An explicit comparison between $2$-complicial sets and $\Theta_2$-spaces

TL;DR

This paper establishes a direct equivalence between two models of (infinity,2)-categories, bridging the complete Segal $ heta_2$-spaces and 2-complicial sets, advancing the understanding of higher category theory.

Contribution

It provides the first direct Quillen equivalence between the complete Segal $ heta_2$-spaces and 2-complicial sets models of (infinity,2)-categories.

Findings

Established a Quillen equivalence between the two models.

Unified different approaches to (infinity,2)-categories.

Enhanced the theoretical framework for higher category models.

Abstract

We produce a direct Quillen equivalence between two models of $(\infty,2)$-categories: the complete Segal $\Theta_2$-spaces due to Rezk and the $2$-complicial sets due to Verity.