In the case of (∞, 1)-categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched categories and of quasi-categories. This shows that homotopy coherent diagrams of (∞, 1)-categories can equivalently be defined as functors of quasi-categories or as simplicially enriched functors out of the homotopy coherent categorifications.
In this paper, we construct a homotopy coherent nerve for (∞, n)-categories. We show that it realizes a right Quillen equivalence between the models of categories strictly enriched in (∞, n −1)-categories and of Segal category objects in (∞, n −1)-categories. This similarly enables us to define homotopy coherent diagrams of (∞, n)-categories equivalently as functors of Segal category objects or as strictly enriched functors out of the homotopy coherent categorifications.