Let \(C\) be a lex category. We write \(\rho (C):\mathord {\textnormal {\textsf {R}}}_{\bullet }(C)\rightarrow \mathord {\textnormal {\textsf {R}}}(C)\) for the universal representable map of presheaves on \(C\); see Definition 5.2 of [Nguyen--Uemura--2022-0000].