question about discrete op-fibrations

Hi all, Here's a quick question perhaps someone here can answer easily. Let DOF denote the category whose objects are small categories C,D, etc. and in which Hom(C,D) is the set of discrete op-fibrations C-->D. For a category C, let DOF_{C/} denote the coslice over C. Question: Does there exist a terminal object in DOF_{C/}? Thanks! David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]