Dear all, The following question was privately raised by one of my correspondant:

In Set we have a large (but exponentiable) canonical category of finite sets. Question: What is the relation of (any) of the small (= internal) categories S_f with the notions of finite object in a topos ?.

Let me try to answer it: The internal stack of finite sets S_f is classifying finite objects exactly like the Lawvere object is classifying monomorphisms. Is there another answer? Best, André [For admin and other information see: http://www.mta.ca/~cat-dist/ ]