The Euler characteristics of categories and the barycentric subdivision

Abstract

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.

26 pages, 2 figures

References in corpus (1)

• The Euler characteristic of a category as the sum of a divergent series