TY - JOUR
ID - 87119
TI - Some aspects of cosheaves on diffeological spaces
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Ahmadi, Alireza Alireza
AU - Dehghan Nezhad, Akbar
AD - Department of Math. Yazd University
Yazd, Iran
AD - School of Mathematics, Iran University of Science and Technology,
Narmak,Tehran, 16846--13114, Iran
Y1 - 2020
PY - 2020
VL - 12
IS - 1
SP - 123
EP - 147
KW - Cosheaves
KW - quasi-cosheaves
KW - site of plots
KW - covering generating families
KW - quasi-v{C}ech homology
KW - diffeological spaces
DO -
N2 - 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.
UR - http://cgasa.sbu.ac.ir/article_87119.html
L1 - http://cgasa.sbu.ac.ir/article_87119_6b625005860bfe6a4bd5da17a099b89b.pdf
ER -