The notion of pseudovarieties of homomorphisms onto finite monoids
was recently introduced by Straubing as an algebraic characterization
for certain classes of regular languages.
In this paper we provide a mechanism of equational description
of these pseudovarieties based on an appropriate
generalization of the notion of implicit operations.
We show that the resulting metric monoids of implicit operations
coincide with the standard ones,
the only difference being the actual interpretation of pseudoidentities.
As an example, an equational characterization of the pseudovariety
corresponding to the class of regular languages in AC0 is given.