Example 4.5.6.4. Let $\operatorname{\mathcal{C}}= \{ X\} $ be a category having a single object and a single morphism. Then a diagram $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ is determined by the simplicial set $\mathscr {F}(X)$. The diagram $\mathscr {F}$ is isofibrant (in the sense of Definition 4.5.6.3) if and only if the simplicial set $\mathscr {F}(X)$ is an $\infty $-category.
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