Synthetic topos theory
[001C] Proposition

Let \(U\) be a universe and let \(V\) be a universe strictly greater than \(U\). Then the Yoneda embedding \(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U)\rightarrow \mathord {\textnormal {\textsf {Sh}}}(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U),V)\) preserves finite limits and \(U\)-small products.

Proof

This is because the Yoneda embedding preserves arbitrary limits.