\begin{definition}[Definition:Morphism Property]
Let $\phi: \struct {S, \circ} \to \struct {T, *}$ be a mapping from one algebraic structure $\struct {S, \circ}$ to another $\struct {T, *}$.
Then $\circ$ has the '''morphism property''' under $\phi$ {{iff}}:
:$\forall x, y \in S: \map \phi {x \circ y} = \map \phi x * \map \phi y$
\end{definition}