Categorical graph minor conjecture

Let $cmathcal{GM}$ be the category of graphs and minor morphisms. A category is Noetherian over a ring if its associated module categories satisfy the relevant ascending-chain finiteness property. Categorical graph minor conjecture. The category $cmathcal{GM}$ is Noetherian over any Noetherian ring. This is a categorical strengthening of the Robertson–Seymour graph minor theorem. The paper states that, together with the categorical Robertson conjecture, it would imply universal finite generation for homology of graph configuration spaces.