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@inproceedings{1802654,
author = {Adámek, Jiří and Rosický, Jiří},
address = {Saarbrücken/Wadern},
booktitle = {CALCO 2021: 9th Conference on Algebra and Coalgebra in Computer Science},
doi = {http://dx.doi.org/10.4230/LIPIcs.CALCO.2021.6},
editor = {Gadducci, Fabio; Silva, Alexandra},
keywords = {variety; many-sorted algebra; abstractly finite object; effective object; strong generator},
howpublished = {elektronická verze "online"},
language = {eng},
location = {Saarbrücken/Wadern},
isbn = {978-3-95977-212-9},
pages = {"6:1"-"6:14"},
publisher = {Schloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing},
title = {Which Categories Are Varieties?},
url = {https://drops.dagstuhl.de/opus/volltexte/2021/15361/},
year = {2021}
}
TY - JOUR
ID - 1802654
AU - Adámek, Jiří - Rosický, Jiří
PY - 2021
TI - Which Categories Are Varieties?
PB - Schloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing
CY - Saarbrücken/Wadern
SN - 9783959772129
KW - variety
KW - many-sorted algebra
KW - abstractly finite object
KW - effective object
KW - strong generator
UR - https://drops.dagstuhl.de/opus/volltexte/2021/15361/
N2 - 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.
ER -
ADÁMEK, Jiří a Jiří ROSICKÝ. Which Categories Are Varieties?. Online. In Gadducci, Fabio; Silva, Alexandra. \textit{CALCO 2021: 9th Conference on Algebra and Coalgebra in Computer Science}. Saarbrücken/Wadern: Schloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing, 2021, s.~''6:1''-''6:14'', 14 s. ISBN~978-3-95977-212-9. Dostupné z: https://dx.doi.org/10.4230/LIPIcs.CALCO.2021.6.
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