IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p2082-d449116.html
   My bibliography  Save this article

Coalgebras on Digital Images

Author

Listed:
  • Sunyoung 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
    The authors contributed equally to this work.)

  • 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
    The authors contributed equally to this work.)

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 1 R 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.

Suggested Citation

  • Sunyoung Lee & Dae-Woong Lee, 2020. "Coalgebras on Digital Images," Mathematics, MDPI, vol. 8(11), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2082-:d:449116
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/2082/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/11/2082/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Huaiwen Guo & Shuanhong Wang, 2023. "A Duality Theorem for Hopf Quasimodule Algebras," Mathematics, MDPI, vol. 11(6), pages 1-16, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dae-Woong Lee, 2020. "On the Digital Cohomology Modules," Mathematics, MDPI, vol. 8(9), pages 1-21, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2082-:d:449116. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.