Coverings of small categories and nerves

2012/10/21 by Kazunori Noguchi, Noguchi, Kazunori
Mathematics · #18G30 #55R05 #55U10 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #math.AT #math.CT #msc:18G30 #msc:55R05 #msc:55U10

paper · pdf · doi:10.48550/arxiv.1210.5678

arxiv created 2012/10/21 · arxiv updated 2012/10/23

Abstract

We prove a certain proposition which states a relationship between coverings of small categories and nerves. As its application, we prove that for a covering \mapPEB of finite categories, the zeta function of E is the zeta function of B to the number of sheet of P. Moreover, we prove the formula χ(E)=χ(F)χ(B) for Euler characteristic of categories and coverings.

Related

• Čech complexes for covers of small categories
• Ramified coverings of small categories
• The zeta function of a finite category
• The zeta function of a finite category and the series Euler characteristic
• The zeta function of a finite category which has Möbius inversion