I have a question about the statement of Lemma 5.5.2.1 in Lurie's HTT.

``Let $S$ be a small simplicial set, let $f: S\rightarrow \mathcal{S}$ be an object of $\mathcal{P}(S^{op})$, and let $F: \mathcal{P}(S^{op})\rightarrow \widehat{\mathcal{S}}$ be the functor corepresented by $f$. Then the composition $$S\overset{j}{\rightarrow}\mathcal{P}(S^{op})\overset{F}{\rightarrow}\widehat{\mathcal{S}}$$ is equivalent to $f$. "

The Yoneda embedding $j$ should be from $S$ to $\mathcal{P}(S)$, but the last line doesn't seem to be just a typo. Do I miss something? Thanks!

I have a question about the statement of Lemma 5.5.2.1 in Lurie's `Higher Topos Theory'.

``Let $S$ be a small simplicial set, let $f: S\rightarrow \mathcal{S}$ be an object of $\mathcal{P}(S^{op})$, and let $F: \mathcal{P}(S^{op})\rightarrow \widehat{\mathcal{S}}$ be the functor corepresented by $f$. Then the composition $$S\overset{j}{\rightarrow}\mathcal{P}(S^{op})\overset{F}{\rightarrow}\widehat{\mathcal{S}}$$ is equivalent to $f$. "

The Yoneda embedding $j$ should be from $S$ to $\mathcal{P}(S)$, but the last line doesn't seem to be just a typo. Do I miss something? Thanks!