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short exact sequence (Definition)

Let $ A,B,C$ be objects in an abelian category. A short exact sequence is an exact sequence of the form

$\displaystyle 0 \to A \to B \to C \to 0.$
Note that in this case, the homomorphism $ A \to B$ must be a monomorphism, and the homomorphism $ B \to C$ must be an epimorphism.



"short exact sequence" is owned by antizeus. [ full author list (2) ]
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See Also: categorical sequence
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Cross-references: homomorphism, exact sequence, abelian category, objects
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This is version 3 of short exact sequence, born on 2002-01-05, modified 2008-06-29.
Object id is 1355, canonical name is ShortExactSequence.
Accessed 6420 times total.

Classification:
AMS MSC: 16E05 (Associative rings and algebras :: Homological methods :: Syzygies, resolutions, complexes)
Pending Errata and Addenda
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