Precosheaves of pro-sets and abelian pro-groups are smooth |
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Authors: | Andrei V Prasolov |
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Institution: | Institute of Mathematics and Statistics, University of Tromsø, N-9037 Tromsø, Norway |
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Abstract: | Let 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 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. Constant cosheaves are constructed, and there are established connections with shape theory. |
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Keywords: | primary 18F10 18F20 secondary 55P55 55Q07 |
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