Now, for a category C which is locally U-small in the restricted sense [C^op,U] is locally U-small in the restricted sense as shown by Paul's argument. But if C' is locally U-small in the liberal sense then [C'^op,U] \cong [C^op,U] and the latter is locally U-small in the restricted sense and thus [C'^op,U] is locally U-small in the liberal sense.

What I meant was that C is U-small and C' isomorphic to it. Usually one considers [C^op,U] only for categories C living in U. But [Ord(U)^op,U] is a topos which one may want to consideralthough its Omega has as many global elements as there are sets in U. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]