Remark 9.3.2.17. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. Then:
If $F$ preserves finite limits, then it carries discrete objects of $\operatorname{\mathcal{C}}$ to discrete objects of $\operatorname{\mathcal{D}}$ (see Remark 9.3.1.12).
If $F$ preserves pairwise products, then it carries subterminal objects of $\operatorname{\mathcal{C}}$ to subterminal objects of $\operatorname{\mathcal{D}}$ (see Remark 9.3.2.16).