Kerodon

Theorem 9.3.7.9. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be small filtered $\infty $-categories. Then a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is right cofinal if and only if the induced functor $\operatorname{Ind}(F): \operatorname{Ind}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{Ind}(\operatorname{\mathcal{D}})$ preserves final objects.