published on February 23, 2026
Illustration in Mathematics and CS — Made Broadly Accessible by AI: From Opportunity to Practice
By Erika Berenice Roldan Roa
The Van Est isomorphism for higher stacks
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.
