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.