  On a finite-dimensional real vector space, we give a microlocal
characterization of (derived) piecewise linear sheaves (PL sheaves) and prove
that the triangulated category of such sheaves is generated by sheaves
associated with convex polyhedra. We then give a similar theorem for PL
gamma-sheaves, that is, PL sheaves associated with the gamma-topology, for a
closed convex polyhedral proper cone gamma. Our motivation is that convex
polyhedra may be considered as building blocks for higher dimensional barcodes.
