Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Definition 2.5.3.7. Let $\operatorname{\mathcal{C}}$ be a differential graded category. We let $\operatorname{N}_{\bullet }^{\operatorname{dg}}(\operatorname{\mathcal{C}})$ denote the simplicial set whose value on an object $[n] \in \operatorname{{\bf \Delta }}^{\operatorname{op}}$ is the set $\operatorname{N}_{n}^{\operatorname{dg}}(\operatorname{\mathcal{C}})$ of Construction 2.5.3.1, and whose value on a nondecreasing function $\alpha : [n] \rightarrow [m]$ is the function $\alpha ^{\ast }: \operatorname{N}_{m}^{\operatorname{dg}}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{N}_{n}^{\operatorname{dg}}(\operatorname{\mathcal{C}})$ of Proposition 2.5.3.5. We will refer to $\operatorname{N}_{\bullet }^{\operatorname{dg}}(\operatorname{\mathcal{C}})$ as the differential graded nerve of $\operatorname{\mathcal{C}}$.