Definition:Monotone (Order Theory)

Let $$\left({S; \le_1}\right)$$ and $$\left({T; \le_2}\right)$$ be posets.

Let $$\phi: \left({S; \le_1}\right) \to \left({T; \le_2}\right)$$ be a mapping.

Then $$\phi$$ is monotone if it is either increasing or decreasing.

This can also be called "monotonic".