Comparison of models for $(\infty, n)$-categories, II

TL;DR

This paper establishes a series of explicit Quillen equivalences linking different models for $( , n)$-categories, advancing the understanding of their homotopical relationships.

Contribution

It completes a chain of explicit Quillen equivalences between models for $( , n)$-categories, connecting Segal objects, complete Segal objects, and $ heta_{n+1}$-spaces.

Findings

Established explicit Quillen equivalences between models for $( , n)$-categories.

Connected Segal category objects and $ heta_{n+1}$-spaces.

Enhanced the framework for comparing different models of higher categories.

Abstract

In this paper we complete a chain of explicit Quillen equivalences between the model category for $\Theta_{n+1}$-spaces and the model category of small categories enriched in $\Theta_n$-spaces. The Quillen equivalences given here connect Segal category objects in $\Theta_n$-spaces, complete Segal objects in $\Theta_n$-spaces, and $\Theta_{n+1}$-spaces.