The functors Wbar and Diag o Nerve are simplicially homotopy equivalent
Algebraic Topology
2011-03-31 v1 K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.0804.1082,
title = {The functors Wbar and Diag o Nerve are simplicially homotopy equivalent},
author = {Sebastian Thomas},
journal= {arXiv preprint arXiv:0804.1082},
year = {2011}
}