- #1
PsychonautQQ
- 781
- 10
http://en.wikipedia.org/wiki/Exact_sequence
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
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