1 citations · 2 across the 4 of their papers we have counts for
6 papers
Cosheaf homology
Andrei V. Prasolov
In this paper the cosheaf homology is investigated from different viewpoints: the behavior under site morphisms, connections with Cech homology via spectral sequences, and descript…
Cosheaves
Andrei V. Prasolov
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…
Cosheafification
Andrei V. Prasolov
It is proved that for any Grothendieck site , there exists a coreflection (called ) from the category of precosheaves on with values in a category…
On the universal coefficients formula for shape homology
Andrei V. Prasolov
In this paper it is investigated whether various shape homology theories satisfy the Universal Coefficients Formula (UCF). It is proved that pro-homology and strong homology satisf…
Precosheaves of pro-sets and abelian pro-groups are smooth
Andrei V. Prasolov
Let be the category of pro-sets (or abelian pro-groups). It is proved that for any Grothendieck site , there exists a reflector from the category of precosheaves on…
Quasi-shape theory of locally finite and paracompact spaces
Andrei V. Prasolov
Shape theory works nice for (Hausdorff) paracompact spaces, but for spaces with no separation axioms, it seems to be quite poor. However, for finite and locally finite spaces their…