A completely regular semigroup is a structure S = (S,·,−1) such that
· is associative: (xy)z = x(yz),
−1 is an inverse: xx−1x = x and (x−1)−1 = x and
xx−1 = x−1x.
Let S and T be completely regular semigroups. A morphism from S to T is a function h : S→T that is a homomorphism: h(xy) = h(x)h(y) and h(x−1) = h(x)−1.
|Congruence extension property||No|
|Definable principal congruences|
|Equationally definable principal congruences||No|
|Strong amalgamation property|
|Epimorphisms are surjective|