Does any abelian category admits direct sums?
If not, categories admiting direct sums have a special name?
I'm asking this since I am writing a proof that requires direct sums but I only know that the category is abelian.
Thank you very much for your answer!
Edit. In the tag description is written that indeed they posses finite direct sums.
On
In an abelian category you have much more than direct sums(=coproducts); you have biproducts, so that the object part is the same for binary products and coproducts and the arrows satisfy some very nice relations..http://en.wikipedia.org/wiki/Biproduct
On
You should clarify what you mean by direct sum. If you mean 'finite direct sum' then this is included in the definition of an abelian category. Arbitrary direct sums don't necessarily exist, like the category of finite abelian groups. An abelian category is called 'cocomplete' if it possesses all direct sums.
Yes, by the definition of an Abelian category, it contains all finite coproducts ("direct sums"). Just look back to your definition of an Abelian product to see all the extra things an Abelian category is assumed to have.