Ebook: Abelian categories with Applications to Rings and Modules

London: Academic Press, 1973. — 480 p. — ISBN: 0125615507, 9780125615501The theory of abelian categories begins almost with the first studies on abelian groups. A first systematization of the notions and results is made by Cartan and Eilenberg for categories of modules and subsequently generalized by Buchsbaum through the introduction of the notion of exact category.
An important advance was made by Grothendieck who exhibited new aspects and results in the theory of abelian categories. A few years later, Gabriel developed the theory of localization and laid the foundation of the theory of duality for abelian categories.