The edgewise subdivision criterion for 2-Segal objects

TL;DR

This paper demonstrates that the edgewise subdivision of a 2-Segal object always results in a Segal object and establishes that this property uniquely characterizes 2-Segal objects.

Contribution

It introduces a new characterization of 2-Segal objects through their edgewise subdivision property.

Findings

Edgewise subdivision of 2-Segal objects yields Segal objects.

This property characterizes 2-Segal objects uniquely.

The result bridges 2-Segal and Segal objects via subdivision.

Abstract

We show that the edgewise subdivision of a $2$-Segal object is always a Segal object, and furthermore that this property characterizes $2$-Segal objects.