(joint with Ethan Kowalenko) Category O of a complex semi-simple Lie algebra has rich structure and is connected to the algebraic geometry of the cotangent bundle of the associated flag variety. Braden-Licata-Proudfoot-Webster discovered that similarly rich representation theory, which they named hypertoric category O, can be extracted from the geometry of hypertoric (a.k.a. toric hyperkahler) varieties. Motivated by this discovery, they and others introduced and studied other `geometric’ categories O associated to more general symplectic resolutions. In the current work, we generalize their notion of hypertoric category O in a different direction, to the purely combinatorial setting of oriented matroids. We are motivated in part by earlier joint work with Braden on matroidal Schur algebras.