On Thu, Jun 21, 2012 at 9:34 AM, Michael Barr <barr@math.mcgill.ca> wrote:
Googling around, I have come on several claims that there are no non-trivial injectives in the category of groups (e.g., Mac Lane in the 1950 Duality for groups paper credits Baer with an elegant proof, but gives no hint of what it might be and Baer's earlier paper on injectives doesn't mention it). I have not come on any proof of this, however.
An easy proof is given in:
A short proof of Eilenberg and Moores theorem Maria Nogin CENTRAL EUROPEAN JOURNAL OF MATHEMATICS Volume 5, Number 1 (2007), 201-204, DOI: 10.2478/s11533-006-0040-7 http://www.springerlink.com/content/ev4756g8n3p81541/ -FL
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?
Michael
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