Talk:Splitting lemma
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this needs some pretty printing :) It's difficult to read...
While the statement is correct in any abelian category, the given proof applies only to categories of abelian groups, modules over a ring, etc. This should be noted. (Perhaps it would be satisfactory to note that the general case follows by Freyd's embedding theorem).
- Erm. I have a question as regards non-abelian groups. There is a natural inclusion u from quotient C to B=A⋊C, but what is the natural projection t from B=A⋊C to normal factor A, unless B is actually a direct product A×C ?? --192.75.48.150 17:38, 27 July 2007 (UTC)
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- Removed. I'm confident enough in group theory to say something is not correct, or at least badly stated, but not confident enough in category theory to state the correct version. --192.75.48.150 19:46, 1 August 2007 (UTC)
In the statement of the lemma: would it be helpful to clarify that by hypothesis, the maps q and r are in a short exact sequence, but that we don't require this a priori of t and u? Jaswenso 03:15, 6 September 2007 (UTC)
