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 characteristiccite{Leib}.
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.
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机译：我们定义一个有限类别的zeta函数。 我们证明了一个定理，该定理陈述了有限类别的zeta函数与有限类别的Euler特征之间的关系，称为级Euler特征 cite {Leib}。 此外，表明对于有限类别的覆盖物 map {P} E {B} $，$ E $的zeta函数是$ B $随覆盖物中页数的幂而变的。 这是对代数数域和Dedekind zeta函数的Dedekind的未经证明的猜想的绝对分类。
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