Can one define a "category of all mathematical objects"?

Dear Categorists, I would be interested in hearing what you think of an idea that seems rather wild: Is it possible to define a category with nice properties such that any locally small category becomes isomorphic to a subcategory of that category? In the absence of such a category, can a category such as the category of all Grothendieck topoi and geometric morphisms between them serve as a "category of all mathematical objects" for practical purposes? Mattias Wikstrom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]