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Short exact sequences

  1. May 2, 2015 #1
    Let's look at the following short exact sequence:

    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
  2. jcsd
  3. May 6, 2015 #2


    Staff: Mentor

    Tell us about your understanding.
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