Internal Categorical Structures and Their Applications
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/3/660 |
| _version_ | 1797623809533018112 |
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| author | Nelson Martins-Ferreira |
| author_facet | Nelson Martins-Ferreira |
| author_sort | Nelson Martins-Ferreira |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T09:34:01Z |
| format | Article |
| id | doaj.art-18c6103a78d14bfe99389124f6720002 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:34:01Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-18c6103a78d14bfe99389124f67200022023-11-16T17:22:45ZengMDPI AGMathematics2227-73902023-01-0111366010.3390/math11030660Internal Categorical Structures and Their ApplicationsNelson Martins-Ferreira0Politécnico de Leiria, 2411-901 Leiria, PortugalWhile 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.https://www.mdpi.com/2227-7390/11/3/660Mal’tsev categorynaturally Mal’tsevweakly Mal’tsevinternal categoryinternal groupoidmultiplicative graph |
| spellingShingle | Nelson Martins-Ferreira Internal Categorical Structures and Their Applications Mathematics Mal’tsev category naturally Mal’tsev weakly Mal’tsev internal category internal groupoid multiplicative graph |
| title | Internal Categorical Structures and Their Applications |
| title_full | Internal Categorical Structures and Their Applications |
| title_fullStr | Internal Categorical Structures and Their Applications |
| title_full_unstemmed | Internal Categorical Structures and Their Applications |
| title_short | Internal Categorical Structures and Their Applications |
| title_sort | internal categorical structures and their applications |
| topic | Mal’tsev category naturally Mal’tsev weakly Mal’tsev internal category internal groupoid multiplicative graph |
| url | https://www.mdpi.com/2227-7390/11/3/660 |
| work_keys_str_mv | AT nelsonmartinsferreira internalcategoricalstructuresandtheirapplications |