Exercise 2.5.9.17. Let $\operatorname{\mathcal{C}}$ be a differential graded category, and let $\mathfrak {Z}: \operatorname{N}^{\operatorname{hc}}_{\bullet }( \operatorname{\mathcal{C}}^{\Delta } ) \rightarrow \operatorname{N}^{\operatorname{dg}}_{\bullet }(\operatorname{\mathcal{C}})$ be the functor of $\infty $-categories supplied by Proposition 2.5.9.10. Show that $\mathfrak {Z}$ is bijective on simplices of dimension $n \leq 2$ (for the case $n=2$, this is essentially the content of Remark 2.5.4.4).
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