# reference request – Explicit homotopy of the chain for the Alexander-Whitney couple, Eilenberg-Zilber

Let $$A$$ and $$B$$ to be abelian simplicial groups, and let $$N_ ast (-)$$ denotes the complex complex chain normalizer. Let
$$AW_ {A, B} colon N_ ast (A otimes B) longrightarrow N_ ast (A) otimes N_ ast (B)$$
and
$$EZ_ {A, B} colon N_ Ast (A) otimes N_ Ast (B) longrightarrow N_ ast (A otimes B)$$
denote the Alexander-Whitney map
and the Eilenberg-Zilber map, respectively.
Does anyone know an explicit chain homotopy realizing
$$EZ_ {A, B} cir AW_ {A, B} sim Id_ {N_ Ast (A otimes B)}.$$

The motivation for its existence can be found in the comments of this question.