# Math Help - Special Property?

1. ## Special Property?

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

2. By definition, an isomorphism is a function.

Two functions are identical only if the domains and ranges are the same.

So unless $S = S' = S''$ it's not possible for the same isomorphism to be used for $\phi: S \to S'$ as it is for $\phi: S' \to S''$ because by definition the two isomorphism would need to be different.

As to whether there's a name for this or not, I haven't a clue, but unless there are some unspoken assumptions (or it's a trick question), I'd question what's going on here.