English

Coverings of small categories and nerves

Category Theory 2012-10-23 v1 Algebraic Topology

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\map{P}{E}{B} of finite categories, the zeta function of EE is the zeta function of BB to the number of sheet of PP. Moreover, we prove the formula χ(E)=χ(F)χ(B)\chi(E)=\chi(F)\chi(B) for Euler characteristic of categories and coverings.

Keywords

Cite

@article{arxiv.1210.5678,
  title  = {Coverings of small categories and nerves},
  author = {Kazunori Noguchi},
  journal= {arXiv preprint arXiv:1210.5678},
  year   = {2012}
}