Involutive Semigroup

An involutive semigroup is a Semigroup $S$ equipped with an involution $(-)^{\dagger}:S^{\mathrm{op}}\to S$.

Examples

• Free semigroups with $x^{\dagger}=\mathrm{reverse}(x)$.
• Every Group is an involutive semigroup with $x^{\dagger}=x^{-1}$