Corollary 6.1.5.6. Let $\operatorname{\mathcal{C}}$ be a $2$-category containing $1$-morphisms $u: C \rightarrow D$ and $v: D \rightarrow E$. If $u$ and $v$ admit left adjoints, then $v \circ u$ admits a left adjoint. If $u$ and $v$ admit right adjoints, then $v \circ u$ admits a right adjoint.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$