Example 4.5.9.16. The inclusion map $\operatorname{N}_{\bullet }( \{ 0 < 2 \} ) \hookrightarrow \Delta ^2$ is an isofibration of $\infty $-categories which is not exponentiable. Note that there is a pullback diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ \{ 0 \} \coprod \{ 2\} \ar [r] \ar [d] & \operatorname{N}_{\bullet }( \{ 0 < 2 \} ) \ar [d] \\ \Lambda ^{2}_{1} \ar [r] & \Delta ^2 } \]
where the lower horizontal map is a categorical equivalence, but the upper horizontal map is not.