群胚的重心重分与同构
Barycentric Subdivision and Isomorphisms of Groupoids
摘要：
给定群胚$\mathscr G$和$\mathscr H$以及细分之间的同构$Ψ:\text{Sd}\,\mathscr G\cong\text{Sd}\,\mathscr H$，我们构造了一个同构$P:\mathscr G\cong\mathscr H$ .如果对于某个函子$F$，$Ψ$等于$\text{Sd} F$，则构造的同构$P$等于$F$。由此可见，将$\text{Sd}$限制到群胚范畴是保守的。这些结果不适用于任意类别。
英文摘要：
Given groupoids $\mathscr G$ and $\mathscr H$ as well as an isomorphism $Ψ:\text{Sd}\,\mathscr G\cong\text{Sd}\,\mathscr H$ between subdivisions, we construct an isomorphism $P:\mathscr G\cong\mathscr H$. If $Ψ$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
