Kerodon

Example 9.2.5.4. Let $\operatorname{\mathcal{C}}_0$ be a category and let $\operatorname{\mathcal{C}}= \operatorname{N}_{\bullet }( \operatorname{\mathcal{C}}_0 )$ denote its nerve. Then lifting problems $\sigma $ in the $\infty $-category $\operatorname{\mathcal{C}}$ (in the sense of Definition 9.2.5.1) can be identified with lifting problems $\sigma _0$ in the ordinary category $\operatorname{\mathcal{C}}_0$ (in the sense of Definition 1.5.4.1). In this case, we can also identify solutions to $\sigma $ with solutions to $\sigma _0$.