Partial groups as symmetric simplicial sets

TL;DR

This paper introduces a new way to understand partial groups using symmetric simplicial sets, providing tools for computing colimits and extending the concept to partial groupoids that include groupoids.

Contribution

It offers a novel characterization of partial groups as a subcategory of symmetric simplicial sets with an explicit reflection, and defines partial groupoids encompassing groupoids and partial groups.

Findings

Characterization of partial groups within symmetric simplicial sets

Explicit reflection enabling colimit computations

Introduction of partial groupoids combining groupoids and partial groups

Abstract

We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the notion of a partial groupoid, which encompasses both groupoids and partial groups.