Remark 7.6.3.21. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between $\infty $-categories, where $\operatorname{\mathcal{C}}$ admits pullbacks. Then $F$ preserves pullbacks if and only if, for each object $X \in \operatorname{\mathcal{C}}$, the induced functor $\operatorname{\mathcal{C}}_{/X} \rightarrow \operatorname{\mathcal{D}}_{ / F(X) }$ preserves finite products.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$