Kerodon

Corollary 9.3.7.12. Let $\kappa $ be a small regular cardinal and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between small $\kappa $-filtered $\infty $-categories. Then $F$ is right cofinal if and only if the functor $\operatorname{Ind}_{\kappa }(F): \operatorname{Ind}_{\kappa }(\operatorname{\mathcal{C}}) \rightarrow \operatorname{Ind}_{\kappa }(\operatorname{\mathcal{D}})$ preserves final objects.