I have two

*commutative groups*[tex](G,\circ, I_\circ)[/tex] and [tex](G,\bullet,I_\bullet)[/tex], and I defined an

*isomorphism*[tex]f[/tex] between them: so we have [tex]f(u \circ v)=f(u) \bullet f(v)[/tex]

How can I formalize the fact that I want also an

*unary operation*[tex]\ast : G \rightarrow G[/tex] which is preserved by the isomorphism? namely, an unary operation such that [tex]f(u^{\ast}) = f(u)^{\ast}[/tex] ?

Is it possible somehow to embed the unary operation into the group in order to form an already-known algebraic structure? or it is just not possible to formalize it better than I already did?

Thanks in advance!