The zeta function of a finite category (Q2437872)

From the abstract: ``We define the zeta function of a finite category\dots a relationship between the zeta function of a finite category and the Euler characteristic of finite categories\dots it is shown that for a covering of finite categories \(P:E\to B\), the zeta function of \(E\) is that of \(B\) to the power of the number of sheets in the covering.'' The Euler characteristic of a finite category has been studied by Berger and Leinster. In the article the author introduces the concept of a zeta function for a finite category (though it is not invariant under equivalences of categories). The article is rather self-contained, starting with an exemplification of the concept for groupoids, acyclic categories, and categories with at most two objects. In these cases the zeta function can be computed explicitly. A brief account of the Euler characteristic of a finite category then precedes the proof of the main result, relating the zeta function and the Euler characteristic.