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/
Adámek, Jiří ;
Rosický, Jiří
Which Categories Are Varieties? ((Co)algebraic pearls)
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 |