Corollary 6.171.
If \(C\) and \(C'\) are loci, and \(F\colon C' \to C\) is accessible and preserves pullbacks and weakly contractible colimits, then also the fibers of \(F\) are loci.
Proof
For an object \(c \in C\), the fiber \(F^{-1}(c)\) is the pullback of \(C' \xrightarrow{F} C \leftarrow *\). Since \(F\) is accessible, this pullback is an accessible category. Pullbacks and weakly contractible colimits in the fiber are computed in \(C'\), since both \(F\) and the inclusion \(c\colon * \to C\) preserve them. The functor \(F^{-1}(c) \to C'\) is conservative, so the claim follows from the previous lemma.