The zeta function of a finite category

2012/03/28 by Kazunori Noguchi, Noguchi, Kazunori
Mathematics · #18G30 #Category Theory (math.CT) #FOS: Mathematics #Number Theory (math.NT) #math.CT #math.NT #msc:18G30

paper · pdf · doi:10.48550/arxiv.1203.6133

arxiv created 2012/05/09 · arxiv updated 2012/05/10

Abstract

We define the zeta function of a finite category. And we propose a conjecture which states the relationship between the Euler characteristic of finite categories and the zeta function of finite categories. This conjecture is verified when categories are finite groupoids, finite acyclic categories, categories with 2-objects and finite categories satisfying certain condition.

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