Ramified coverings of small categories

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 (E) over tilde for a ramified covering (P) over tilde: (E) over tilde -> B of finite categories, and the nerve of a d-fold ramified covering of small categories is also a simplicial d-fold ramified covering.