{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T12:28:51Z","timestamp":1761654531521,"version":"build-2065373602"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T00:00:00Z","timestamp":1733875200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T00:00:00Z","timestamp":1733875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T00:00:00Z","timestamp":1733875200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"National Science Foundation","award":["1916439"],"award-info":[{"award-number":["1916439"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2024,11,7]]},"abstract":"<jats:p>Categories of lenses\/optics and Dialectica categories are both comprised of bidirectional morphisms of basically the same form. In this work we show how they can be considered a special case of an overarching fibrational construction, generalizing Hofstra's construction of Dialectica fibrations and Spivak's construction of generalized lenses. This construction turns a tower of Grothendieck fibrations into another tower of fibrations by iteratively twisting each of the components, using the opposite fibration construction.<\/jats:p>\n                  <jats:p>Comment: v3: 18 pp. Project results from the American Mathematical Society's   Math Research Community on Applied Category Theory 2022. v4: Final version   for proceedings of MFPS 2024. Updated author affiliation. v5: Corrected   author typo, added MPIM report no and DOI<\/jats:p>","DOI":"10.46298\/entics.14638","type":"journal-article","created":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T11:50:54Z","timestamp":1733917854000},"source":"Crossref","is-referenced-by-count":0,"title":["On a fibrational construction for optics, lenses, and Dialectica categories"],"prefix":"10.46298","volume":"Volume 4 - Proceedings of...","author":[{"given":"Matteo","family":"Capucci","sequence":"first","affiliation":[]},{"given":"Bruno","family":"Gavranovi\u0107","sequence":"additional","affiliation":[]},{"given":"Abdullah","family":"Malik","sequence":"additional","affiliation":[]},{"given":"Francisco","family":"Rios","sequence":"additional","affiliation":[]},{"given":"Jonathan","family":"Weinberger","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,12,11]]},"container-title":["Electronic Notes in Theoretical Informatics and Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2403.16388v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2403.16388v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T12:23:50Z","timestamp":1761654230000},"score":1,"resource":{"primary":{"URL":"http:\/\/entics.episciences.org\/14638"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,11]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/entics.14638","relation":{"is-same-as":[{"id-type":"arxiv","id":"2403.16388","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2403.16388","asserted-by":"subject"}]},"ISSN":["2969-2431"],"issn-type":[{"type":"electronic","value":"2969-2431"}],"subject":[],"published":{"date-parts":[[2024,12,11]]},"article-number":"14638"}}