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 …

ALGEBRAIC COHOMOLOGY OF TOPOLOGICAL GROUPS Page 1 TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 178, April 1973 ALGEBRAIC COHOMOLOGY …

We suppose the reader is familiar with the terminology of abelian categories. However, we
shall deal only with abelian categories which are categories of modules over some ring, or …

If S: 0 GG A u GG B v GG C GG 0 is a short exact sequence of abelian group objects of a
topos E, then it is well known that the global section functor Γ (−)= HomE (1,−) when applied …

The next simplest case to having no fixed points at all is when the fixed points lie in an
abelian group. The study of this case leads to the cohomology theory of groups. We consider …

Well-known techniques from homological algebra and algebraic topology allow one to
construct a cohomology theory for groups on which the action of a fixed group is given. After …

This chapter discusses the cohomology of groups. The cohomology of groups is one of the
crossroads of mathematics. It has its origins in the representation theory, class field theory …

Given a category g and a dirarcted set A, there is. of course, the well-known cate-gory &+ t
of& ““~ c: r S~ SWRS in C OEW, A. AIoreover, if tf is cocompletc there is a co-limit functor …

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 …

A useful topological mode1 for a group G is a connected CW'-complex K such that I [t (K) z G
and n;(K) z 0 for i> 1. Such a cell complex (which always exists) depends, up to homotopy …