Dimension and partial groups
Group Theory
2026-03-13 v2 Algebraic Topology
Category Theory
Abstract
A partial group with elements is, when regarded as a symmetric simplicial set, of dimension at most . This dimension is if and only if the partial group is a group. As a consequence of the first statement, finite partial groups are genuinely finite, despite being seemingly specified by infinitely much data. In particular, finite partial groups have only finitely many im-partial subgroups. We also consider dimension of partial groupoids.
Cite
@article{arxiv.2406.19854,
title = {Dimension and partial groups},
author = {Philip Hackney and Rémi Molinier},
journal= {arXiv preprint arXiv:2406.19854},
year = {2026}
}
Comments
8 pages. Accepted version to appear in Proc. Amer. Math. Soc