Homology, Homotopy and Applications

Volume 16 (2014)

Number 2

Ramified coverings of small categories

Pages: 159 – 169

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n2.a8

Author

Kazunori Noguchi (Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto, Japan)

Abstract

We introduce ramified coverings of small categories, and we prove three properties of the notion: the Riemann-Hurwitz formula holds for a ramified covering of finite categories, the zeta function of $B$ divides that of $\widetilde{E}$ for a ramified covering $\widetilde{P}\colon \widetilde{E}\to B$ of finite categories, and the nerve of a $d$-fold ramified covering of small categories is also a simplicial $d$-fold ramified covering.

Keywords

ramified covering of small categories, zeta function of a finite category, Euler characteristic of categories

2010 Mathematics Subject Classification

18G30, 55R05, 55U10

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