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Hypercovers in topology

Daniel Dugger·Daniel C. Isaksen
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Abstract

We show that if U is a hypercover of a topological space X then the natural map from hocolim U to X is a weak equivalence. This fact is used to construct topological realization functors for the A^1-homotopy theory of schemes over real and complex fields.

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Daniel Dugger, Daniel C. Isaksen. 2001-11-27. Hypercovers in topology. https://arxiv.org/abs/math/0111287

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