Nerves of 2-categories and 2-categorification of $(\infty ,2)$-categories

Abstract

We show that the homotopy theory of strict 2-categories embeds in that of $(\infty ,2)$-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.

References in corpus (5)

• Higher Topos Theory
• A Quillen model structure for Gray-categories
• A homotopy coherent cellular nerve for bicategories
• Weak Omega Categories I
• Towards a Thomason model structure on the category of strict n-categories

Cited by in corpus (1)

• A double $(\infty ,1)$-categorical nerve for double categories