Résumé
Given a bundle of chain complexes, the algebra of functions on its shifted cotangent bundle has a natural structure of a shifted Poisson algebra. We show that if two such bundles are homotopy equivalent, the corresponding Poisson algebras are homotopy equivalent.
We apply this result to L-infinity-algebroids to show that two homotopy equivalent bundles have the same L-infinity-algebroid structures and explore some consequences about the theory of shifted Poisson structures.