= Solution
The <Yoneda embedding> sends $c$ to the <representable presheaf> $H_c=\mathcal C(-,c)$. On a <morphism> $f:c\to d$, it sends a map $u:a\to c$ to $fu:a\to d$, giving $H_f:H_c\to H_d$.
The <Yoneda lemma> states that for every <categorical presheaf> $P$ there is a <bijection>, natural in both variables,
$$
\operatorname{Nat}(H_c,P)\cong P(c),\qquad \alpha\longmapsto\alpha_c(1_c).
$$
Its inverse sends $x\in P(c)$ to the transformation $u:a\to c\mapsto P(u)x$. Apply it to $P=H_d$ to obtain
$$
\operatorname{Nat}(H_c,H_d)\cong H_d(c)=\mathcal C(c,d).
$$
Under this <bijection> $H_f$ corresponds exactly to $f$, so the map induced by the embedding on each <hom-set> is bijective. Therefore \b[the <Yoneda embedding> is <full and faithful>].
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