2-quasi-categories vs Segal 2-categories

Alexander Campbell – 5 June 2019

I will begin this talk with an "easy" (in the sense of Simpson) proof that the underlying bisimplicial set of a 2-quasi-category is a quasi-category-enriched Segal category. Using this result, I will then give another construction of the homotopy bicategory of a 2-quasi-category, prove a Quillen equivalence between Ara's model structure for 2-quasi-categories and the Hirschowitz--Simpson--Pellissier model structure for Segal 2-categories, and prove Ara's conjecture that a 2-functor is a biequivalence if and only if it is sent by the strict 2-cellular nerve functor to a weak equivalence in the model structure for 2-quasi-categories.