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arXiv · 1607.06942

Dualities between Cellular Sheaves and Cosheaves

Justin Curry
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Abstract

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.

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Justin Curry. 2016-07-23. Dualities between Cellular Sheaves and Cosheaves. https://arxiv.org/abs/1607.06942

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