Jump to content

Talk:Splitting lemma

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia

Pretty printing

[edit]

this needs some pretty printing :) It's difficult to read...

Proof is not general

[edit]

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).

I noticed the same think. It seems that we could get it much more easily by the definition of biproduct. (which definition in http://ncatlab.org/nlab/show/biproduct is more clear to me than the one in wikipedia)
  • 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)[reply]
AKA Mitchell's embedding theorem the redlink above should be a redirect. 84.15.184.13 (talk) 10:37, 16 July 2023 (UTC)[reply]

Unclear hypothesis

[edit]

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)[reply]

Proof incomplete

[edit]

Proof incomplete?

I thought it is not sufficient to prove that . Why do we then prove only this in the implication "1=>3"? Freeze S (talk) 00:36, 15 January 2017 (UTC)[reply]