Which Categories Are Varieties?
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Proceedings |
| Conference | CALCO 2021: 9th Conference on Algebra and Coalgebra in Computer Science |
| MU Faculty or unit | |
| Citation | |
| Web | https://drops.dagstuhl.de/opus/volltexte/2021/15361/ |
| Doi | http://dx.doi.org/10.4230/LIPIcs.CALCO.2021.6 |
| Keywords | variety; many-sorted algebra; abstractly finite object; effective object; strong generator |
| Description | 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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