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
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]