One example of a monotone map would the simple substitution cipher mapping letters to numbers, so given \$$(A,\le_A) \$$= ({a,b, ... , z}, alphabetical order ) and \$$(B,\le_B) \$$ = ({1,2, ... , 26}, numerical order), then the **monotone map** from \$$A\$$ to \$$B\$$ is \$$f : a \to 1 , b \to 2 , ... , z \to 26 \$$.

apologies if my mathematical notation isn't correct...