An embedding of 2-categories into (oo,2)-categories

Martina Rovelli – 27 November 2019

It is desirable that a good candidate model for the homotopy theory of (oo,n)-categories should interact nicely with the existent homotopy theory of strict n-categories. When n = 0,1, it is understood that the homotopy theory of sets and of strict 1-categories embeds in that of oo-categories and oo-groupoids, essentially for all existing models. When n = 2 and we consider saturated 2-complicial sets as a model of (oo, 2)-categories, the picture is more complicated. In this talk we will describe a homotopically fully faithful nerve construction that embeds the homotopy theory of 2-categories in that of (oo, 2)-categories in the form of saturated 2-complicial sets. More precisely, this nerve construction is a right Quillen functor that creates the model structure for 2-categories. This is joint work with V. Ozornova.