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Article

Coalgebras on Digital Images

Department of Mathematics, and Institute of Pure and Applied Mathematics, Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do 54896, Korea
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Author to whom correspondence should be addressed.
The authors contributed equally to this work.
Mathematics 2020, 8(11), 2082; https://doi.org/10.3390/math8112082
Submission received: 10 November 2020 / Revised: 18 November 2020 / Accepted: 19 November 2020 / Published: 22 November 2020

Abstract

In this article, we investigate the fundamental properties of coalgebras with coalgebra comultiplications, counits, and coalgebra homomorphisms of coalgebras over a commutative ring R with identity 1R based on digital images with adjacency relations. We also investigate a contravariant functor from the category of digital images and digital continuous functions to the category of coalgebras and coalgebra homomorphisms based on digital images via the category of unitary R-modules and R-module homomorphisms.
Keywords: digital image; digital (co)homology module; coalgebra; coalgebra comultiplication; coalgebra counit digital image; digital (co)homology module; coalgebra; coalgebra comultiplication; coalgebra counit

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MDPI and ACS Style

Lee, S.; Lee, D.-W. Coalgebras on Digital Images. Mathematics 2020, 8, 2082. https://doi.org/10.3390/math8112082

AMA Style

Lee S, Lee D-W. Coalgebras on Digital Images. Mathematics. 2020; 8(11):2082. https://doi.org/10.3390/math8112082

Chicago/Turabian Style

Lee, Sunyoung, and Dae-Woong Lee. 2020. "Coalgebras on Digital Images" Mathematics 8, no. 11: 2082. https://doi.org/10.3390/math8112082

APA Style

Lee, S., & Lee, D.-W. (2020). Coalgebras on Digital Images. Mathematics, 8(11), 2082. https://doi.org/10.3390/math8112082

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