Re: Final objects in 2-categories

["Eduardo J. Dubuc" <edubuc@dm.uba.ar>]

Perhaps an adequate definition should be that of being a pseudocolimit
of the identity (or bicolimit ?). Or that the pseudocolimit (or
bicolimit ?) of any 2-diagram X_a indexed by C should be A_x.


On 25/07/14 23:04, David Roberts wrote:
> Hi Adam,
>
> There are three definitions one could think of for a final object x in a
> 2-category C:
>
> 1) C(a,x) is equivalent to * for all a (the usual notion)
>
> 2) C(a,x) has a terminal object for all a (and perhaps a condition like the
> obvious functors induced by b ->  a preserve it). I vaguely recall seeing
> this before, but not where. Perhaps others on the list know.
>
> 3) C(a,x) has a contractible nerve for all a.
>
> Clearly 1)=>2)=>3), but it depends on your application as to what you use.
> Given what you wrote, the last two don't seem inappropriate.
>
> Best regards,
> David
>



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