Kerodon

Proposition 2.5.4.10. Let $\operatorname{\mathcal{C}}$ be a differential graded category and let $\operatorname{N}_{\bullet }^{\operatorname{dg}}(\operatorname{\mathcal{C}})$ denote the differential graded nerve of $\operatorname{\mathcal{C}}$. Then the homotopy category $\mathrm{h} \mathit{\operatorname{N}}_{\bullet }^{\operatorname{dg}}(\operatorname{\mathcal{C}})$ (Definition 1.4.5.3) is canonically isomorphic to the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ (Construction 2.5.4.6).