Partial groups as symmetric simplicial sets

Philip Hackney; Justin Lynd

doi:10.1016/j.jpaa.2025.107864

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arXiv · 2310.01513

Partial groups as symmetric simplicial sets

Philip Hackney·Justin Lynd

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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.

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Philip Hackney, Justin Lynd. 2023-10-02. Partial groups as symmetric simplicial sets. https://doi.org/10.1016/j.jpaa.2025.107864

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