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alternative definition of an Abelian category
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(Definition)
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The following is an alternative definition of an Abelian category (according to Barry Mitchell):
The following theorem from ref.[1] is also relevant as it relates key properties of Abelian categories:
``The following statements are equivalent:
- $\A$ is an Abelian category;
- $\A$ has kernels, cokernels, finite products, finite coproducts, and is both normal and comormal;
- $\A$ 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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"alternative definition of an Abelian category" is owned by bci1.
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Cross-references: properties, key, theorem, products, finite, additive category
There are 29 references to this entry.
This is version 30 of alternative definition of an Abelian category, born on 2008-08-02, modified 2009-02-13.
Object id is 10906, canonical name is AlternativeDefinitionOfAnAbelianCategory.
Accessed 1432 times total.
Classification:
| AMS MSC: | 18E10 (Category theory; homological algebra :: Abelian categories :: Exact categories, abelian categories) | | | 18A15 (Category theory; homological algebra :: General theory of categories and functors :: Foundations, relations to logic and deductive systems) | | | 18E05 (Category theory; homological algebra :: Abelian categories :: Preadditive, additive categories) | | | 18-00 (Category theory; homological algebra :: General reference works ) |
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Pending Errata and Addenda
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