In a category with a zero
object, products and coproducts and in which the map
is an epimorphism, we define abelian objects. We show that the product of
abelian objects is also a coproduct for the subcategory consisting of all the
abelian objects. Moreover, we prove that abelian objects constitute abelian
subcategories of certain not-necessarily abelian categories, thus obtaining a
generalization of the subcategory of the category of groups consisting of all abelian
groups.
