# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Corollary 4.5.5.19. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category and let $i: A \hookrightarrow B$ be a monomorphism of simplicial sets. If $i$ is a categorical equivalence, then the restriction functor $\operatorname{Fun}(B, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}(A, \operatorname{\mathcal{C}})$ is a trivial Kan fibration of simplicial sets.

Proof. Apply Proposition 4.5.5.18 in the special case $S = \Delta ^0$. $\square$