Some aspects of cosheaves on diffeological spaces | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 7، دوره 12، شماره 1، فروردین 2020، صفحه 123-147 اصل مقاله (762.19 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.12.1.123 | ||
| نویسندگان | ||
| Alireza Alireza Ahmadi1؛ Akbar Dehghan Nezhad2 | ||
| 1Department of Math. Yazd University Yazd, Iran | ||
| 2School of Mathematics, Iran University of Science and Technology, Narmak,Tehran, 16846--13114, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Cosheaves؛ quasi-cosheaves؛ site of plots؛ covering generating families؛ quasi-v{C}ech homology؛ diffeological spaces | ||
| مراجع | ||
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