Let \(U\) be a universe and let \(V\) be a universe strictly greater than \(U\). Then the Yoneda embedding \(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U)\rightarrow \mathord {\textnormal {\textsf {Fun}}}({(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U))}^{\mathord {\textnormal {\textsf {op}}}},V)\) factors through \(\mathord {\textnormal {\textsf {Sh}}}(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U),V)\).
Proof
This is because representable presheaves preserve arbitrary limits.