{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T01:34:25Z","timestamp":1777253665211,"version":"3.51.4"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T00:00:00Z","timestamp":1759708800000},"content-version":"unspecified","delay-in-days":278,"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":[[2025]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The Kock-Lawvere axiom has two formulations that are equivalent in the usual models of Synthetic Differential Geometry. We show that, in the classifier of integral rigs, and some of its pre-cohesive subtoposes, the generic model satisfies one version of the axiom but not the other.<\/jats:p>","DOI":"10.1017\/s0960129525100236","type":"journal-article","created":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T04:36:30Z","timestamp":1759725390000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Why the Kock-Lawvere axiom holds, and also doesn\u2019t, in the classifier of integral rigs"],"prefix":"10.1017","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-6711-1375","authenticated-orcid":false,"given":"Mat\u00edas","family":"Menni","sequence":"first","affiliation":[{"name":"Conicet - Centro de Matem\u00e1tica de La Plata"}]}],"member":"56","published-online":{"date-parts":[[2025,10,6]]},"reference":[{"key":"S0960129525100236_ref4","volume-title":"Sketches of an Elephant: A Topos Theory Compendium","author":"Johnstone","year":"2002"},{"key":"S0960129525100236_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511550812"},{"key":"S0960129525100236_ref7","doi-asserted-by":"publisher","DOI":"10.70930\/tac\/rwez60o2"},{"key":"S0960129525100236_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-0214-1_13"},{"key":"S0960129525100236_ref11","first-page":"451","article-title":"A basis theorem for 2-rigs and rig geometry","volume":"62","author":"Menni","year":"2021","journal-title":"Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques"},{"key":"S0960129525100236_ref10","first-page":"450","article-title":"Level \n\n\n\n$epsilon$","volume":"60","author":"Marmolejo","year":"2019","journal-title":"Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques"},{"key":"S0960129525100236_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s10485-013-9312-0"},{"key":"S0960129525100236_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084232"},{"key":"S0960129525100236_ref14","doi-asserted-by":"publisher","DOI":"10.70930\/tac\/qgtafibn"},{"key":"S0960129525100236_ref12","doi-asserted-by":"publisher","DOI":"10.70930\/tac\/xnycc7b9"},{"key":"S0960129525100236_ref8","doi-asserted-by":"publisher","DOI":"10.70930\/tac\/ag8jrxkb"},{"key":"S0960129525100236_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2016.04.014"},{"key":"S0960129525100236_ref1","volume-title":"Introduction to Commutative Algebra","author":"Atiyah","year":"1969"},{"key":"S0960129525100236_ref6","first-page":"115","article-title":"Affine combinations in affine schemes","volume":"58","author":"Kock","year":"2017","journal-title":"Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129525100236","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T01:00:06Z","timestamp":1777251606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129525100236\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":14,"alternative-id":["S0960129525100236"],"URL":"https:\/\/doi.org\/10.1017\/s0960129525100236","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}],"article-number":"e25"}}