\begin{definition}[Definition:Ordered Structure Monomorphism]
Let $\left({S, \circ, \preceq}\right)$ and $\left({T, *, \preccurlyeq}\right)$ be ordered structures.
An '''ordered structure monomorphism''' from $\left({S, \circ, \preceq}\right)$ to $\left({T, *, \preccurlyeq}\right)$ is a mapping $\phi: S \to T$ that is both:
:$(1): \quad$ A monomorphism, i.e. an injective homomorphism, from the structure $\left({S, \circ}\right)$ to the structure $\left({T, *}\right)$
:$(2): \quad$ An order embedding from the ordered set $\left({S, \preceq}\right)$ to the ordered set $\left({T, \preccurlyeq}\right)$.
\end{definition}