{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:20Z","timestamp":1753894400775,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We introduce a bicategorical model of linear logic which is a novel variation\nof the bicategory of groupoids, profunctors, and natural transformations. Our\nmodel is obtained by endowing groupoids with additional structure, called a\nkit, to stabilize the profunctors by controlling the freeness of the groupoid\naction on profunctor elements. The theory of generalized species of structures,\nbased on profunctors, is refined to a new theory of \\emph{stable species} of\nstructures between groupoids with Boolean kits. Generalized species are in\ncorrespondence with analytic functors between presheaf categories; in our\nrefined model, stable species are shown to be in correspondence with\nrestrictions of analytic functors, which we characterize as being stable, to\nfull subcategories of stabilized presheaves. Our motivating example is the\nclass of finitary polynomial functors between categories of indexed sets, also\nknown as normal functors, that arises from kits enforcing free actions. We show\nthat the bicategory of groupoids with Boolean kits, stable species, and natural\ntransformations is cartesian closed. This makes essential use of the logical\nstructure of Boolean kits and explains the well-known failure of cartesian\nclosure for the bicategory of finitary polynomial functors between categories\nof set-indexed families and cartesian natural transformations. The paper\nadditionally develops the model of classical linear logic underlying the\ncartesian closed structure and clarifies the connection to stable domain\ntheory.<\/jats:p>","DOI":"10.46298\/lmcs-20(1:17)2024","type":"journal-article","created":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T10:25:11Z","timestamp":1709893511000},"source":"Crossref","is-referenced-by-count":0,"title":["Stabilized profunctors and stable species of structures"],"prefix":"10.46298","volume":"Volume 20, Issue 1","author":[{"given":"Marcelo","family":"Fiore","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeinab","family":"Galal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hugo","family":"Paquet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2024,2,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/13199\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/13199\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T10:25:12Z","timestamp":1709893512000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/11048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(1:17)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2303.04795v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2303.04795v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2303.04795","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2303.04795","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,2,29]]},"article-number":"11048"}}