%0 Journal Article
%T Some aspects of cosheaves on diffeological spaces
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Ahmadi, Alireza Alireza
%A Dehghan Nezhad, Akbar
%D 2020
%\ 01/01/2020
%V 12
%N 1
%P 123-147
%! Some aspects of cosheaves on diffeological spaces
%K Cosheaves
%K quasi-cosheaves
%K site of plots
%K covering generating families
%K quasi-v{C}ech homology
%K diffeological spaces
%R
%X We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of the D-topological structure. We also study quasi-cosheaves, defined by pre-cosheaves which respect the colimit over covering generating families, and prove that cosheaves are quasi-cosheaves. Finally, a so-called quasi-v{C}ech homology with values in pre-cosheaves is established for diffeological spaces.
%U http://cgasa.sbu.ac.ir/article_87119_6b625005860bfe6a4bd5da17a099b89b.pdf