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Homestandard Abelian category

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# standard Abelian category

The following is an alternative definition of an *Abelian category* (according to Barry Mitchell’s textbook):

###### Definition 0.1.

An *Abelian category* is an exact
additive category with finite products.

The following theorem from ref.[1] is also relevant as it relates key properties of Abelian categories:

“The following statements are equivalent:

1. $\mathcal{A}$ is an Abelian category;

2. $\mathcal{A}$ has kernels, cokernels, finite products, finite coproducts, and is both normal and comormal;

3.

# References

- 1
Barry Mitchell.
*Theory of Categories*, Academic Press: New York and London, 1965, (Theorem 20.1 on p.33).

Defines:

Ab-6 category

Keywords:

Abelian category, Theorem, exact additive category with finite products,exact additive category with finite products, pushouts and pullbacks

Related:

CategoricalSequence,LocalGrothendieckCategory, C_3CategoryTheorem, CategoryOfAdditiveFractions

Synonym:

abelian category, Abelian category

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

18-00*no label found*18E05

*no label found*18A15

*no label found*18E10

*no label found*

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