Re: Final objects in 2-categories

[David Roberts <david.roberts@adelaide.edu.au>]

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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