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What are some applications of cosheaf homology within mathematics? Some ones I've heard of Sheaves (not cosheaves) are computing global sections and the Picard Group with a sheaf on projective space.

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    $\begingroup$ I do not know anything about cosheaf homology. However, cosheaves were used quite seriously by Anibal Medina in his PhD thesis. $\endgroup$ – Jason Starr May 16 '16 at 20:09

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