In a previous paper, we constructed products for certain Ext-functors, in particular for where
Ax denotes the structure sheaf of an object X in a ringed site. If U is a covering of X, it must …

In an abelian category with enough projectives, one can define S, F (, 4) the first satellite (left
derived functor) of an additive right exact functor F at A, to be the kernel of F (ker (P--z A))+ F …

Introduction. The natural setting for a theory of sheaves is a site, iea category C topologized
in the sense of Grothendieck(cf. VERDIER[1963]). We shall consider a sheaf A of rings on a …

In [1], the existence of the functor Ext in an exact category having sufficiently many
projectives and/or injectives was established. Moreover, a fairly general uniqueness …

Introduction. The study of homologically finite subcategories has turned out to be important
in several contexts, especially in the representation theory of artin algebras. In this paper we …

In this note we discuss algebraic cohomology groups of topological groups. Eilenberg-
Maclane [3] and Hopf [ô] introduced the notion of algebraic cohomology of abstract groups …

In [3], Cartan and Eilenberg showed that if A is a ring (with identity element) and A and C are
two (left) A-modules, then one can define for each integer n> 0 an abelian group Extn (A, C) …

1. Preliminaries. Let dº be the catcgory of chain complexes over an abelian category/. In [3]
Kamps proved the following PRoPosToN. A chain map f: X–-Y is a fibration iff it is a normal …

Throughout let be faithful. 1.1. A U-morphism with domain X is a pair (e, A), where e∈ Hom
(X, UA). A [U-morphism (e, A) is called U-epi (= generating) provided that r, s∈ Hom (A, A') …

There have been two main avenues of work on categorical set theory. The first, the theory of
closed categories, deals with the unique position of the category of sets as the category in …