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 [BL08]. Moreover, it is shown that for a covering of finite categories, 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.
|Number of pages||32|
|Publication status||Published - 2013 Jan 1|
- Coverings of small categories
- Dedekind conjecture
- Euler characteristics of categories
- Zeta function of a finite category
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