@article { author = {Ahmadi, Alireza and Dehghan Nezhad, Akbar}, title = {Some aspects of cosheaves on diffeological spaces}, journal = {Categories and General Algebraic Structures with Applications}, volume = {12}, number = {1}, pages = {123-147}, year = {2020}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {10.29252/cgasa.12.1.123}, abstract = {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.}, keywords = {Cosheaves,quasi-cosheaves,site of plots,covering generating families,quasi-v{C}ech homology,diffeological spaces}, url = {https://cgasa.sbu.ac.ir/article_87119.html}, eprint = {https://cgasa.sbu.ac.ir/article_87119_6b625005860bfe6a4bd5da17a099b89b.pdf} }