A homotopy coherent nerve for $(\infty,n)$-categories
Abstract
In the case of -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 -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 -categories. We show that it realizes a right Quillen equivalence between the models of categories strictly enriched in -categories and of Segal category objects in -categories. This similarly enables us to define homotopy coherent diagrams of -categories equivalently as functors of Segal category objects or as strictly enriched functors out of the homotopy coherent categorifications.
Keywords
Cite
@article{arxiv.2208.02745,
title = {A homotopy coherent nerve for $(\infty,n)$-categories},
author = {Lyne Moser and Nima Rasekh and Martina Rovelli},
journal= {arXiv preprint arXiv:2208.02745},
year = {2024}
}
Comments
55 pages; v3: final version to appear in JPAA. v2 supersedes v1, which contains some errors. v2 is a complete rewrite that proves a similar main result to v1 but in the model of Segal category objects in (oo,n-1)-categories instead of complete Segal objects in (oo,n-1)-categories