The Euler characteristics of categories and the barycentric subdivision

Details The Euler characteristics of categories and the barycentric subdivision The Euler characteristics of categories and the barycentric subdivision

2011-04-19

arxiv.org/abs/1104.3630v2

Mathematics

Category Theory

26 pages, 2 figures

Scientific paper

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.

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