## The zeta function of a finite category

### Summary

Summary: We define the zeta function of a finite category. We prove a theorem that states a relationship between the zeta function of a finite category and the Euler characteristic of finite categories, called the series Euler characteristic citeLeib. Moreover, it is shown that for a covering of finite categories, $\map{P}E{B}$, the zeta function of $E$ is that of $B$ to the power of the number of sheets in the covering. This is a categorical analogue of the unproved conjecture of Dedekind for algebraic number fields and the Dedekind zeta functions.

### Mathematics Subject Classification

18G30, 18D30, 30B10, 30B40

### Keywords/Phrases

zeta function of a finite category, Euler characteristics of categories, coverings of small categories, Dedekind conjecture