2025/04/22 by Andrei V. Prasolov, Prasolov, Andrei V.
Mathematics · Social Sciences · #18G #Algebraic Topology (math.AT) #Category Theory (math.CT) #Diverse Cultural and Historical Studies #FOS: Mathematics #History and Theory of Mathematics
paper · pdf · doi:10.48550/arxiv.2504.16149
openalex publication_date 2025/04/22 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
In this paper the cosheaf homology is investigated from different viewpoints: the behavior under site morphisms, connections with Cech homology via spectral sequences, and description of cosheaf homology using hypercoverings. It is proved that in the case of Hausdorff paracompact spaces, the cosheaf homology in general is isomorphic to the Cech homology, and for a constant cosheaf is isomorphic to the shape pro-homology. In the case of Alexandroff spaces, including finite and locally finite spaces, the cosheaf homology is isomorphic to the singular homology.