English

Partial groups as symmetric simplicial sets

Group Theory 2025-03-10 v2 Algebraic Topology Category Theory

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.

Keywords

Cite

@article{arxiv.2310.01513,
  title  = {Partial groups as symmetric simplicial sets},
  author = {Philip Hackney and Justin Lynd},
  journal= {arXiv preprint arXiv:2310.01513},
  year   = {2025}
}

Comments

22 pages, accepted version

R2 v1 2026-06-28T12:38:43.702Z