Coalgebras on digital images

Sunyoung Lee; Dae Woong Lee

doi:10.3390/math8112082

Coalgebras on digital images

Sunyoung Lee
, Dae Woong Lee^*

^*Corresponding author for this work

Department of Mathematics

Jeonbuk National University

Research output: Contribution to journal › Journal article › peer-review

1 Scopus citations

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.

Original language	English
Article number	2082
Pages (from-to)	1-21
Number of pages	21
Journal	Mathematics
Volume	8
Issue number	11
DOIs	https://doi.org/10.3390/math8112082
State	Published - 2020.11

Keywords

Coalgebra
Coalgebra comultiplication
Coalgebra counit
Digital (co)homology module
Digital image

Quacquarelli Symonds(QS) Subject Topics

Mathematics

Access to Document

10.3390/math8112082

Cite this

@article{681ea04b0a7b4888b5324cb7135a3d93,

title = "Coalgebras on digital images",

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 = "Coalgebra, Coalgebra comultiplication, Coalgebra counit, Digital (co)homology module, Digital image",

author = "Sunyoung Lee and Lee, \{Dae Woong\}",

note = "Publisher Copyright: {\textcopyright}2020 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2020",

month = nov,

doi = "10.3390/math8112082",

language = "English",

volume = "8",

pages = "1--21",

journal = "Mathematics",

issn = "2227-7390",

number = "11",

}

TY - JOUR

T1 - Coalgebras on digital images

AU - Lee, Sunyoung

AU - Lee, Dae Woong

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - Coalgebra

KW - Coalgebra comultiplication

KW - Coalgebra counit

KW - Digital (co)homology module

KW - Digital image

UR - https://www.scopus.com/pages/publications/85096501387

U2 - 10.3390/math8112082

DO - 10.3390/math8112082

M3 - Journal article

AN - SCOPUS:85096501387

SN - 2227-7390

VL - 8

SP - 1

EP - 21

JO - Mathematics

JF - Mathematics

IS - 11

M1 - 2082

ER -

Coalgebras on digital images

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

Other files and links

Fingerprint

Cite this