Short Exact Sequences

Algebraic Topology · Axiom Academy

0 → A → B → C → 0, exactness at each position 1. Definition of Short Exact Sequence A short exact sequence is a sequence of groups and homomorphisms: What does exactness at A mean? Exactness at B is the heart of the sequence: Putting it all together, a short exact sequence tells us: i is injective (A embeds in B) p is surjective (B projects onto C) im(i) = ker(p) (the copy of A in B is exactly what p kills)

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