\begin{definition}[Definition:Monotone (Order Theory)/Mapping]
Let $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ be ordered sets.
Let $\phi: \struct {S, \preceq_1} \to \struct {T, \preceq_2}$ be a mapping.
Then $\phi$ is '''monotone''' {{iff}} it is either increasing or decreasing.
Note that this definition also holds if $S = T$.
\end{definition}