We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.
We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors (notion introduced by Djament and Vespa) from a small symmetric monoidal category whose unit is an initial object to an abelian category. We prove in particular that the category of polynomial functors from the category of free abelian groups ℤⁿ with split monomorphisms to abelian groups is "almost" locally noetherian. We also give an...