Kerodon

Corollary 4.5.6.12. Let $\operatorname{\mathcal{C}}$ be a small category and let $\mathscr {E}, \mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be diagrams of simplicial sets. If $\mathscr {F}$ is isofibrant, then the simplicial set $\operatorname{Hom}_{ \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{Set_{\Delta }}) }( \mathscr {E}, \mathscr {F} )_{\bullet }$ is an $\infty $-category.