Limit varieties of J-trivial monoids

We show that limit varieties of monoids recently discovered by Gusev, Zhang and Luo and their subvarieties are generated by monoids of the form M-tau (W) for certain congruences tau on the free monoid. The construction M-tau ( W) is a generalization of widely used Dilworth-Perkins construction. Using this construction, we find explicit generators for Gusev limit varieties and give a short reproof to the fact that Zhang-Luo limit variety is non-finitely based.