Ahmadi, A., Dehghan Nezhad, A. (2019). Some aspects of cosheaves on diffeological spaces. Categories and General Algebraic Structures with Applications, (), -.

Alireza Alireza Ahmadi; Akbar Dehghan Nezhad. "Some aspects of cosheaves on diffeological spaces". Categories and General Algebraic Structures with Applications, , , 2019, -.

Ahmadi, A., Dehghan Nezhad, A. (2019). 'Some aspects of cosheaves on diffeological spaces', Categories and General Algebraic Structures with Applications, (), pp. -.

Ahmadi, A., Dehghan Nezhad, A. Some aspects of cosheaves on diffeological spaces. Categories and General Algebraic Structures with Applications, 2019; (): -.

^{1}Department of Math. Yazd University Yazd, Iran

^{2}School of Mathematics, Iran University of Science and Technology, Narmak,Tehran, 16846--13114, Iran

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.

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