ScalingStacks

Proof. Recall that a right adjoint preserves $\kappa$-filtered colimits if and only if its left adjoint preserves $\kappa$-compact objects [52, 5.5.1.4]. Since functors which preserve filtered colimits also preserve $\kappa$-filtered colimits and $\Ind(-)$ takes exact functors to functors which preserve compact objects, the result follows. ∎