Re: Two questions

[Peter LeFanu Lumsdaine <p.l.lumsdaine@gmail.com>]

On Thu, Jun 21, 2012 at 2:54 PM, Michael Shulman <mshulman@ucsd.edu> wrote:
> On Thu, Jun 21, 2012 at 6:34 AM, Michael Barr <barr@math.mcgill.ca> wrote:
>> Somewhere I have seen a proof that all monics in the category of groups
>> are regular.  I think it was in a paper by Eilenberg and ??? and it  needed
>> a special argument if there were elements of order 2.  Can someone help me
>> find this?
>
> I don't know the original reference, but this is exercise 7H in The
> Joy of Cats, which contains a substantial hint for a proof (not
> involving a special case for order-2 elements, so maybe it is a
> different proof).

There was some discussion of this a couple of years ago on Andrej
Bauer’s blog and mathoverflow:

http://math.andrej.com/2010/11/10/subgroups-are-equalizers-constructively/
http://mathoverflow.net/questions/41208/are-all-group-monomorphisms-regular-constructively/

(the chronology/causality between the two is a little non-obvious: the
MO question predates the blog post, but the eventual solution at MO
follows it)

The discussion there is on proving this constructively, but as often,
the first step is looking at the classical proof with a magnifying
glass.

–p.


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