范畴的欧拉示性数与重心重分
The Euler characteristics of categories and the barycentric subdivision
摘要：
证明了$L^2$ -欧拉示性数仅对有限个无圈范畴在重心重分下具有不变性。并对$L^2$ -欧拉示性数的定义进行了推广，证明了推广的$L^2$ -欧拉示性数线对更广泛的有限范畴在重心重分下具有不变性。
英文摘要：
We prove the $L^2$-Euler characteristic has the invariance under the barycentric subdivision only for finite acyclic categories. And we extend the definition of $L^2$-Euler characteristic and prove the extended $L^2$-Euler characteristic has the invariance under the barycentric subdivision for more wide class of finite 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。
