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arXiv · 1510.08026

Barycentric Subdivision and Isomorphisms of Groupoids

Jasha Sommer-Simpson
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Abstract

Given groupoids $\mathscr G$ and $\mathscr H$ as well as an isomorphism $\Psi:\text{Sd}\,\mathscr G\cong\text{Sd}\,\mathscr H$ between subdivisions, we construct an isomorphism $P:\mathscr G\cong\mathscr H$. If $\Psi$ equals $\text{Sd} F$ for some functor $F$, then the constructed isomorphism $P$ is equal to $F$. It follows that the restriction of $\text{Sd}$ to the category of groupoids is conservative. These results do not hold for arbitrary categories.

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Jasha Sommer-Simpson. 2015-10-27. Barycentric Subdivision and Isomorphisms of Groupoids. https://arxiv.org/abs/1510.08026

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