Corollary 9.4.7.18 (Adjoints are Accessible). Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be accessible $\infty $-categories and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor which admits a right adjoint $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$. Then $F$ and $G$ are accessible functors.
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Proof. The functor $F$ preserves all colimits which exist in $\operatorname{\mathcal{C}}$ (Corollary 7.1.4.28) and is therefore accessible. To show that $G$ is accessible, it will suffice to show that for each object $C \in \operatorname{\mathcal{C}}$, the composite functor
\[ \operatorname{\mathcal{D}}\xrightarrow {G} \operatorname{\mathcal{C}}\xrightarrow { \operatorname{Hom}_{\operatorname{\mathcal{C}}}(C, \bullet ) } \operatorname{\mathcal{S}} \]
is accessible (Proposition 9.4.7.17). Since $G$ is right adjoint to $F$, this composite functor is corepresented by the object $F(C) \in \operatorname{\mathcal{D}}$, so the desired result follows from Example 9.4.7.16. $\square$