{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:10:15Z","timestamp":1783901415328,"version":"3.55.0"},"reference-count":15,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,8,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>This paper deals with the notions of U-small set, U-small category, and U-locally small category (U is non-empty Grothendieck universe). We reuse the first Mizar formalization of categories contained in CAT_* series of Mizar articles in order to show the expressive power of the Tarski-Grothendieck set theory (which is the base for the Mizar Mathematical Library) in this area. We encode parts of SGA 4 by Nicolas Bourbaki.<\/jats:p>","DOI":"10.2478\/forma-2024-0006","type":"journal-article","created":{"date-parts":[[2024,12,16]],"date-time":"2024-12-16T16:44:10Z","timestamp":1734367450000},"page":"77-92","source":"Crossref","is-referenced-by-count":0,"title":["U-Small and U-Locally Small Categories"],"prefix":"10.2478","volume":"32","author":[{"given":"Roland","family":"Coghetto","sequence":"first","affiliation":[{"name":"cafr-MSA2P asbl Rue de la Brasserie 5 7100 La Louvi\u00e8re , Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2024,12,12]]},"reference":[{"key":"2026071214473599242_j_forma-2024-0006_ref_001","doi-asserted-by":"crossref","unstructured":"Michael Artin, Alexander Grothendieck, and Jean-Louis Verdier. Th\u00e9orie des topos et cohomologie \u00e9tale des sch\u00e9mas. Tome 1: Th\u00e9orie des topos (expos\u00e9s i\u00e0 iv). In S\u00e9minaire de G\u00e9om\u00e9trie Alg\u00e9brique du Bois Marie, 1963\/64, SGA 4, volume 269 of Lecture Notes in Mathematics. Springer, 1972.","DOI":"10.1007\/BFb0081552"},{"key":"2026071214473599242_j_forma-2024-0006_ref_002","doi-asserted-by":"crossref","unstructured":"Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, Karol P\u0105k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261\u2013279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007\/978-3-319-20615-8 17.","DOI":"10.1007\/978-3-319-20615-8_17"},{"key":"2026071214473599242_j_forma-2024-0006_ref_003","doi-asserted-by":"crossref","unstructured":"Chad E. Brown and Karol P\u0105k. A tale of two set theories. In Cezary Kaliszyk, Edwin Brady, Andrea Kohlhase, and Claudio Sacerdoti Coen, editors, Intelligent Computer Mathematics \u2013 12th International Conference, CICM 2019, CIIRC, Prague, Czech Republic, July 8-12, 2019, Proceedings, volume 11617 of Lecture Notes in Computer Science, pages 44\u201360. Springer, 2019. doi:10.1007\/978-3-030-23250-4 4.","DOI":"10.1007\/978-3-030-23250-4"},{"key":"2026071214473599242_j_forma-2024-0006_ref_004","unstructured":"Czes\u0142aw Byli\u0144ski. Introduction to categories and functors. Formalized Mathematics, 1 (2):409\u2013420, 1990."},{"key":"2026071214473599242_j_forma-2024-0006_ref_005","doi-asserted-by":"crossref","unstructured":"Roland Coghetto. Non-trivial universes and sequences of universes. Formalized Mathematics, 30(1):53\u201366, 2022. doi:10.2478\/forma-2022-0005.","DOI":"10.2478\/forma-2022-0005"},{"key":"2026071214473599242_j_forma-2024-0006_ref_006","doi-asserted-by":"crossref","unstructured":"Masaki Kashiwara and Pierre Schapira. 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