{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:49:00Z","timestamp":1760147340575,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T00:00:00Z","timestamp":1674864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia FCT\/MCTES (PIDDAC)","award":["LA\/P\/\u20130112\/2020","UIDP\/04044\/2020","UIDB\/04\u2013044\/2020","PAMI\u2013ROTEIRO\/0328\/2013 (N\u00ba 022158)","MATIS (CEN\u2013TRO-01-0145-FEDER-000014 - 3362)","CENTRO-01-0247-FEDER-069665","POCI-01-0247-FEDER-069603","POCI-01-0247-FEDER-039958","CENTRO-01-0247-FEDER-039969","POCI-01-0247-FEDER-039863","POCI-01-0247-FEDER-024533"],"award-info":[{"award-number":["LA\/P\/\u20130112\/2020","UIDP\/04044\/2020","UIDB\/04\u2013044\/2020","PAMI\u2013ROTEIRO\/0328\/2013 (N\u00ba 022158)","MATIS (CEN\u2013TRO-01-0145-FEDER-000014 - 3362)","CENTRO-01-0247-FEDER-069665","POCI-01-0247-FEDER-069603","POCI-01-0247-FEDER-039958","CENTRO-01-0247-FEDER-039969","POCI-01-0247-FEDER-039863","POCI-01-0247-FEDER-024533"]}]},{"name":"Polytechnic Institute of Leiria","award":["LA\/P\/\u20130112\/2020","UIDP\/04044\/2020","UIDB\/04\u2013044\/2020","PAMI\u2013ROTEIRO\/0328\/2013 (N\u00ba 022158)","MATIS (CEN\u2013TRO-01-0145-FEDER-000014 - 3362)","CENTRO-01-0247-FEDER-069665","POCI-01-0247-FEDER-069603","POCI-01-0247-FEDER-039958","CENTRO-01-0247-FEDER-039969","POCI-01-0247-FEDER-039863","POCI-01-0247-FEDER-024533"],"award-info":[{"award-number":["LA\/P\/\u20130112\/2020","UIDP\/04044\/2020","UIDB\/04\u2013044\/2020","PAMI\u2013ROTEIRO\/0328\/2013 (N\u00ba 022158)","MATIS (CEN\u2013TRO-01-0145-FEDER-000014 - 3362)","CENTRO-01-0247-FEDER-069665","POCI-01-0247-FEDER-069603","POCI-01-0247-FEDER-039958","CENTRO-01-0247-FEDER-039969","POCI-01-0247-FEDER-039863","POCI-01-0247-FEDER-024533"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/math11030660","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T09:18:21Z","timestamp":1675070301000},"page":"660","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Internal Categorical Structures and Their Applications"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4199-7367","authenticated-orcid":false,"given":"Nelson","family":"Martins-Ferreira","sequence":"first","affiliation":[{"name":"Polit\u00e9cnico de Leiria, 2411-901 Leiria, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,28]]},"reference":[{"key":"ref_1","first-page":"22","article-title":"On the structure of a triangulation","volume":"5","year":"2015","journal-title":"Scripta-Ingenia"},{"unstructured":"Mac Lane, S. 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