Kerodon

Remark 2.4.3.6. The homotopy coherent nerve $\operatorname{N}_{\bullet }^{\operatorname{hc}}(\operatorname{\mathcal{C}})$ was introduced by Cordier in [MR648798] (motivated by earlier work of Vogt on the theory of homotopy coherence; see [MR0331376]). Beware that Cordier uses slightly different conventions: [MR648798] defines the homotopy coherent nerve of a simplicial category $\operatorname{\mathcal{C}}$ to be the simplicial set $\operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{\mathcal{C}}^{\operatorname{c}} )$, where $\operatorname{\mathcal{C}}^{\operatorname{c}}$ denotes the conjugate of the simplicial category $\operatorname{\mathcal{C}}$ (Example 2.4.2.12).