Partial groups as symmetric simplicial sets

Published 2 Oct 2023 in math.GR, math.AT, and math.CT | (2310.01513v2)

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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