  q-Matroids form the q-analogue of classical matroids. In this paper we
introduce various types of maps between q-matroids. These maps are not
necessarily linear, but they map subspaces to subspaces and respect the
q-matroid structure in certain ways. The various types of maps give rise to
different categories of q-matroids. We show that only one of these categories
possesses a coproduct. This is the category where the morphisms are linear weak
maps, that is, the rank of the image of any subspace is not larger than the
rank of the subspace itself. The coproduct in this category is the very
recently introduced direct sum of q-matroids.
