Dear categorists, it is well known that the Yoneda embedding Y: A -> [A^op,Set] preserves existing function spaces (and also, for instance, the subobject classifier if there is one). Does anybody know if the presheaf category [A^op,Set] contains the `relatively free' cartesian closed category (topos, ...) over A as a (full?) subcategory, generated by Y[A] in the obvious sense? Here, relatively free means universal w.r.t. functors that, like Y, preserve all existing structure. Thanks a lot, Lutz -- ----------------------------------------------------------------------------- Lutz Schroeder Phone +49-421-218-4683 Dept. of Computer Science Fax +49-421-218-3054 University of Bremen lschrode@informatik.uni-bremen.de P.O.Box 330440, D-28334 Bremen http://www.informatik.uni-bremen.de/~lschrode -----------------------------------------------------------------------------