{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,24]],"date-time":"2024-04-24T13:31:24Z","timestamp":1713965484299},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"9","license":[{"start":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T00:00:00Z","timestamp":1611878400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2021,10]]},"abstract":"Abstract<\/jats:title>In Hyland et al. (1980), Hyland, Johnstone and Pitts introduced the notion of tripos<\/jats:italic> for the purpose of organizing the construction of realizability toposes in a way that generalizes the construction of localic toposes from complete Heyting algebras. In Pitts (2002), one finds a generalization of this notion eliminating an unnecessary assumption of Hyland et al. (1980). The aim of this paper is to characterize triposes over a base topos ${\\cal S}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> in terms of so-called constant objects<\/jats:italic> functors from ${\\cal S}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> to some elementary topos. Our characterization is slightly different from the one in Pitts\u2019s PhD Thesis (Pitts, 1981) and motivated by the fibered view of geometric morphisms as described in Streicher (2020). In particular, we discuss the question whether triposes over Set<\/jats:bold> giving rise to equivalent toposes are already equivalent as triposes.<\/jats:p>","DOI":"10.1017\/s0960129520000304","type":"journal-article","created":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T04:51:36Z","timestamp":1611895896000},"page":"1024-1033","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Triposes as a generalization of localic geometric morphisms"],"prefix":"10.1017","volume":"31","author":[{"given":"Jonas","family":"Frey","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6725-0168","authenticated-orcid":false,"given":"Thomas","family":"Streicher","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,1,29]]},"reference":[{"key":"S0960129520000304_ref5","author":"Jibladze","year":"1989"},{"key":"S0960129520000304_ref11","unstructured":"Streicher, T. (2020). Fibered Categories \u00e0 la Jean B\u00e9nabou. arXiv:1801.02927"},{"key":"S0960129520000304_ref3","author":"Frey","year":"2013"},{"key":"S0960129520000304_ref1","volume-title":"Logique Cat\u00e9gorique","author":"B\u00e9nabou","year":"1974"},{"key":"S0960129520000304_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100057534"},{"key":"S0960129520000304_ref6","volume-title":"Topos Theory","author":"Johnstone","year":"1977"},{"key":"S0960129520000304_ref9","volume-title":"The Theory of Triposes","author":"Pitts","year":"1981"},{"key":"S0960129520000304_ref2","unstructured":"B\u00e9nabou, J. (1980). Des Cat\u00e9gories Fibr\u00e9es, Handwritten Lecture Notes by J.-R. Roisin of a course at Univ. Louvain-la-Neuve."},{"key":"S0960129520000304_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129520000079"},{"key":"S0960129520000304_ref8","unstructured":"Miquel, A. (2020b). Implicative Algebras II: Completeness w.r.t. Set-based Triposes. arXiv:2011.09085."},{"key":"S0960129520000304_ref12","volume-title":"Realizability. An Introduction to its Categorical Side","author":"van Oosten","year":"2008"},{"key":"S0960129520000304_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S096012950200364X"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129520000304","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,21]],"date-time":"2022-06-21T05:54:58Z","timestamp":1655790898000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129520000304\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,29]]},"references-count":12,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["S0960129520000304"],"URL":"https:\/\/doi.org\/10.1017\/s0960129520000304","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,29]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}