\begin{definition}[Definition:Isomorphism (Abstract Algebra)]
An '''isomorphism''' is a homomorphism which is a bijection.
That is, it is a mapping which is both a monomorphism and an epimorphism.
An algebraic structure $\struct {S, \circ}$ is '''isomorphic to''' another algebraic structure $\struct {T, *}$ {{iff}} there exists an isomorphism from $\struct {S, \circ}$ to $\struct {T, *}$, and we can write $S \cong T$ (although notation may vary).
\end{definition}