Limit varieties of J-trivial monoids

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