Talk:Exact sequence

message: there were a couple of corrections by anonymous editors recently that I've just reverted.  There seem to be three different choices for 
the example exact sequence:
# 0 → Z → Z → Z/2Z → 0
# 0 → Z → 2Z → Z/2Z → 0
# 0 → 2Z → Z → Z/2Z → 0
The first two are pretty much the same, the second map is n to 2n, and the only question is how you want to label it.  The third one is slightly different, the second arrow is an inclusion map.  The anonymous editors have gone through all three, and I reverted back to the original, which is #1.  But actually, I prefer #3, because it shows more explicitly the general paradigm that for any quotient group B/A, you have an exact sequence 1 → A → B → B/A → 1, whereas the other sequences don't have the names in the right places.  I wonder what others think. -lethe talk 01:26, 27 January 2006 (UTC)
replies: text: Actually, I think the second one is wrong: the image of 2Z →  Z/2Z  is 0, while the kernel of  Z/2Z → 0 is {0,1}, so that's not exact. -lethe talk 07:05, 27 January 2006 (UTC)
replies: text: The second one could be correct, but the map  \mathbb{Z} \to 2 \mathbb{Z} would have to be n \mapsto 4n (or n goes to -4n), and that seems kind of pointless. 156.56.139.205 (talk) 14:44, 13 September 2011 (UTC)

text: I'm not sure what you mean by "external diagram".  Can you explain?  Cute handle by the way. -lethe talk [ +] 06:42, 14 May 2006 (UTC)
replies: text:  Thanks and sure. It comes from a nice categorical set theory book "Sets For Mathematics" Lawvere, Rosenbrugh. External diagram labels objects and arrows, internal diagram shows behavior of arrows on points in object. \mathbb Z and \mathbb Z/\mathbb Z_2  are objects. n\mathbb Z is not an object, unless it's another name for \mathbb Z. Anyway, I think it is bad style, as is evident from the confusion. The first one is nice. MotherFunctor 05:46, 17 May 2006 (UTC)

text: 2\mathbb{Z} \;{\hookrightarrow}\; \mathbb{Z} \twoheadrightarrow \mathbb{Z}/2\mathbb{Z} 
in most math books with the inclusion being simply the (deceivingly "identity"-like) map 2n \mapsto 2n. The problem with the current presentation is that's not clear how the Z ends up being 2Z until you specify the function, while with this version the function should be said in text for completeness, but it's mostly obvious. 86.127.138.67 (talk) 19:50, 4 April 2015 (UTC)
thread_title:  2Z --> Z or Z -->2Z 

message: This article is OK, especially the examples grad ⇒ rot ⇒ div are really nice. But it should be augmented by the fact, that short exact sequences are equivalently defined by a pair of functions with some properties, which in the split case often is used for the definition of semi-direct products (or sums). So the relation to the 2nd cohomology can be given more explicitely. In addition if the definition of split is applied to the other morphism in the sh.ex.seq then semi-direct reduces to direct. This case some-times is called "retract".  — Preceding unsigned comment added by 134.60.206.14 (talk) 11:05, 11 April 2013 (UTC)
thread_title:  Short exact sequences 

message: I found the way that  markup can tune arrow lengths and spaces automatically. -- Cedar101 (talk) 09:56, 25 January 2018 (UTC)
replies: text: Wow! Thanks! Cool! I always wondered how to do that!  Different question ... What's H_1 and L_2 and what's Hilbert spaces got to do with it? (I assume you added the above content to the article, which mentions Hilbert spaces...) 67.198.37.16 (talk) 06:59, 9 May 2019 (UTC)
thread_title:  {{xtag|ce}} markup for automatic tuning of arrow lengths and spaces 

message: Someone reverted the addition of: 
--External links--
Short Exact Sequences, explanation by Matthew Salomone
I think that's a shame because it gives a much better explanation than anything contained in the article, which is not very well written. Perhaps it should be restored?
Stikko (talk) 21:44, 26 September 2021 (UTC)
replies: text: Please, read WP:EL, and specifically the first item of WP:ELNO (). This applies to this external link. Also WP:NOR applies to this video, which, in any case is not a reliable source for Wikipedia. More specifically, in mathematics, YouTube videos are generally not accepted, except in very exceptional cases. Instead of trying to link this YouTube video, I suggest you to use it for proposing here specific improvements to the article. D.Lazard (talk) 09:20, 27 September 2021 (UTC)
thread_title:  Link 

message: At the beginning of the section, there is the claim that "for non-commutative groups, this is the semidirect product". It seems straight up incorrect. I do not think semidirect products are any kind of products for starters: One does not have uniqueness without a pre-specified homomorphism
\phi : H \to Aut(K). I could still be missing something, but the amount of clarification is rather inadequate. Yeetcode (talk) 05:16, 24 November 2023 (UTC)
replies: text: D.Lazard (talk) 09:02, 24 November 2023 (UTC)
thread_title:  Properties