Classifying Spaces and Fibrations of Simplicial Sheaves

Matthias Wendt

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.

Journal of Homotopy and Related Structures, Vol. 6(2011), No. 1, p. 1-38