Configurations spaces and Theta_n

TL;DR

This paper shows that Joyal's category Theta_n encodes the homotopy types of configuration spaces of points in R^n, linking higher category theory with topological configuration spaces.

Contribution

It reveals a natural connection between Theta_n and configuration spaces, providing a new perspective in the study of (infinity,n)-categories.

Findings

Theta_n encodes the homotopy type of configuration spaces in R^n

The approach uses elementary combinatorics and homotopy theory techniques

Provides a self-contained exposition linking higher categories and topology

Abstract

We demonstrate that Joyal's category Theta_n, which is central to numerous definitions of (infinity,n)-categories, naturally encodes the homotopy type of configuration spaces of marked points in R^n. This article is largely self-contained and uses only elementary techniques in combinatorics and homotopy theory.