Classifying spaces and fibrations of simplicial sheaves
arXiv:1009.2930
Abstract
In this paper, we discuss the construction of classifying spaces of fibre sequences in model categories of simplicial sheaves. One construction proceeds via Brown representability and provides a classification in the pointed model category. The second construction is given by the classifying space of the monoid of homotopy self-equivalences of a simplicial sheaf and provides the unpointed classification.
34 pages; minor changes, cleaned bibliography, section on Brown representability now uses only Jardine's result