I want to test some \\( \LaTeX \\) out.

**Definition.** A **monotone function** from a preorder \\((X,\le_X)\\) to \\((Y,\le_Y)\\) is a function \\(f : X \to Y\\) such that the following diagram commutes,

$$
\large\begin{matrix}
x & \overset{\le_X}{\longrightarrow} & x' \\\\
f\downarrow & & \downarrow f \\\\
f(x) & \overset{\le_Y}{\longrightarrow} & f(x')
\end{matrix}
$$

for all elements \\(x,x' \in X\\).