Keywords: enriched category, quantale, final coalgebra}
}
  • Refine by Author
  • 1 Adámek, Jiří
  • 1 Balan, Adriana
  • 1 Dostál, Matěj
  • 1 Kurz, Alexander
  • 1 Velebil, Jiri
  • Show More...

  • Refine by Classification
  • 1 Theory of computation → Equational logic and rewriting

  • Refine by Keyword
  • 1 enriched category
  • 1 final coalgebra
  • 1 quantale
  • 1 quantitative algebras
  • 1 strongly finitary monads
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2015
  • 1 2023

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact