I'm reading Awodey's Category Theory (1st ed) and at page 166 I did not found out the proof of one of the remarks (remark 8.4):
If $C$ is locally small, then $\mathsf{Sets}^{C^{\text{op}}}$ needs not be locally small. In this case, the Yoneda Lemma tells us that $\mathrm{Hom}(yC,P)$ is always a set.
I understand well what is the Yoneda lemma, and its proof, but I didn't understand why it could tell that $\mathrm{Hom}(yC,P)$ is a set... Note: here, $yC$ is the covariant Yoneda embedding applied to $C$, that is $\mathrm{Hom}(-,C)$.
Could anyone help me with some track?