Precoshieves of pro-sets and abelian pro-groups are smooth

Details Precoshieves of pro-sets and abelian pro-groups are smooth Precoshieves of pro-sets and abelian pro-groups are smooth

2011-05-16

arxiv.org/abs/1105.3167v1

Mathematics

Algebraic Topology

Scientific paper

Let $\mathbb{D}$ be the category of pro-sets (or abelian pro-groups). It is proved that for any Grothendieck site $X$, there exists a reflector from the category of precosheaves on $X$ with values in $\mathbb{D}$ to the full subcategory of cosheaves. In the case of precosheaves on topological spaces, it is proved that any precosheaf is smooth, i.e. is locally isomorphic to a cosheaf. Locally constant cosheaves are constructed, and there are established connections with shape theory.

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