Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585312120200101Some aspects of cosheaves on diffeological spaces12314787119ENAlireza AlirezaAhmadiDepartment of Math. Yazd University
Yazd, IranAkbarDehghan NezhadSchool of Mathematics, Iran University of Science and Technology,
Narmak,Tehran, 16846--13114, IranJournal Article20181017We 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.http://cgasa.sbu.ac.ir/article_87119_6b625005860bfe6a4bd5da17a099b89b.pdf