Example 2.5.2.7. Let $B_{\bullet }\operatorname{Ch}(\operatorname{\mathbf{Z}})$ denote the classifying simplicial set of the monoidal category of chain complexes. For each nonnegative integer $n \geq 0$, we can use the analysis of Remark 2.5.1.18 to identify $n$-simplices of $B_{\bullet }\operatorname{Ch}(\operatorname{\mathbf{Z}})$ with differential graded categories $\operatorname{\mathcal{C}}$ satisfying $\operatorname{Ob}(\operatorname{\mathcal{C}}) = \{ 0, 1, \cdots , n \} $ and
\[ \operatorname{Hom}_{\operatorname{\mathcal{C}}}(i, j)_{\ast } = \begin{cases} \operatorname{\mathbf{Z}}[0] & \text{ if } i = j \\ 0 & \text{ if } i > j. \end{cases} \]