Model independence of $(\infty ,2)$-categorical nerves

Abstract

For most models of $(\infty ,2)$-categories an embedding of the $\infty$-category of 2-categories into that of $(\infty ,2)$-categories has been constructed in the form of a nerve construction of some flavor. We prove that all those nerve embeddings induce equivalent functors, modulo change of model. We also show that all the nerve embeddings realize the $\infty$-category of 2-categories as the sub-$\infty$-category of $(\infty ,2)$-categories that are local with respect to a certain class of maps.