  The Van Est homomorphism for a Lie groupoid $G \rightrightarrows M$, as
introduced by Weinstein-Xu, is a cochain map from the complex $C^\infty(BG)$ of
groupoid cochains to the Chevalley-Eilenberg complex $C(A)$ of the Lie
algebroid $A$ of $G$. It was generalized by Weinstein, Mehta, and Abad-Crainic
to a morphism from the Bott-Shulman-Stasheff complex $\Omega(BG)$ to a
(suitably defined) Weil algebra $W(A)$. In this paper, we will give an approach
to the Van Est map in terms of the Perturbation Lemma of homological algebra.
This approach is used to establish the basic properties of the Van Est map. In
particular, we show that on the normalized subcomplex, the Van Est map
restricts to an algebra morphism.
