Geodesic
Cosheafification
Theory and applications of categories, Tome 31 (2016), pp. 1134-1175.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

It is proved that for any small Grothendieck site X, there exists a coreflection (called \emph{cosheafification}) from the category of precosheaves on X with values in a category $K$, to the full subcategory of cosheaves, provided either $K$ or $K^{op}$ is locally presentable. If $K$ is cocomplete, such a coreflection is built explicitly for the (pre)cosheaves with values in the category $Pro(K)$ of pro-objects in $K$. In the case of precosheaves on topological spaces, it is proved that any precosheaf with values in $Pro(K)$ is smooth, i.e. is strongly locally isomorphic to a cosheaf. Constant cosheaves are constructed, and there are established connections with shape theory.
Publié le :
Classification : Primary 18F10, 18F20, Secondary 55P55, 55Q07, 14F20
Keywords: Cosheaves, smooth precosheaves, cosheafification, pro-category, cosheaf homology, locally presentable categories, accessible categories 
@article{TAC_2016_31_a37,
     author = {Andrei V. Prasolov},
     title = {Cosheafification},
     journal = {Theory and applications of categories},
     pages = {1134--1175},
     publisher = {mathdoc},
     volume = {31},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2016_31_a37/}
}
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Andrei V. Prasolov. Cosheafification. Theory and applications of categories, Tome 31 (2016), pp. 1134-1175. http://geodesic.mathdoc.fr/item/TAC_2016_31_a37/