Let \(U\) be a universe and let \(V\) be a universe greater than or equal to \(U\). Then the functor \(C\mapsto \mathop {\Uparrow ^{V}}C:\mathord {\textnormal {\textsf {Logos}}}(U)\rightarrow \mathord {\textnormal {\textsf {Logos}}}(V)\) preserves étale morphisms. More precisely, for any \(U\)-logos \(C\) and any object \(A:C\), the embedding \(C/A\rightarrow \mathop {\Uparrow ^{V}}C/A\) induces an equivalence \(\mathop {\Uparrow ^{V}}(C/A)\simeq \mathop {\Uparrow ^{V}}C/A\).