Re: Canonical quotients

[Thorsten Palm <palm@iti.cs.tu-bs.de>]

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/ ]