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They say "...In this case we can assemble the quotient modules $C_n / B_n$ into a chain complex $$ \cdots \xrightarrow{d} C_{n+1}/B_{n+1} \xrightarrow{d} C_{n}/B_{n} \xrightarrow{d} \cdots $$

But how is each $d_n$ defined?

My attempt shows that $d_n : C_n/B_n \to C_{n-1}/B_{n-1}$ defined by mapping $x + B_n \to d_n^{(C)}(x) + B_{n-1}$. I've shown on paper that it is a indeed a differential of the sequence. I haven't proven well-definedness though. $x + B_n = y + B_n \implies d_n^{(C)}(x - y) \in B_{n-1} \implies$ ?

Here's complete info from the book:

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Najib Idrissi
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Daniel Donnelly
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    I dont have Weibel. please give more information, or a picture. – user 1 Jun 14 '15 at 06:01
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    $x + B_n = y + B_n \implies d_n^{(C)}(x - y) \in B_{n-1} \implies d_n^{(C)}(x )- d_n^{(C)}(y) \in B_{n-1} \implies d_n^{(C)}(x) + B_{n-1}= d_n^{(C)}(y) + B_{n-1}$ – user 1 Jun 14 '15 at 06:28
  • @user1 that seems simple enough. I usually see those types of tricks right away. I must have been tired last night. – Daniel Donnelly Jun 14 '15 at 16:17
  • I could guess; you are above 5k. BTW, the comment may help others that will read the question. – user 1 Jun 14 '15 at 18:56

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