Matroid correspondence

Motivated by algebraic correspondences and linear operators associated with volume and Lorentzian polynomials, we introduce matroid correspondences and their polymatroid analogues.

A matroid correspondence defines a functor between poset categories of matroids whose morphisms are matroid quotients, and various standard functors, including deletion, contraction, free extension, truncation, intersection, union, and pullback, arise in this way.

We show that these correspondences preserve representability and algebraicity under natural hypotheses.

In the polymatroid setting, we establish compatibility with multisymmetric lifts.

Finally, we relate this construction to the supports of linear operators with Lorentzian symbols.