objectwise kappa compact functor as kappa compact object

Let \(\kappa\) be a regular cardinal, \(S\) a kappa-small simplicial set and \(\mathcal{C}\) an infinity category
Let \(\mathcal{F}: S \rightarrow \mathcal{C}\) be an infinity functor such that

\begin{align*} \mathcal{F}(s) \end{align*}

is a kappa compact objects for \(s \in S\)

Then \(\mathcal{F}\) is also a \(kappa\)-compact object.

HTT 5.3.4.13