Which Categories Are Varieties?
| Autoři | |
|---|---|
| Rok publikování | 2021 |
| Druh | Článek ve sborníku |
| Konference | CALCO 2021: 9th Conference on Algebra and Coalgebra in Computer Science |
| Fakulta / Pracoviště MU | |
| 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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