We have a natural bijection
\[ \left\{ \begin{gathered} \text{Adjunctions in $\boldsymbol {\mathsf{Rel}}^{\mathord {\mathbin {\square }}}$}\\ \text{from $A$ to $B$} \end{gathered} \right\} \cong \left\{ \begin{gathered} \text{Functions}\\ \text{from $B$ to $A$} \end{gathered} \right\} , \]
with every adjunction in $\boldsymbol {\mathsf{Rel}}^{\mathord {\mathbin {\square }}}$ being of the form $(f^{-1})^{\textsf{c}}\dashv \operatorname {\mathrm{Gr}}(f)^{\textsf{c}}$ for some function $f\colon B\to A$.
