Hi all, Has someone studied the notion of final objects in a 2-category? I know that we can define it using the classifying space, and that in this sense Quillen's theorem A holds and tells us this is equivalent to some fibers being contractible. This seems to be a bit too coarse though. For instance in our recent paper (with E. Gal) we wanted to prove that something is final, and what we showed is that these fibers have an initial and final object. So they definitely have contractible classifying spaces, but it seems that we can say something more precise than this. The question is if this fits into some finer notion of final object in 2-categories which has been studied. Thanks, Adam [For admin and other information see: http://www.mta.ca/~cat-dist/ ]