Appears in collection : 2023 - T2 - WS3 - Dg-manifolds in geometry and physics

A classical theorem of Van Est relates the differentiable cohomology of a Lie group to the cohomology of its Lie algebra. I will discuss a version of this result for homotopy-theoretic variants of Lie group(oid)s, such as the string group. This relates the derived category of representations of such a groupoid to the derived category of representations of its Lie algebroid. In particular, this relies on a version of Koszul duality for Lie algebroids.