The early 60s was a great time in America for a young mathematician. Washington had
responded to Sputnik with a lot of money for science education and the scientists, bless …

A number of sophisticated people tend to disparage category theory as consistently as
others disparage certain kinds of classical music. When obliged to speak of a category they …

Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

We survey the basics of homological algebra in exact categories in the sense of Quillen. All
diagram lemmas are proved directly from the axioms, notably the five lemma, the 3× 3 …

Abstract Contents Introduction § 1. Projectively generated proper classes § 2. Projective
proper classes § 3. Injectively generated and injective proper classes § 4. Spectral …

The notion of a derived functor for a functor T: Q—* fB (with suitable conditions imposed on
the categories (2 and S3 and on the functor 7") is one of the key notions of homological …

Category theory is a general mathematical theory of structures and of structures of
structures. It occupied a central position in contemporary mathematics as well as computer …

We initiate the study of derived functors in the setting of extriangulated categories. By using
coends, we adapt Yoneda's theory of higher extensions to this framework. We show that …

A class of resolutions of objects of an abelian category determines a theory of derived
functors if each morphism between objects extends to a morphism, unique to within …

Abstract CONTENTS Introduction § 1. The definition of a category § 2. Isomorphism. Duality.
Functors § 3. Functors of several variables § 4. Subcategories. Concrete categories § 5 …