The functors Wbar and Diag Nerve are simplicially homotopy equivalent
Sebastian Thomas
Journal of Homotopy and Related Structures 3(1) (2008), pp. 359-378.
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.
fulltext, arXiv:0804.1082, journal, MR2481463, Zbl 1186.55011
