Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 4.5.2.11. Let $f: A \hookrightarrow B$ be an inner anodyne morphism of simplicial sets. Then $f$ is a categorical equivalence.

Proof. By virtue of Proposition 4.5.2.8, it will suffice to show that for every $\infty $-category $\operatorname{\mathcal{C}}$, the restriction map $f^{\ast }: \operatorname{Fun}(B, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}(A, \operatorname{\mathcal{C}})$ is an equivalence of $\infty $-categories. This follows from Corollary 4.5.2.10, since $f^{\ast }$ is a trivial Kan fibration (Proposition 1.4.7.6). $\square$