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Classifying spaces and fibrations of simplicial sheaves. (English) Zbl 1278.18025
Summary: 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.

MSC:
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
55R15 Classification of fiber spaces or bundles in algebraic topology
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