A Homotopy Coherent Nerve for (∞,N)-Categories

In the case of (infinity, 1)-categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched categories and of quasicategories. This shows that homotopy coherent diagrams of (infinity, 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 (infinity, n)-categories. We show that it realizes a right Quillen equivalence between the models of categories strictly enriched in (infinity, n - 1)-categories and of Segal category objects in (infinity, n - 1)-categories. This similarly enables us to define homotopy coherent diagrams of (infinity, n)-categories equivalently as functors of Segal category objects or as strictly enriched functors out of the homotopy coherent categorifications. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org/licenses/by/4.0/).