Some aspects of cosheaves on diffeological spaces

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AHMADI ALIREZA; Dehghan Nezhad Akbar

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Journal: CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS Year:2020 | Volume:12 | Issue:1 Page(s): 123-147

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Title

Some aspects of cosheaves on diffeological spaces

Author(s)

AHMADI ALIREZA | Dehghan Nezhad Akbar | Issue Writer Certificate

Keywords

CosheavesQ4

quasi-cosheavesQ4

site of plotsQ4

covering generating familiesQ4

quasi-Cech homologyQ4

diffeological spacesQ4

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 Poincaré 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 quasiCosheaves, defined by pre-Cosheaves which respect the colimit over covering generating families, and prove that Cosheaves are quasi-Cosheaves. Finally, a so-called quasi-Cech homology with values in pre-Cosheaves is established for diffeological spaces.

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APA: Copy

AHMADI, ALIREZA, & Dehghan Nezhad, Akbar. (2020). Some aspects of cosheaves on diffeological spaces. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, 12(1 ), 123-147. SID. https://sid.ir/paper/255399/en

Vancouver: Copy

AHMADI ALIREZA, Dehghan Nezhad Akbar. Some aspects of cosheaves on diffeological spaces. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS[Internet]. 2020;12(1 ):123-147. Available from: https://sid.ir/paper/255399/en

IEEE: Copy

ALIREZA AHMADI, and Akbar Dehghan Nezhad, “Some aspects of cosheaves on diffeological spaces,” CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, vol. 12, no. 1 , pp. 123–147, 2020, [Online]. Available: https://sid.ir/paper/255399/en

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