Mal’cev classes of left quasigroups and quandles

In this paper we investigate some Mal’cev classes of varieties of left quasigroups. We prove that the weakest non-trivial Mal’cev condition for a variety of left quasigroups is having a Mal’cev term and that every congruence meet-semidistributive variety of left quasigroups is congruence arithmetic. Then we specialize to the setting of quandles for which we prove that the congruence distributive varieties are those which have no non-trivial finite models.