Categorial quasivarieties of Abelian groupoids and quasigroups (Q1068874)

An algebraic system A is said to be categorical if the quasivariety generated by A is categorical in some infinite power not smaller than the cardinality of A. It is proved that an Abelian groupoid generating a categorical quasivariety is necessarily a quasigroup. Every categorical quasigroup is isotopic to an Abelian group. A description of categorical quasigroups is given.