Corrigendum to "The join of the pseudovarieties of idempotent semigroups and locally trivial semigroups".
A representation of cyclically ordered sets by means of partial semigroups with an additional unary operation is constructed.
We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms.