Ramified coverings of small categories

2013/03/28 by Kazunori Noguchi, Noguchi, Kazunori
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT #msc:18G30 #msc:55R05 #msc:55U10

paper · pdf · doi:10.48550/arxiv.1303.7046

arxiv created 2013/03/28 · arxiv updated 2013/03/29

Abstract

We introduce a ramified covering of small categories, and we show three properties of the notion: the Riemann-Hurwitz formula holds for a ramified covering of finite categories, the zeta function of C divides that of \widetildeC for a ramified covering \mapP\widetildeCC of finite categories, and the classifying space of a d-fold ramified covering of small categories is also a d-fold ramified covering in the sense of Dold \citeDol86.

Related

• Coverings of small categories and nerves
• Gradings, smash products and Galois coverings of a small category
• Counting ramified coverings and intersection theory on Hurwitz spaces II (Local structure of Hurwitz spaces and combinatorial results)
• A model structure on the category of small categories for coverings
• Covering semigroups