Remark 6.149.
Let \(C\) be a compactly assembled category. Then there is an equivalence
\[\Pt(\Fun^{\omega}(C,\An)) \simeq C,\]
under which \(X \in C\) corresponds to the evaluation functor \(\ev_X\colon \Fun^{\omega}(C,\An) \to \An\).
Higher Topos Theory Section 6.10: Compactly assembled categories and exponentiability
Remark 6.149.
Let \(C\) be a compactly assembled category. Then there is an equivalence
under which \(X \in C\) corresponds to the evaluation functor \(\ev_X\colon \Fun^{\omega}(C,\An) \to \An\).