Let \(U\) be a universe and let \(V\) be a universe strictly greater than \(U\). Then \(\mathord {\textnormal {\textsf {R}}}_{\bullet }(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U)):\mathord {\textnormal {\textsf {Sh}}}(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U),V)/\mathord {\textnormal {\textsf {R}}}(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U))\) is \(\mathbb {I}\)-categorically fibrant.