Coverings of small categories and nerves

Original · EN

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 PEB 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.