  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
$\widetilde{C}$ for a ramified covering $\map{P}{\widetilde{C}}{C}$ 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
\cite{Dol86}.
