Nerves of 2-categories and 2-categorification of $(\infty,2)$-categories
Algebraic Topology
2019-02-15 v1 Category Theory
Abstract
We show that the homotopy theory of strict 2-categories embeds in that of -categories in the form of 2-precomplicial sets. More precisely, we construct a nerve-categorification adjunction that is a Quillen pair between Lack's model structure for 2-categories and Riehl-Verity's model structure for 2-complicial sets. Furthermore, we show that Lack's model structure is transferred along this nerve and that the nerve is homotopically fully faithful.
Keywords
Cite
@article{arxiv.1902.05524,
title = {Nerves of 2-categories and 2-categorification of $(\infty,2)$-categories},
author = {Viktoriya Ozornova and Martina Rovelli},
journal= {arXiv preprint arXiv:1902.05524},
year = {2019}
}