Bounding volume by systoles of 3-manifolds

We prove a new systolic volume lower bound for non-orientable n-manifolds, involving the stable 1-systole as well as the codimension-1 systole with coe. cients in Z(2). As an application, we prove that Lusternik-Schnirelmann category and systolic category agree for non-orientable closed manifolds of dimension 3, extending our earlier result in the orientable case. Finally, we prove the homotopy invariance of systolic category.