License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2021.6
URN: urn:nbn:de:0030-drops-153610
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15361/
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Adámek, Jiří ; Rosický, Jiří

Which Categories Are Varieties? ((Co)algebraic pearls)

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LIPIcs-CALCO-2021-6.pdf (0.6 MB)

Abstract

Categories equivalent to single-sorted varieties of finitary algebras were characterized in the famous dissertation of Lawvere. We present a new proof of a slightly sharpened version: those are precisely the categories with kernel pairs and reflexive coequalizers having an abstractly finite, effective strong generator. A completely analogous result is proved for varieties of many-sorted algebras provided that there are only finitely many sorts. In case of infinitely many sorts a slightly weaker result is presented: instead of being abstractly finite, the generator is required to consist of finitely presentable objects.

BibTeX - Entry

@InProceedings{adamek_et_al:LIPIcs.CALCO.2021.6,
  author =	{Ad\'{a}mek, Ji\v{r}{\'\i} and Rosick\'{y}, Ji\v{r}{\'\i}},
  title =	{{Which Categories Are Varieties?}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15361},
  URN =		{urn:nbn:de:0030-drops-153610},
  doi =		{10.4230/LIPIcs.CALCO.2021.6},
  annote =	{Keywords: variety, many-sorted algebra, abstractly finite object, effective object, strong generator}
}

Keywords: variety, many-sorted algebra, abstractly finite object, effective object, strong generator
Collection: 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)
Issue Date: 2021
Date of publication: 08.11.2021

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