  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.
