Theorem 9.2.5.8. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. Then:
- $(1)$
If the functor $F$ is right exact (in the sense of Definition 9.2.5.5), then it preserves finite colimits.
- $(2)$
If the $\infty $-category $\operatorname{\mathcal{C}}$ admits finite colimits and $F$ preserves finite colimits, then $F$ is right exact.