  We use semigroup theory to describe the group of automorphisms of some
semigroups of interest in holomorphic dynamical systems. We show, with some
examples, that representation theory of semigroups is related to usual
constructions in holomorphic dynamics. The main tool for our discussion is a
theorem due to Schreier. We extend this theorem, and our results in semigroups,
to the setting of correspondences and holomorphic correspondences.
