Kerodon

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 $\operatorname{Fun}(B, \operatorname{\mathcal{C}})^{\simeq } \rightarrow \operatorname{Fun}(A, \operatorname{\mathcal{C}})^{\simeq }$.