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Abelian category
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(Definition)
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The following is the definition of an Abelian category according to Barry Mitchell (1965).
The following theorem from ref.[1] is also relevant as it relates key properties of Abelian categories:
“The following statements are equivalent:
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 is an Abelian category;
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 has kernels, cokernels, finite products, finite coproducts, and is both normal and comormal;
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 has pushouts and pullbacks and is both normal and conormal”.
- 1
- Barry Mitchell. Theory of Categories, Academic Press: New York and London, 1965, (Theorem 20.1 on p.33).
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"Abelian category" is owned by bci1.
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See Also: non-Abelian theory, Yoneda lemma, center of Abelian category
| Other names: |
abelian category |
| Keywords: |
Abelian, category, Abelian category, commuativity and Abelian axioms |
Cross-references: theorem, additive category
There are 24 references to this object.
This is version 2 of Abelian category, born on 2009-02-13, modified 2009-02-13.
Object id is 517, canonical name is AbelianCategory.
Accessed 1024 times total.
Classification:
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Pending Errata and Addenda
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