Remark 4.5.9.13. Suppose we are given a pullback diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}' \ar [d]^{U'} \ar [r] & \operatorname{\mathcal{C}}\ar [d]^{U} \\ \operatorname{\mathcal{B}}' \ar [r] & \operatorname{\mathcal{B}}. } \]
If $U$ is exponentiable, then $U'$ is also exponentiable.