# Kerodon

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Corollary 4.4.5.4. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category, let $B$ be a simplicial set, and let $A \subseteq B$ be a simplicial subset. Then the restriction functor $\operatorname{Fun}(B, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}(A, \operatorname{\mathcal{C}})$ induces a Kan fibration of simplicial sets $\operatorname{Fun}(B, \operatorname{\mathcal{C}})^{\simeq } \rightarrow \operatorname{Fun}(A, \operatorname{\mathcal{C}})^{\simeq }$.

Proof. Combine Corollary 4.4.5.3 with Proposition 4.4.3.7. $\square$