摘要：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 ly 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 ly finite, the generator is required to consist of finitely presentable objects.
