Matroids, Feynman categories, and Koszul duality

We show that various combinatorial invariants of matroids such as Chow rings and Orlik–Solomon algebras may be assembled into “operad-like” structures. Specifically, one obtains several operads over a certain Feynman category which we introduce and study in detail. In addition, we establish a Koszul-type duality between Chow rings and Orlik–Solomon algebras, vastly generalizing a celebrated result of Getzler. This provides a new interpretation of combinatorial Leray models of Orlik–Solomon algebras.