Vol. 23, No. 1, 1967

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Abelian objects

Mary Gray

Vol. 23 (1967), No. 1, 69–78
Abstract

In a category with a zero object, products and coproducts and in which the map

     (     )
(1   0)
0  1
A+ B   −→   A × B

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.

Mathematical Subject Classification
Primary: 18.10
Milestones
Received: 6 January 1965
Published: 1 October 1967
Authors
Mary Gray