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From: Peter LeFanu Lumsdaine
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Subject: Re: Two questions
Date: Thu, 21 Jun 2012 21:25:12 -0300
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On Thu, Jun 21, 2012 at 2:54 PM, Michael Shulman wrote:
> On Thu, Jun 21, 2012 at 6:34 AM, Michael Barr wrote=
:
>> Somewhere I have seen a proof that all monics in the category of groups
>> are regular. =C2=A0I think it was in a paper by Eilenberg and ??? and it=
needed
>> a special argument if there were elements of order 2. =C2=A0Can 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=E2=80=99s 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.
=E2=80=93p.
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