{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:14Z","timestamp":1753894394674,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2023,4,5]],"date-time":"2023-04-05T00:00:00Z","timestamp":1680652800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We define and study LNL polycategories, which abstract the judgmental\nstructure of classical linear logic with exponentials. Many existing structures\ncan be represented as LNL polycategories, including LNL adjunctions, linear\nexponential comonads, LNL multicategories, IL-indexed categories, linearly\ndistributive categories with storage, commutative and strong monads,\nCBPV-structures, models of polarized calculi, Freyd-categories, and skew\nmulticategories, as well as ordinary cartesian, symmetric, and planar\nmulticategories and monoidal categories, symmetric polycategories, and linearly\ndistributive and *-autonomous categories. To study such classes of structures\nuniformly, we define a notion of LNL doctrine, such that each of these classes\nof structures can be identified with the algebras for some such doctrine. We\nshow that free algebras for LNL doctrines can be presented by a sequent\ncalculus, and that every morphism of doctrines induces an adjunction between\ntheir 2-categories of algebras.<\/jats:p>","DOI":"10.46298\/lmcs-19(2:1)2023","type":"journal-article","created":{"date-parts":[[2023,4,5]],"date-time":"2023-04-05T11:40:19Z","timestamp":1680694819000},"source":"Crossref","is-referenced-by-count":1,"title":["LNL polycategories and doctrines of linear logic"],"prefix":"10.46298","volume":"Volume 19, Issue 2","author":[{"given":"Michael","family":"Shulman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2023,4,5]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/11160\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/11160\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:20:11Z","timestamp":1687292411000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/7662"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,5]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-19(2:1)2023","relation":{"has-preprint":[{"id-type":"arxiv","id":"2106.15042v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2106.15042v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2106.15042","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2106.15042","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2023,4,5]]},"article-number":"7662"}}