Final objects in 2-categories

[Adam Gal <adamgpol@gmail.com>]

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


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