Kerodon

Remark 2.3.4.2. Combining Theorem 2.3.4.1, Theorem 2.3.2.1, and Remark 2.2.8.8, we see that the construction $\operatorname{\mathcal{C}}\mapsto \operatorname{N}^{\operatorname{D}}_{\bullet }(\operatorname{\mathcal{C}})$ determines a fully faithful embedding from the ordinary category of $(2,1)$-categories (where morphisms are strictly unitary functors in the sense of Definition 2.2.4.17) to the ordinary category of $\infty $-categories (where morphisms are functors in the sense of Definition 1.5.0.1).