Let G be a Lie groupoid, and A the corresponding Lie algebroid.

In their 1991 article, Weinstein-Xu described a Van Est map from the complex of smooth groupoid cochains on G to the Chevalley-Eilenberg Lie algebroid complex of A. It is an algebra morphism on the normalized cochains. In this talk, we will give an explanation of this Van Est map in terms of the fundamental lemma of homological perturbation theory. This talk is based on an article with David Li-Bland in L'Ens. Math. 61, 2015, and is an expanded version of my talk at the FI a few years ago.