Dualities between Cellular Sheaves and Cosheaves
Algebraic Topology
2016-07-26 v1 Category Theory
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.1607.06942,
title = {Dualities between Cellular Sheaves and Cosheaves},
author = {Justin Curry},
journal= {arXiv preprint arXiv:1607.06942},
year = {2016}
}
Comments
32 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1303.3255