Let \(U\) be a universe and let \(V\) be a universe strictly greater than \(U\). We say a morphism \(f:C\rightarrow D\) in \(\mathord {\textnormal {\textsf {LexCocomp}}}(U,V)\) is étale if it is in the image of the functor \(\mathord {\textnormal {\textsf {E}}}_{C}:{C}^{\mathord {\textnormal {\textsf {op}}}}\rightarrow \mathord {\textnormal {\textsf {LexCocomp}}}(U,V)\backslash C\).