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.