Let \(U\) be a universe and let \(V\) be a universe strictly greater than \(U\). Then the Yoneda embedding \(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U)\rightarrow \mathord {\textnormal {\textsf {Sh}}}(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U),V)\) takes étale colimits to colimits.
Proof
This follows from the Yoneda lemma and the definition of sheaves on \(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U)\).