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arXiv · 0804.1082

The functors Wbar and Diag o Nerve are simplicially homotopy equivalent

Sebastian Thomas
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Abstract

Given a simplicial group G, there are two known classifying simplicial set constructions, the Kan classifying simplicial set Wbar G and Diag N G, where N denotes the dimensionwise nerve. They are known to be weakly homotopy equivalent. We will show that Wbar G is a strong simplicial deformation retract of Diag N G. In particular, Wbar G and Diag N G are simplicially homotopy equivalent.

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Sebastian Thomas. 2008-04-07. The functors Wbar and Diag o Nerve are simplicially homotopy equivalent. https://arxiv.org/abs/0804.1082

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