Corollary 6.141.
The functor \(\Pt\colon \Topos \to \Cat^{\acc, \kappa}\) admits a (\(2\)-categorical) left adjoint
\[\Cat^{\acc,\kappa} \to \Topos, \qquad C \mapsto \Fun^{\kappa}(C,\An).\]
Higher Topos Theory Section 6.10: Compactly assembled categories and exponentiability
Corollary 6.141.
The functor \(\Pt\colon \Topos \to \Cat^{\acc, \kappa}\) admits a (\(2\)-categorical) left adjoint