Is there any name given to this: Suppose $\displaystyle \langle S, * \rangle $, $\displaystyle \langle S', *' \rangle $ and $\displaystyle \langle S'', *'' \rangle $ are binary structures. Suppose there is an isomorphism $\displaystyle \phi $ between $\displaystyle S $ and $\displaystyle S' $. Also suppose $\displaystyle S $ and $\displaystyle S' $ are isomorphic. Also $\displaystyle S' $ and $\displaystyle S'' $ are isomorphic, and the same isomorphism $\displaystyle \phi $ are used.