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On the Digital Cohomology Modules

Author

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  • Dae-Woong Lee

    (Department of Mathematics, and Institute of Pure and Applied Mathematics, Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do 54896, Korea)

Abstract

In this paper, we consider the digital cohomology modules of a digital image consisting of a bounded and finite subset of Z n and an adjacency relation. We construct a contravariant functor from the category of digital images and digital continuous functions to the category of unitary R -modules and R -module homomorphisms via the category of cochain complexes of R -modules and cochain maps, where R is a commutative ring with identity 1 R . We also examine the digital primitive cohomology classes based on digital images and find the relationship between R -module homomorphisms of digital cohomology modules induced by the digital convolutions and digital continuous functions.

Suggested Citation

  • Dae-Woong Lee, 2020. "On the Digital Cohomology Modules," Mathematics, MDPI, vol. 8(9), pages 1-21, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1451-:d:405933
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    References listed on IDEAS

    as
    1. Dae-Woong Lee, 2020. "Comultiplications on the Localized Spheres and Moore Spaces," Mathematics, MDPI, vol. 8(1), pages 1-19, January.
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