Seminar Algebra and Geometry: Clemens Berger (Université de Nice)

Euler characteristic and Moebius inversion for finite categories

The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite, the sum diverges. Nevertheless, this infinite sum can sometimes be evaluated using generating power series. We show that this is in particular the case when the complex is the simplicial nerve of a finite category. We discuss the relationship with Rota's notion of Moebius inversion and Noguchi's notion of zeta-function of a finite category.

This talk is based on joint work with Tom Leinster (Glasgow).

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