Geodesic
Cosheaves
Theory and applications of categories, Tome 37 (2021), pp. 1080-1148 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : Primary 18F10, 18F20, 18G05, 18G10, Secondary 55P55, 55Q07, 14F20
Keywords: Cosheaves, precosheves, cosheafification, pro-category, cosheaf homology, precosheaf homology, Čech homology, shape theory, pro-homology, pro-homotopy, locally presentable categories. 
@article{TAC_2021_37_a32,
     author = {Andrei V. Prasolov},
     title = {Cosheaves},
     journal = {Theory and applications of categories},
     pages = {1080--1148},
     year = {2021},
     volume = {37},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_37_a32/}
}
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Andrei V. Prasolov. Cosheaves. Theory and applications of categories, Tome 37 (2021), pp. 1080-1148. http://geodesic.mathdoc.fr/item/TAC_2021_37_a32/