Fully Invariant Relations

We started a systematic study of varieties of completely regular semigroups and the associated lattice \(\mathcal {L(CR)}\) of varieties of completely regular semigroups, in [PR1, Chapter VIII] by considering the varieties of completely simple semigroups. Ibid Chapter IX on Mal’cev products serves as an introduction to the study of general varieties of completely regular semigroups. The present chapter aims to resume this introduction by considering fully invariant congruences on a free unary semigroup as well as on a free completely regular semigroup.