{"id":"https://openalex.org/W2010611147","doi":"https://doi.org/10.2307/2586761","title":"Cartesian isomorphisms are symmetric monoidal: A justification of linear logic","display_name":"Cartesian isomorphisms are symmetric monoidal: A justification of linear logic","publication_year":1999,"publication_date":"1999-03-01","ids":{"openalex":"https://openalex.org/W2010611147","doi":"https://doi.org/10.2307/2586761","mag":"2010611147"},"language":"en","primary_location":{"id":"doi:10.2307/2586761","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586761","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018558191","display_name":"Kosta Do\u0161en","orcid":null},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["FR","SK"],"is_corresponding":false,"raw_author_name":"Kosta Do\u0161en","raw_affiliation_strings":["Irit, University of Toulouse III, 31062 Toulouse Cedex, France","Mathematical Institute, P. O. Box 367, 11001 Belgrade, Yugoslavia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Irit, University of Toulouse III, 31062 Toulouse Cedex, France","institution_ids":["https://openalex.org/I4210119061","https://openalex.org/I134560555"]},{"raw_affiliation_string":"Mathematical Institute, P. O. Box 367, 11001 Belgrade, Yugoslavia","institution_ids":["https://openalex.org/I4210120676"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030384983","display_name":"Zoran Petri\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Zoran Petri\u0107","raw_affiliation_strings":["University of Belgrade, Faculty of Mining and Geology, Dju\u0161ina 7, 11000 Belgrade, Yugoslavia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Belgrade, Faculty of Mining and Geology, Dju\u0161ina 7, 11000 Belgrade, Yugoslavia","institution_ids":["https://openalex.org/I4068193"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0414,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.8150784,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"1","first_page":"227","last_page":"242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9659000039100647,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cartesian-closed-category","display_name":"Cartesian closed category","score":0.7858045101165771},{"id":"https://openalex.org/keywords/closed-monoidal-category","display_name":"Closed monoidal category","score":0.7457315921783447},{"id":"https://openalex.org/keywords/symmetric-monoidal-category","display_name":"Symmetric monoidal category","score":0.6918264031410217},{"id":"https://openalex.org/keywords/enriched-category","display_name":"Enriched category","score":0.6720280051231384},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6380720734596252},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.607302725315094},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.5384312868118286},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.518955647945404},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.5089108943939209},{"id":"https://openalex.org/keywords/monoidal-category","display_name":"Monoidal category","score":0.5078042149543762},{"id":"https://openalex.org/keywords/arrow","display_name":"Arrow","score":0.4934958219528198},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46402719616889954},{"id":"https://openalex.org/keywords/higher-category-theory","display_name":"Higher category theory","score":0.4380333721637726},{"id":"https://openalex.org/keywords/concrete-category","display_name":"Concrete category","score":0.41298460960388184},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39709994196891785},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39167654514312744},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2641916573047638},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10138019919395447},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.07563585042953491}],"concepts":[{"id":"https://openalex.org/C171032842","wikidata":"https://www.wikidata.org/wiki/Q1725874","display_name":"Cartesian closed category","level":2,"score":0.7858045101165771},{"id":"https://openalex.org/C56208153","wikidata":"https://www.wikidata.org/wiki/Q5135347","display_name":"Closed monoidal category","level":4,"score":0.7457315921783447},{"id":"https://openalex.org/C98912367","wikidata":"https://www.wikidata.org/wiki/Q17103860","display_name":"Symmetric monoidal category","level":3,"score":0.6918264031410217},{"id":"https://openalex.org/C156163052","wikidata":"https://www.wikidata.org/wiki/Q5379515","display_name":"Enriched category","level":3,"score":0.6720280051231384},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6380720734596252},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.607302725315094},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.5384312868118286},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.518955647945404},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.5089108943939209},{"id":"https://openalex.org/C2779904274","wikidata":"https://www.wikidata.org/wiki/Q1945014","display_name":"Monoidal category","level":2,"score":0.5078042149543762},{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.4934958219528198},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46402719616889954},{"id":"https://openalex.org/C76069219","wikidata":"https://www.wikidata.org/wiki/Q5758318","display_name":"Higher category theory","level":4,"score":0.4380333721637726},{"id":"https://openalex.org/C128520899","wikidata":"https://www.wikidata.org/wiki/Q1575634","display_name":"Concrete category","level":3,"score":0.41298460960388184},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39709994196891785},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39167654514312744},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2641916573047638},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10138019919395447},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.07563585042953491},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2586761","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586761","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745702","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745702","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4000000059604645,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W37089806","https://openalex.org/W148623806","https://openalex.org/W960577102","https://openalex.org/W1503796635","https://openalex.org/W2032563292","https://openalex.org/W2063687250","https://openalex.org/W2067172985","https://openalex.org/W2120713972","https://openalex.org/W2124764481","https://openalex.org/W2145018595","https://openalex.org/W2950142396"],"related_works":["https://openalex.org/W2288880934","https://openalex.org/W2316040467","https://openalex.org/W2072617459","https://openalex.org/W1986885420","https://openalex.org/W4244360710","https://openalex.org/W3100624102","https://openalex.org/W2156541639","https://openalex.org/W2415965387","https://openalex.org/W2010611147","https://openalex.org/W4221164648"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,59],"proved":[3],"that":[4],"all":[5],"the":[6,9,32,39],"isomorphisms":[7],"in":[8,27,54],"cartesian":[10,57],"category":[11,35,58],"freely":[12,36],"generated":[13,37],"by":[14,38],"a":[15,20],"set":[16,41],"of":[17,29,42],"objects":[18],"(i.e.,":[19],"graph":[21],"without":[22],"arrows)":[23],"can":[24],"be":[25],"written":[26],"terms":[28],"arrows":[30],"from":[31],"symmetric":[33],"monoidal":[34],"same":[40],"objects.":[43],"This":[44],"proof":[45],"yields":[46],"an":[47,52,60],"algorithm":[48],"for":[49],"deciding":[50],"whether":[51],"arrow":[53],"this":[55],"free":[56],"isomorphism.":[61]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
