 Internal Categorical Structures and Their ApplicationsNelson Martins-Ferreira ()
Mathematics, 2023, vol. 11, issue 3, 1-34 Abstract: While surveying some internal categorical structures and their applications, it is shown that triangulations and internal groupoids can be unified as two different instances of the same common structure, namely a multi-link. A brief survey includes the categories of directed graphs, reflexive graphs, links, multi-links, triangulations, trigraphs, multiplicative graphs, groupoids, pregroupoids, internal categories, kites, directed kites and multiplicative kites. Most concepts are well-known, and all of them have appeared in print at least once. For example, a multiplicative directed kite has been used as a common generalization for an internal category and a pregroupoid. The scope of the notion of centralization for equivalence relations is widened into the context of digraphs while providing a new characterization of internal groupoids. Keywords: Mal’tsev category; naturally Mal’tsev; weakly Mal’tsev; internal category; internal groupoid; multiplicative graph; directed kite; strong relation; triangulation; link; multi-link (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:3:p:660-:d:1049171 Access Statistics for this article Mathematics is currently edited by Ms. Emma He More articles in Mathematics from MDPI |
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