Unary algebra

Summary

A unary algebra is a set with a family of unary operations, maps from the set to itself, and no operations of other arities. It is the simplest kind of algebraic structure, and yet it already contains the theory of functional graphs and of automata. A unary algebra with operations indexed by a set $I$ is the same as an action of the free monoid on $I$. A unary algebra with one operation is called a mono-unary algebra.