Re: Final objects in 2-categories

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/ ]