Uniqueness and $(\infty,2)$-naturality of Yoneda

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