  This is an introductory paper about the category of regular oriented matroids
(ROMs). We compare the homotopy types of the categories of regular and binary
matroids. For example, in the unoriented case, they have the same fundamental
group but we show that the higher homotopy groups are different for rank three
regular and binary matroids. We also speculate on the possible impact of a
recent theorem of Galatius [Gal] computing the stable cohomology of the
category of graphs and on possible applications to higher Reidemeister torsion.
