Definition 7.7.3.14. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We say that $\operatorname{\mathcal{C}}$ is locally cartesian closed if, for every object $Y \in \operatorname{\mathcal{C}}$, the slice $\infty $-category $\operatorname{\mathcal{C}}_{/Y}$ is cartesian closed.
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