{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:41:01Z","timestamp":1776724861919,"version":"3.51.2"},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T00:00:00Z","timestamp":1713139200000},"content-version":"unspecified","delay-in-days":14,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2024,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Consider a locally cartesian closed category with an object <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000094_inline1.png\"\/><jats:tex-math>\n$\\mathbb{I}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and a class of trivial fibrations, which admit sections and are stable under pushforward and retract as arrows. Define the fibrations to be those maps whose Leibniz exponential with the generic point of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000094_inline2.png\"\/><jats:tex-math>\n$\\mathbb{I}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> defines a trivial fibration. Then the fibrations are also closed under pushforward.<\/jats:p>","DOI":"10.1017\/s0960129524000094","type":"journal-article","created":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T09:33:46Z","timestamp":1713173626000},"page":"258-280","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["A 2-categorical proof of Frobenius for fibrations defined from a generic point"],"prefix":"10.1017","volume":"34","author":[{"given":"Sina","family":"Hazratpour","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8465-8859","authenticated-orcid":false,"given":"Emily","family":"Riehl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,4,15]]},"reference":[{"key":"S0960129524000094_ref9","unstructured":"Shulman, M. (2019). All $(\\infty,1)$ -toposes have strict univalent universes, arXiv:1904.07004"},{"key":"S0960129524000094_ref2","unstructured":"Awodey, S. (2023). Cartesian cubical model categories, arXiv:2305.00893"},{"key":"S0960129524000094_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2017.02.013"},{"key":"S0960129524000094_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0063101"},{"key":"S0960129524000094_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084229"},{"key":"S0960129524000094_ref3","unstructured":"Barton, R. (2024). A short proof of Frobenius for generic fibrations, arXiv:2402.04227"},{"key":"S0960129524000094_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129521000347"},{"key":"S0960129524000094_ref4","unstructured":"Coquand, C , T. Variation on Cubical sets, https:\/\/www.cse.chalmers.se\/coquand\/diag.pdf"},{"key":"S0960129524000094_ref7","unstructured":"Newstead, C. (2018). Algebraic Models of Dependent Type Theory. Phd thesis, Carnegie Mellon University."},{"key":"S0960129524000094_ref10","unstructured":"Swan, A. W. (2022). Definable and Non-definable Notions of Structure, arXiv:2206.13643"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129524000094","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T01:47:48Z","timestamp":1727315268000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129524000094\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["S0960129524000094"],"URL":"https:\/\/doi.org\/10.1017\/s0960129524000094","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}