Uniqueness and $(\mathrm{\infty },2)$-Naturality of Yoneda

We show that the Yoneda embedding extends to an $(\mathrm{\infty },2)$-natural transformation. Furthermore, as such, it is uniquely determined by its value at the trivial $\mathrm{\infty }$-category. We also study the naturality of the Yoneda lemma in its arguments, showing that it is an isomorphism of $(\mathrm{\infty },2)$-natural transformations.