Cosheaves
Algebraic Topology
2018-04-24 v1
Abstract
The categories pCS(X,Pro(k)) of precosheaves and CS(X,Pro(k)) of cosheaves on a small Grothendieck site X, with values in the category Pro(k) of pro-k-modules, are constructed. It is proved that pCS(X,Pro(k)) satisfies the AB4 and AB5* axioms, while CS(X,Pro(k)) satisfies AB3 and AB5*. Homology theories for cosheaves and precosheaves, based on quasi-projective resolutions, are constructed and investigated.
Cite
@article{arxiv.1804.07988,
title = {Cosheaves},
author = {Andrei V. Prasolov},
journal= {arXiv preprint arXiv:1804.07988},
year = {2018}
}