I am trying to understand the proof in the hatcher topology book (pag $265$) on exact sequences ($6$):
What I don't understand is because when we use the zig-zag lemma we have the sequence we need. could someone explain to me please, thank you very much.
Edit: What I mean is that according to what is said in Hatcher's book, using the exact sequence given $0\to B\to C\to D\to 0$, I can build an exact chain complex $0\to F_*\otimes B\to F_*\otimes C\to F_*\otimes D\to 0$, so if I use the zigzag lemma, I get an exact sequence $...\to H_n(F_*\otimes B)\to H_n(F_*\otimes C)\to H_n(F_*\otimes D)\to H_{n-1}(F_*\otimes B)\to ...$ but how can I get what I want from this last sequence? Thank you.