{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T18:42:59Z","timestamp":1785436979712,"version":"3.56.0"},"reference-count":27,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T00:00:00Z","timestamp":1772582400000},"content-version":"unspecified","delay-in-days":62,"URL":"https:\/\/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":[[2026]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, we show that the Day monoidal product generalises in a straightforward way to other algebraic constructions and partial algebraic constructions on categories. This generalisation was motivated by its applications in logic, for example, in hybrid and separation logic. We use the description of the Day monoidal product using profunctors to show that the definition generalises to an extension of an arbitrary algebraic structure on a category to a pseudo-algebraic structure on a functor category. We provide two further extensions. First, we consider the case where some of the operations on the category are partial, and second, we show that the resulting operations on the functor category have adjoints (they are residuated).<\/jats:p>","DOI":"10.1017\/s096012952510039x","type":"journal-article","created":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T06:31:20Z","timestamp":1772605880000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Day algebras"],"prefix":"10.1017","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3075-2217","authenticated-orcid":false,"given":"Edmund","family":"Robinson","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/026zzn846","id-type":"ROR","asserted-by":"publisher"}],"name":"Queen Mary University of London"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joshua","family":"Wrigley","sequence":"additional","affiliation":[{"name":"Universite Paris Cite"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,3,4]]},"reference":[{"key":"S096012952510039X_ref18","volume-title":"Categories for the Working Mathematician","author":"Mac Lane","year":"1969"},{"key":"S096012952510039X_ref24","first-page":"257","volume-title":"Theoretical Computer Science","volume":"315","author":"Pym","year":"2004"},{"key":"S096012952510039X_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2012.06.027"},{"key":"S096012952510039X_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0074298"},{"key":"S096012952510039X_ref12","volume-title":"Topoi: The Categorial Analysis of Logic","volume":"98","author":"Goldblatt","year":"1984"},{"key":"S096012952510039X_ref21","first-page":"1","volume-title":"Computer Science Logic","author":"O\u2019Hearn","year":"2001"},{"key":"S096012952510039X_ref19","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511525896"},{"key":"S096012952510039X_ref9","doi-asserted-by":"crossref","unstructured":"Day, B. (1973). On closed categories of functors II. In: Category Seminar: Proceedings Sydney Category Theory Seminar 1972\/1973, Springer, 20\u201354.","DOI":"10.1007\/BFb0063098"},{"key":"S096012952510039X_ref22","doi-asserted-by":"publisher","DOI":"10.2307\/421090"},{"key":"S096012952510039X_ref8","first-page":"1","volume-title":"Reports of the Midwest Category Seminar IV","author":"Day","year":"1970"},{"key":"S096012952510039X_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-09719-0_19"},{"key":"S096012952510039X_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-53291-8_13"},{"key":"S096012952510039X_ref7","unstructured":"D\u2019Espalunge D\u2019Arros, S. (2023). Operads in 2-Categories and Models of Structure Interchange. Phd dissertation, Universit\u00e9 de Lille. https:\/\/theses.hal.science\/tel-04617115v1\/"},{"key":"S096012952510039X_ref13","first-page":"103","article-title":"Relations et carr\u00e9s exacts","volume":"IV","author":"Guitart","year":"1980","journal-title":"Annales Des Sciences Math\u00e9matiques Du Qu\u00e9bec"},{"key":"S096012952510039X_ref16","unstructured":"Kavvos, G. A. (2024). Two-Dimensional Kripke Semantics I: Presheaves. In: Rehof, J. (ed.) 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024), ser. Leibniz International Proceedings in Informatics (LIPIcs), Vol. 299, Dagstuhl, Germany: Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik, 14:1\u201314:23."},{"key":"S096012952510039X_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/9781108778657"},{"key":"S096012952510039X_ref15","doi-asserted-by":"publisher","DOI":"10.1145\/360204.375719"},{"key":"S096012952510039X_ref20","doi-asserted-by":"publisher","DOI":"10.1145\/3211968"},{"key":"S096012952510039X_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(64)90018-3"},{"key":"S096012952510039X_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-0002-4"},{"key":"S096012952510039X_ref25","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2002.1029817"},{"key":"S096012952510039X_ref27","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1939-1501995-3"},{"key":"S096012952510039X_ref10","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/318\/05545"},{"key":"S096012952510039X_ref23","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1977.32"},{"key":"S096012952510039X_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2017.12.006"},{"key":"S096012952510039X_ref6","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198537793.001.0001"},{"key":"S096012952510039X_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810275"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096012952510039X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T08:29:06Z","timestamp":1777278546000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096012952510039X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":27,"alternative-id":["S096012952510039X"],"URL":"https:\/\/doi.org\/10.1017\/s096012952510039x","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"\u00a9 The Author(s), 2026. 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 (https:\/\/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"}],"article-number":"e6"}}