On the Digital Cohomology Modules

Dae-Woong Lee
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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

Mathematics, 2020, vol. 8, issue 9, 1-21

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.

Keywords: pointed digital homotopy; digital cohomology module; digital convolution; digital primitive cohomology class (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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