2018/04/21 by Prasolov, Andrei V.
#14F20 #18F20 #18G05 #18G10 #55Q07 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary 18F10 #Secondary 55P55
paper · doi:10.48550/arxiv.1804.07988
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.