The Euler characteristics of categories and the barycentric subdivision
  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. 
Kazunori Noguchi
math.CT