Classifying spaces and fibrations of simplicial sheaves

Matthias Wendt

Published 2010-09-15, updated 2010-11-09Version 3

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.