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Article

On the Concept of Algebraic Crystallography

UR 2597, LMPA-Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville, Université Littoral Côte d’Opale, F-62100 Calais, France
Mathematics 2025, 13(21), 3404; https://doi.org/10.3390/math13213404 (registering DOI)
Submission received: 9 September 2025 / Revised: 15 October 2025 / Accepted: 23 October 2025 / Published: 26 October 2025
(This article belongs to the Section A: Algebra and Logic)

Abstract

Category Theory provides us with a clear notion of what is an internal algebraic structure. This will allow us to focus our attention on a certain kind of relationship between context and structure; namely on categories E (context) in which, on any object X, there is, at most, one algebraic structure of some type S.
Keywords: internal structures; uniqueness of structures; context; varieties and categories; context vs. structure internal structures; uniqueness of structures; context; varieties and categories; context vs. structure

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MDPI and ACS Style

Bourn, D. On the Concept of Algebraic Crystallography. Mathematics 2025, 13, 3404. https://doi.org/10.3390/math13213404

AMA Style

Bourn D. On the Concept of Algebraic Crystallography. Mathematics. 2025; 13(21):3404. https://doi.org/10.3390/math13213404

Chicago/Turabian Style

Bourn, Dominique. 2025. "On the Concept of Algebraic Crystallography" Mathematics 13, no. 21: 3404. https://doi.org/10.3390/math13213404

APA Style

Bourn, D. (2025). On the Concept of Algebraic Crystallography. Mathematics, 13(21), 3404. https://doi.org/10.3390/math13213404

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