Corollary 4.1.4.2. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $i: A \hookrightarrow B$ be a monomorphism of simplicial sets. Then the restriction functor $\operatorname{Fun}(B, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}(A,\operatorname{\mathcal{C}})$ is an inner fibration.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Proposition 4.1.4.1 in the special case $S = \Delta ^0$. $\square$