Let C be a small category and R a commutative ring with a 1. A representation of C over R is
a functor F: C→ R-mod where R-mod is the category of R-modules. This general concept …

The language of exact categories allows finite limits and quotients of equivalence relations
and has an axiom which states that quotients are preserved by inverse images of maps. This …

Let k be a field, and A a finite-dimensional linear associative algebra over k. We assume that
A has an identity element, and that a A-module X is left, unital and of finite dimension as a k …

The seminar focuses on a recent solution, by the authors, of a long standing problem
concerning the stable module category (of not necessarily finite dimensional …

We describe cohomologically trivial internal categories in the category C of groups with
operations satisfying certain conditions ([15],[16]). As particular cases we obtain: if C= Gr, H …

This is an account of three 1-hour lectures given at the Instructional Conference on
Representation Theory of Algebraic Groups and Related Finite Groups, Isaac Newton …

Suppose that G is a finite group. We look at the problem of expressing the classifying space
BG, up to mod p cohomology, as a homotopy colimit of classifying spaces of smaller groups …

Dans des travaux précédents (voir [10] et [11]), nous avons défini une notion d'extension de
catégories qui généralise celle, classique, d'extension de groupes (exposée dans [12]). Elle …

This paper describes and exploits connections of the following topics:(A) The cohomology of
categories as introduced by A. Grothendieck [13].(B) Secondary operations of homotopy …

In [6] Brown and Spencer noted that internal categories within the category of groups are
equivalent to crossed modules. As they remarked, this result was known to various others …