The Euler characteristics of categories and the barycentric subdivision

2011/04/19 by Kazunori Noguchi, Noguchi, Kazunori
Mathematics · #18G30 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:18G30

paper · pdf · doi:10.48550/arxiv.1104.3630

26 pages, 2 figures

arxiv created 2011/05/10 · arxiv updated 2011/05/11

Abstract

We prove the L²-Euler characteristic has the invariance under the barycentric subdivision only for finite acyclic categories. And we extend the definition of L²-Euler characteristic and prove the extended L²-Euler characteristic has the invariance under the barycentric subdivision for more wide class of finite categories.

Related

• Euler characteristic for weak n-categories and (∞,1)-categories
• Finiteness obstructions and Euler characteristics of categories
• The Euler characteristic of infinite acyclic categories with filtrations
• The Euler characteristic of an enriched category
• The Euler characteristic of a category as the sum of a divergent series