Kerodon

Example 9.2.3.7. Let $\operatorname{Set}$ be the category of sets, and let $\operatorname{Set}_{\mathrm{fin}}$ be the full subcategory spanned by the finite sets. Then the inclusion functor $\operatorname{Set}_{\mathrm{fin}} \hookrightarrow \operatorname{Set}$ exhibits (the nerve of) $\operatorname{Set}$ as an $\operatorname{Ind}$-completion of the $\operatorname{Set}_{\mathrm{fin}}$. This follows from Corollary 9.2.3.6, since every finite set is a compact object of $\operatorname{Set}$ (Example 9.2.0.4) and every set can be realized as a filtered colimit of finite sets.