{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T13:53:20Z","timestamp":1775138000384,"version":"3.50.1"},"reference-count":9,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:00:00Z","timestamp":1769904000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:00:00Z","timestamp":1769904000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Universit\u00e9 du littoral c\u00f4te d\u2019opale"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We give an elementary characterization of those quantaloids\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\mathcal {Q}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>Q<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    for which the category\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\textsf{Cat}(\\mathcal {Q})$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>Cat<\/mml:mi>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mi>Q<\/mml:mi>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\mathcal {Q}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>Q<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -enriched categories and functors is cartesian closed. We then unify several known cases (previously proven using\n                    <jats:italic>ad hoc<\/jats:italic>\n                    methods) and we give some new examples.\n                  <\/jats:p>","DOI":"10.1007\/s10485-026-09846-2","type":"journal-article","created":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T14:27:10Z","timestamp":1769956030000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["When is $$\\textsf{Cat}(\\mathcal {Q})$$ Cartesian Closed?"],"prefix":"10.1007","volume":"34","author":[{"given":"Isar","family":"Stubbe","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junche","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,1]]},"reference":[{"key":"9846_CR1","doi-asserted-by":"publisher","first-page":"3113","DOI":"10.1016\/j.topol.2005.01.038","volume":"153","author":"MM Clementino","year":"2006","unstructured":"Clementino, M.M., Hofmann, D.: Exponentiation in $$\\cal{V} $$-categories. Top. Appl. 153, 3113\u20133128 (2006)","journal-title":"Top. Appl."},{"key":"9846_CR2","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s10485-007-9104-5","volume":"17","author":"MM Clementino","year":"2009","unstructured":"Clementino, M.M., Hofmann, D., Stubbe, I.: Exponentiable functors between quantaloid-enriched categories. Appl. Categor. Struct. 17, 91\u2013101 (2009)","journal-title":"Appl. Categor. Struct."},{"key":"9846_CR3","first-page":"307","volume":"59","author":"D Hofmann","year":"2018","unstructured":"Hofmann, D., Stubbe, I.: Topology from enrichment: the curious case of partial metrics. Cahiers Topol. G\u00e9om. Diff. Cat\u00e9g. 59, 307\u2013353 (2018)","journal-title":"Cahiers Topol. G\u00e9om. Diff. Cat\u00e9g."},{"key":"9846_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2024.109243","volume":"503","author":"H Lai","year":"2025","unstructured":"Lai, H., Luo, Q.: Cartesian closed and stable subconstructs of $$[0,1]$$-Cat. Fuzzy Sets Syst. 503, 109243 (2025)","journal-title":"Fuzzy Sets Syst."},{"key":"9846_CR5","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.fss.2014.10.031","volume":"282","author":"H Lai","year":"2016","unstructured":"Lai, H., Zhang, D.: Closedness of the category of liminf complete fuzzy orders. Fuzzy Sets Syst. 282, 86\u201398 (2016)","journal-title":"Fuzzy Sets Syst."},{"key":"9846_CR6","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/BF02924844","volume":"43","author":"FW Lawvere","year":"1973","unstructured":"Lawvere, F.W.: Metric spaces, generalized logic and closed categories. Rend. Sem. Mat. Fis. Milano 43, 135\u2013166 (1973). (Republished in: Reprints Theory Appl. Categ. 1 (2002) pp. 1\u201337)","journal-title":"Rend. Sem. Mat. Fis. Milano"},{"key":"9846_CR7","unstructured":"\u0141ukasiewicz, J.: O logice tr\u00f3jwarto\u015bciowej, Ruch filozoficzny 5 (1920) pp. 170\u2013171. English translation: On three-valued logic. In: Borkowski, L. (ed.) Selected works by Jan \u0141ukasiewicz, pp. 87\u201388. North-Holland, Amsterdam (1970)"},{"key":"9846_CR8","unstructured":"Rosenthal, K.I.: The theory of quantaloids, Pitman Research Notes in Mathematics Series 348. Longman, Harlow (1996)"},{"key":"9846_CR9","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.fss.2013.08.009","volume":"256","author":"I Stubbe","year":"2014","unstructured":"Stubbe, I.: An introduction to quantaloid-enriched categories. Fuzzy Sets Syst. 256, 95\u2013116 (2014)","journal-title":"Fuzzy Sets Syst."}],"container-title":["Applied Categorical Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-026-09846-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10485-026-09846-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-026-09846-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T13:06:08Z","timestamp":1775135168000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10485-026-09846-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,1]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["9846"],"URL":"https:\/\/doi.org\/10.1007\/s10485-026-09846-2","relation":{},"ISSN":["0927-2852","1572-9095"],"issn-type":[{"value":"0927-2852","type":"print"},{"value":"1572-9095","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,1]]},"assertion":[{"value":"28 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 February 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"9"}}