David Spivak hat am 31.01.12 geschrieben:
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/}?
Answer: No. The "op-" is irrelevant; let us look at DF_{C/} instead. There is not even a weakly terminal object, for the same reason for which there isn't one in DF itself. (Suppose (T,z) is one. Let A be an arbitrary small category having a terminal object a. From the object (C+A,incl) of DF_{C/} we get a discrete fibration f : A-->T. But then for t = f(a) the slice category T_{/t} is isomorphic to A. There are not enough t to accommodate all possible A.) Thorsten Palm [For admin and other information see: http://www.mta.ca/~cat-dist/ ]