The product bifunctor \(\textup{\textsf{cat}} \times \textup{\textsf{cat}} \xrightarrow{\times} \textup{\textsf{cat}}\) is closed: the operation called currying in computer science defines a family of natural isomorphisms \(\{ A \times B \xrightarrow{f} C \} \cong \{ A \xrightarrow{f} C^B\} \cong \{ B \xrightarrow{f} C^A\}.\) Thus, the product and exponential bifunctors \(\textup{\textsf{cat}} \times \textup{\textsf{cat}} \xrightarrow{\times} \textup{\textsf{cat}}, \quad \textup{\textsf{cat}}^\mathrm{op} \times \textup{\textsf{cat}} \xrightarrow{(-)^{(-)}} \textup{\textsf{cat}}, \quad \textup{\textsf{cat}}^\mathrm{op} \times \textup{\textsf{cat}} \xrightarrow{(-)^{(-)}} \textup{\textsf{cat}}\) define a two-variable adjunction.