Let \$$X\$$ be a set, \$$\mathcal{P}(X)\$$ its power set ordered by inclusion (\$$A \leq B\$$ iff \$$A \subseteq B\$$), and \$$\mathcal{P}(X)^{op}\$$ its power set ordered by containment (\$$A \leq B\$$ iff \$$B \subseteq A\$$). Then the function \$$\mathcal P(X) \rightarrow \mathcal P(X)^{op}\$$ which sends a subset to its complement is monotone. In fact, I think it's an isomorphism, which would make it an adjoint.