{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:44:55Z","timestamp":1762177495211,"version":"3.37.3"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T00:00:00Z","timestamp":1648684800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T00:00:00Z","timestamp":1648684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001230","name":"Macquarie University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001230","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2022,10]]},"abstract":"Abstract<\/jats:title>We prove that for each locally $$\\alpha $$<\/jats:tex-math>\n \u03b1<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-presentable category $${\\mathcal {K}}$$<\/jats:tex-math>\n K<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> there exists a regular cardinal $$\\gamma $$<\/jats:tex-math>\n \u03b3<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> such that any $$\\alpha $$<\/jats:tex-math>\n \u03b1<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-accessible functor out of $${\\mathcal {K}}$$<\/jats:tex-math>\n K<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (into another locally $$\\alpha $$<\/jats:tex-math>\n \u03b1<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-presentable category) is continuous if and only if it preserves $$\\gamma $$<\/jats:tex-math>\n \u03b3<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-small limits; as a consequence we obtain a new adjoint functor theorem specific to the $$\\alpha $$<\/jats:tex-math>\n \u03b1<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-accessible functors out of $${\\mathcal {K}}$$<\/jats:tex-math>\n K<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Afterwards we generalize these results to the enriched setting and deduce, among other things, that a small $${\\mathcal {V}}$$<\/jats:tex-math>\n V<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-category is accessible if and only if it is Cauchy complete.<\/jats:p>","DOI":"10.1007\/s10485-022-09677-x","type":"journal-article","created":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T04:02:45Z","timestamp":1648699365000},"page":"937-946","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On Continuity of Accessible Functors"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1001-6690","authenticated-orcid":false,"given":"Giacomo","family":"Tendas","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,31]]},"reference":[{"key":"9677_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600579","volume-title":"Locally Presentable and Accessible Categories. 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Math."},{"key":"9677_CR4","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/BF01190851","volume":"28","author":"GM Bergman","year":"1991","unstructured":"Bergman, G.M.: Actions of Boolean rings on sets. Algebra Universalis 28, 153\u2013187 (1991)","journal-title":"Algebra Universalis"},{"issue":"3","key":"9677_CR5","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1017\/S0004972700021900","volume":"54","author":"F Borceux","year":"1996","unstructured":"Borceux, F., Quinteiro, C.: Enriched accessible categories. Bull. Aust. Math. Soc. 54(3), 489\u2013501 (1996)","journal-title":"Bull. Aust. Math. Soc."},{"key":"9677_CR6","first-page":"47","volume":"4","author":"F Borceux","year":"1998","unstructured":"Borceux, F., Quinteiro, C., Rosick\u00fd, J.: A theory of enriched sketches. Theory Appl. Categ. 4, 47\u201372 (1998)","journal-title":"Theory Appl. Categ."},{"key":"9677_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059396","volume-title":"Lokal pr\u00e4sentierbare Kategorien. Lecture Notes in Mathematics","author":"P Gabriel","year":"1971","unstructured":"Gabriel, P., Ulmer, F.: Lokal pr\u00e4sentierbare Kategorien. Lecture Notes in Mathematics, vol. 221. Springer, Berlin (1971)"},{"key":"9677_CR8","volume-title":"Basic Concepts of Enriched Category Theory","author":"GM Kelly","year":"1982","unstructured":"Kelly, G.M.: Basic Concepts of Enriched Category Theory. Cambridge University Press, Cambridge (1982)"},{"unstructured":"Kelly, G.M.: Structures defined by finite limits in the enriched context. I. Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle 23(1), 3\u201342 (1982). Third Colloquium on Categories, Part VI (Amiens, 1980)","key":"9677_CR9"},{"key":"9677_CR10","first-page":"555","volume":"8","author":"GM Kelly","year":"2001","unstructured":"Kelly, G.M., Lack, S.: V-Cat is locally presentable or locally bounded if V is so. Theory Appl. Categ. 8, 555\u2013575 (2001)","journal-title":"Theory Appl. Categ."},{"issue":"17","key":"9677_CR11","first-page":"399","volume":"14","author":"GM Kelly","year":"2005","unstructured":"Kelly, G.M., Schmitt, V.: Notes on enriched categories with colimits of some class. Theory Appl. Categ. 14(17), 399\u2013423 (2005)","journal-title":"Theory Appl. Categ."},{"doi-asserted-by":"crossref","unstructured":"Lack, S., Tendas, G.: Flat vs. filtered colimits in the enriched context. arXiv preprint arXiv:2107.08612 (2021)","key":"9677_CR12","DOI":"10.1016\/j.aim.2022.108381"},{"key":"9677_CR13","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/104","volume-title":"Accessible Categories: The Foundations of Categorical Model Theory","author":"M Makkai","year":"1989","unstructured":"Makkai, M., Par\u00e9, R.: Accessible Categories: The Foundations of Categorical Model Theory, vol. 104. Springer, Berlin (1989)"},{"issue":"4","key":"9677_CR14","first-page":"377","volume":"24","author":"R Street","year":"1983","unstructured":"Street, R.: Absolute colimits in enriched categories. Cahiers Topologie G\u00e9om. Diff\u00e9rentielle Cat\u00e9g 24(4), 377\u2013379 (1983)","journal-title":"Cahiers Topologie G\u00e9om. 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