http://en.wikipedia.org/wiki/Exact_sequence(adsbygoogle = window.adsbygoogle || []).push({});

Let's look at the following short exact sequence:

0-->A-->B-->C-->0.

Since the sequence is exact, the mapping from A-->B will be invective and the mapping B-->C will be subjective. The wikipedia article says that we can think of the mapping A-->B as a mapping that embeds A into B. It also says that we can think of the mapping from B-->C as the natural mapping of B-->B/A, and that B/A = C.

Can anyone explain why this is? Why must C = B/A?

EDIT: I understand now, thanks anyone PF

:P

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# Short exact sequences

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