  We explain how to derive an explicit formula for a natural transformation
relating the (left adjoints of) the homotopy coherent nerve and the Dwyer-Kan
simplicial classifying space functor. The formula is derived using a method
introduced by Szczarba when comparing two different chain models of a
fibration. This note may be taken as a companion to section 3 of our previous
article "Categorical models for path spaces".
