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

TL;DR

This paper demonstrates that various models of $( olinebreak\infty,2)$-categories are essentially equivalent through nerve embeddings, establishing a model-independent understanding of their structure.

Contribution

It proves the equivalence of all nerve embeddings across different models of $(\infty,2)$-categories, showing they induce the same functor up to model change.

Findings

All nerve embeddings induce equivalent functors.

The $$-category of 2-categories is a sub-$$-category of $(,2)$-categories.

Nerve embeddings realize 2-categories as local objects with respect to certain maps.

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.