Re: question on finiteness in toposes

Now that the question of finiteness as been reactivated here, may I bring up again the following question ? What concept of finiteness is appropriate for those important mathematical applications in topology for which K/S doesn't seem right ? (For example the equalizer closure of K/S or...??) Especially, a suitably "finite" module should be a vector bundle or a FAC in the sense of Serre so that our simplified topos theory could apply more directly to those things it should. Bill L