size_question_bis

The question arose by considering the usual completion into a small site with finite limits of any small set of generators. You take all finite limits of generators, and repite this dennumerable times. Then, already at the first step, you get a large subcategory. What happens ? If you choose one copy of the limit for each finite diagram, certainly it is not what it is done in the literature. If you do not choose one copy, which set of copies do you take ? Thus the completion of a set of generators into a site with finite limits depend on choice ? e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]