Kerodon

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Remark 4.5.9.13. Suppose we are given a pullback diagram of simplicial sets

\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{D}}' \ar [d]^{U'} \ar [r] & \operatorname{\mathcal{D}}\ar [d]^{U} \\ \operatorname{\mathcal{C}}' \ar [r] & \operatorname{\mathcal{C}}. } \]

If $U$ is exponentiable, then $U'$ is also exponentiable.