Talk:Snake lemma

From Wikipedia, the free encyclopedia

I don't "see" the snake in the 3rd disagram (perhaps because I'm not familiar with how the kernerls and cokernels tie in). Can someone clarify? Chas zzz brown 21:25 Oct 29, 2002 (UTC)

In the last diagram, you want to add (maybe in some other color) arrows from ker a to ker b, from ker b to ker c, from coker a to coker b and from coker b to coker c and then the connecting map from ker c to coker a in the form of a reversed S across the whole diagram. AxelBoldt 22:06 Oct 29, 2002 (UTC)

Yes, d needs to come out to the right from ker c, around the 0 on the right, left directly through the letter c, then the letter b, then the letter a around the 0 on the left, and then pop into coker a. That's the snake. — Toby 10:38 Oct 31, 2002 (UTC)

Like that? Chas zzz brown 09:28 Nov 1, 2002 (UTC)

Yes, that's a beauty. AxelBoldt 00:09 Nov 2, 2002 (UTC)

Exactly! But I don't suppose that you could label the snaky morphism "d"? Somewhere to the right of the "c" and below the nearby "0"? That would make it clearer to people comparing this to the previous diagram with its "d". — Toby 10:17 Nov 3, 2002 (UTC)

I tried it below the "0", but it was getting a bit crowded there, and it becam hard to tell visually whether d might be the 0-morphism C → 0; I think it's more readable when placed at the right as shown here. Hope you like it! Chas zzz brown 03:04 Nov 4, 2002 (UTC)

Great, thanks! — Toby 07:15 Nov 17, 2002 (UTC)

This is probably stupid, but how do you get from the Snake Lemma to the theorem that a short exact sequence of chain complexes induces the familiar long exact sequence?