Warning 1.5.2.11. Let $I$ be a partially ordered set and let $\operatorname{\mathcal{C}}$ be an $\infty $-category. In the case $I = [1] \times [1]$, Exercise 1.5.2.10 implies that every functor of ordinary categories $I \rightarrow \mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ can be lifted to a functor of $\infty $-categories $\operatorname{N}_{\bullet }(I) \rightarrow \operatorname{\mathcal{C}}$. Beware that this conclusion is generally false for more complicated partially ordered sets. For example, it fails for the partially ordered set $I = [1] \times [1] \times [1]$.
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