Which Categories Are Varieties?

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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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ADÁMEK Jiří ROSICKÝ Jiří

Rok publikování 2021
Druh Článek ve sborníku
Konference CALCO 2021: 9th Conference on Algebra and Coalgebra in Computer Science
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://drops.dagstuhl.de/opus/volltexte/2021/15361/
Doi http://dx.doi.org/10.4230/LIPIcs.CALCO.2021.6
Klíčová slova variety; many-sorted algebra; abstractly finite object; effective object; strong generator
Popis 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.
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