Nerves of 2-categories and 2-categorification of -categories
arXiv:1902.05524
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.