Michael Barr hat am 13.09.10 geschrieben:
But that's only an equivalent category; everyone knows that can be done.
Yes, as far as that category of partitions is concerned. But note my last sentence:
On Sun, 12 Sep 2010, Thorsten Palm wrote:
For the remaining sets as sources, additionally choose the identity in case of the trivial quotient, the canonical map otherwise.
Perhaps I should have put the emphasis differently: for a proper quotient of a non-partition, choose the canonical map (its range is a partition); for a quotient of a partition, use the union construction. Of course the case distinction is somewhat unsatisfactory, and so I was trying to hint that there would be a nicer solution if all sets were partitions in the first place. It might be worth mentioning that a similar idea serves to equip the very category of sets with a (binary-)product functor to make it strictly monoidal. Thorsten [For admin and other information see: http://www.mta.ca/~cat-dist/ ]