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short exact sequence
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(Definition)
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Let $A,B,C$ be objects in an abelian category. A short exact sequence is an exact sequence of the form $$0 \to A \to B \to C \to 0.$$ Note that in this case, the homomorphism $A \to B$ must be a monomorphism, and the homomorphism $B \to C$ must be an epimorphism.
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"short exact sequence" is owned by antizeus. [ full author list (2) ]
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Cross-references: homomorphism, exact sequence, abelian category, objects
There are 11 references to this entry.
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 7441 times total.
Classification:
| AMS MSC: | 16E05 (Associative rings and algebras :: Homological methods :: Syzygies, resolutions, complexes) |
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Pending Errata and Addenda
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