  This paper affirms a conjecture of MacPherson: that the derived category of
cellular sheaves is equivalent to the derived category of cellular cosheaves.
We give a self-contained treatment of cellular sheaves and cosheaves and note
that certain classical dualities give rise to an exchange of sheaves with
cosheaves. Following a result of Pitts that states that cosheaves are
cocontinuous functors on the category of sheaves, we use the derived
equivalence provided here to gain a novel description of compactly supported
sheaf cohomology.
