The following is an excerpt from Atiyah-Macdonald on short exact sequences.
I don't understand the part where the author says "Then $d(x'')$ is defined to be the image of $y'$ in Coker ($f'$)". Is $d$ a mapping from $N'$ to Coker ($f'$)?
2026-03-26 14:31:54.1774535514
A question on short exact sequences.
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This is precisely the snake lemma http://en.wikipedia.org/wiki/Snake_lemma
the construction of the so called boundary operator $d$ is a little bit tidious but gets very clear after some time.
You have to do a little bit diagram chasing to see that it is defined and well-defined.
Have a look at this short video taken from the movie "It's my turn"
https://www.youtube.com/watch?v=etbcKWEKnvg
Sorry for only being informative and not constructive, but I think the best way for you is to get it straight yourself - maybe with different literature.