Cohomology with values in a sheaf of crossed groups over a site

TL;DR

This paper presents a translation of Debremaeker's 1976 dissertation on cohomology theory with values in sheaves of crossed groups over a site, expanding the mathematical framework for algebraic topology and sheaf theory.

Contribution

It introduces a novel approach to cohomology with sheaves of crossed groups, providing foundational insights and extending existing cohomological methods.

Findings

Develops a new cohomology theory for sheaves of crossed groups

Provides detailed mathematical framework and definitions

Extends classical cohomology concepts to non-abelian settings

Abstract

This is an English translation of Raymond Debremaeker's 1976 Dutch-language dissertation "Cohomologie met waarden in een gekruiste groepenschoof op een situs" (Katholieke Universiteit te Leuven). I thank the University librarians for sending me a copy of this text and Professor Debremaeker for allowing me to post this translation of his dissertation on this server. Work on this translation was supported by Chile's Fondecyt through grants 1120003 and 1160004.