Kerodon

Remark 8.3.3.16. In the situation of Variant 8.3.3.15, suppose that the $\infty $-category $\operatorname{\mathcal{C}}$ admits $K$-indexed limits. Then the $\infty $-category of representable functors $\operatorname{Fun}^{\mathrm{rep}}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}}^{ < \lambda } )$ also admits $K$-indexed limits, which are preserved by the inclusion functor $\operatorname{Fun}^{\mathrm{rep}}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}}^{ < \lambda } ) \hookrightarrow \operatorname{Fun}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}}^{ < \lambda } )$.