{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:20:44Z","timestamp":1740122444172,"version":"3.37.3"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T00:00:00Z","timestamp":1658707200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T00:00:00Z","timestamp":1658707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2022,12]]},"DOI":"10.1007\/s10485-022-09686-w","type":"journal-article","created":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T03:14:41Z","timestamp":1658718881000},"page":"1153-1176","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Cocartesian Image of Preorders and Equivalence Relations in Regular Categories"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6774-1896","authenticated-orcid":false,"given":"Dominique","family":"Bourn","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,7,25]]},"reference":[{"key":"9686_CR1","first-page":"1","volume-title":"Exact Categories, Lecture Notes in Mathematics","author":"M Barr","year":"1971","unstructured":"Barr, M.: Exact Categories, Lecture Notes in Mathematics, vol. 236, pp. 1\u2013120. Springer, Berlin (1971)"},{"key":"9686_CR2","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1016\/j.aim.2003.09.004","volume":"187","author":"D Bourn","year":"2004","unstructured":"Bourn, D.: Protomodular aspect of the dual of a topos. Adv. Math. 187, 240\u2013255 (2004)","journal-title":"Adv. Math."},{"key":"9686_CR3","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/s00012-004-1880-2","volume":"52","author":"D Bourn","year":"2005","unstructured":"Bourn, D.: Fibration of points and congruence modularity. Algebra Univ. 52, 403\u2013429 (2005)","journal-title":"Algebra Univ."},{"key":"9686_CR4","first-page":"142","volume":"59\u20132","author":"D Bourn","year":"2018","unstructured":"Bourn, D.: Suprema of equivalence relations and non-regular Goursat categories. Cahiers Topol. G\u00e9om. Differ. Categ. 59\u20132, 142\u2013194 (2018)","journal-title":"Cahiers Topol. G\u00e9om. Differ. Categ."},{"key":"9686_CR5","first-page":"77","volume-title":"Galois Theory, Hopf Algebras, and Semiabelian Categories. Fields Institute Communications","author":"D Bourn","year":"2004","unstructured":"Bourn, D., Gran, M.: Categorical aspects of modularity. In: Janelidze, G., Pareigis, B., Tholen, W. (eds.) Galois Theory, Hopf Algebras, and Semiabelian Categories. Fields Institute Communications, vol. 43, pp. 77\u2013100. American Mathematical Society, Providence (2004)"},{"key":"9686_CR6","doi-asserted-by":"publisher","first-page":"3825","DOI":"10.1081\/AGB-200027750","volume":"32","author":"D Bourn","year":"2004","unstructured":"Bourn, D., Gran, M.: Normal sections and direct product decompositions. Commun. Algebra 32, 3825\u20133842 (2004)","journal-title":"Commun. Algebra"},{"key":"9686_CR7","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/BF00872942","volume":"1","author":"A Carboni","year":"1993","unstructured":"Carboni, A., Kelly, G.M., Pedicchio, M.C.: Some remarks on Mal\u2019cev and Goursat categories. Appl. Categ. Struct. 1, 385\u2013421 (1993)","journal-title":"Appl. Categ. Struct."},{"key":"9686_CR8","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/0022-4049(91)90022-T","volume":"69","author":"A Carboni","year":"1991","unstructured":"Carboni, A., Lambek, J., Pedicchio, M.C.: Diagram chasing in Mal\u2019cev categories. J. Pure Appl. Algebra 69, 271\u2013284 (1991)","journal-title":"J. Pure Appl. Algebra"},{"key":"9686_CR9","doi-asserted-by":"publisher","first-page":"505","DOI":"10.21136\/CMJ.1983.101905","volume":"33","author":"I Chadja","year":"1983","unstructured":"Chadja, I., Rachunek, J.: Relational characterizations of permutable and $$n$$-permutable varieties. Czechoslov. Math. J. 33, 505\u2013508 (1983)","journal-title":"Czechoslov. Math. J."},{"key":"9686_CR10","doi-asserted-by":"publisher","first-page":"167","DOI":"10.4153\/CMB-1969-016-6","volume":"12","author":"A Day","year":"1969","unstructured":"Day, A.: A characterization of modularity for congruence lattices of algebras. Can. Math. Bull. 12, 167\u2013173 (1969)","journal-title":"Can. Math. Bull."},{"key":"9686_CR11","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s10485-010-9236-x","volume":"20","author":"M Gran","year":"2012","unstructured":"Gran, M., Rodelo, D.: A new characterization of Goursat categories. Appl. Categ. Struct. 20, 229\u2013238 (2012)","journal-title":"Appl. Categ. Struct."},{"key":"9686_CR12","volume-title":"Geometrical Methods in Congruence Modular Varieties","author":"HP Gumm","year":"1983","unstructured":"Gumm, H.P.: Geometrical Methods in Congruence Modular Varieties, vol. 45. Memoirs of American Mathematical Society, Providence (1983)"},{"key":"9686_CR13","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1007\/BF02945100","volume":"3","author":"J Hagemann","year":"1973","unstructured":"Hagemann, J., Mitschke, A.: On n-permutable congruences. Algebra Univ. 3, 8\u201312 (1973)","journal-title":"Algebra Univ."},{"key":"9686_CR14","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s40062-013-0044-5","volume":"9","author":"Z Janelidze","year":"2014","unstructured":"Janelidze, Z., Rodelo, D., Van der Linden, T.: Hagemann\u2019s theorem for regular categories. J. Homotopy Relat. Struct. 9, 55\u201366 (2014)","journal-title":"J. Homotopy Relat. Struct."},{"key":"9686_CR15","volume-title":"Topos Theory","author":"PT Johnstone","year":"1977","unstructured":"Johnstone, P.T.: Topos Theory. Academic Press, London (1977)"},{"key":"9686_CR16","doi-asserted-by":"publisher","first-page":"223","DOI":"10.36045\/bbms\/1400592620","volume":"21","author":"N Martins-Ferreira","year":"2014","unstructured":"Martins-Ferreira, N., Rodelo, D., Van der Linden, T.: An observation on $$n$$-permutability. Bull. Belg. Math. Soc. Simon Stevin 21, 223\u2013230 (2014)","journal-title":"Bull. Belg. Math. Soc. Simon Stevin"},{"key":"9686_CR17","first-page":"189","volume":"58","author":"S Tull","year":"2017","unstructured":"Tull, S.: Conditions for an n-permutable category to be Mal\u2019tsev. Cahiers Topol. G\u00e9om. Differ. Cat\u00e9g. 58, 189\u2013194 (2017)","journal-title":"Cahiers Topol. G\u00e9om. Differ. Cat\u00e9g."}],"container-title":["Applied Categorical Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-022-09686-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10485-022-09686-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-022-09686-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T12:12:17Z","timestamp":1670242337000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10485-022-09686-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,25]]},"references-count":17,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["9686"],"URL":"https:\/\/doi.org\/10.1007\/s10485-022-09686-w","relation":{},"ISSN":["0927-2852","1572-9095"],"issn-type":[{"type":"print","value":"0927-2852"},{"type":"electronic","value":"1572-9095"}],"subject":[],"published":{"date-parts":[[2022,7,25]]},"assertion":[{"value":"1 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 June 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 July 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}