{"id":"https://openalex.org/W2779132223","doi":"https://doi.org/10.23638/lmcs-15(3:14)2019","title":"Companions, Causality and Codensity","display_name":"Companions, Causality and Codensity","publication_year":2019,"publication_date":"2019-08-08","ids":{"openalex":"https://openalex.org/W2779132223","doi":"https://doi.org/10.23638/lmcs-15(3:14)2019","mag":"2779132223"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-15(3:14)2019","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-15(3:14)2019","pdf_url":"https://lmcs.episciences.org/5680/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/5680/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084356882","display_name":"Damien Pous","orcid":"https://orcid.org/0000-0002-1220-4399"},"institutions":[{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Damien Pous","raw_affiliation_strings":["PLUME - Preuves et Langages (France)","LIP - Laboratoire de l'Informatique du Parall\u00e9lisme (46 All\u00e9e d'Italie 69364 LYON CEDEX 07 - France)"],"affiliations":[{"raw_affiliation_string":"PLUME - Preuves et Langages (France)","institution_ids":[]},{"raw_affiliation_string":"LIP - Laboratoire de l'Informatique du Parall\u00e9lisme (46 All\u00e9e d'Italie 69364 LYON CEDEX 07 - France)","institution_ids":["https://openalex.org/I4210144566","https://openalex.org/I113428412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015520868","display_name":"Jurriaan Rot","orcid":"https://orcid.org/0000-0002-1404-6232"},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jurriaan Rot","raw_affiliation_strings":["LIACS - Leiden Institute of Advanced Computer Science [Leiden] ( Niels Bohrweg 1 2333 CA Leiden  - Netherlands)"],"affiliations":[{"raw_affiliation_string":"LIACS - Leiden Institute of Advanced Computer Science [Leiden] ( Niels Bohrweg 1 2333 CA Leiden  - Netherlands)","institution_ids":["https://openalex.org/I121797337"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084356882"],"corresponding_institution_ids":["https://openalex.org/I113428412","https://openalex.org/I4210144566"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00367788,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Volume 15, Issue 3","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9973999857902527,"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":0.9943000078201294,"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/monad","display_name":"Monad (category theory)","score":0.9301115274429321},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.9201106429100037},{"id":"https://openalex.org/keywords/coalgebra","display_name":"Coalgebra","score":0.8941490054130554},{"id":"https://openalex.org/keywords/coinduction","display_name":"Coinduction","score":0.870659351348877},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.724992573261261},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6179468035697937},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6091627478599548},{"id":"https://openalex.org/keywords/causality","display_name":"Causality (physics)","score":0.5804010629653931},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4816388189792633},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.463897705078125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45490771532058716},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4455212950706482},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37523284554481506},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32387882471084595}],"concepts":[{"id":"https://openalex.org/C33959348","wikidata":"https://www.wikidata.org/wiki/Q1630568","display_name":"Monad (category theory)","level":3,"score":0.9301115274429321},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.9201106429100037},{"id":"https://openalex.org/C2778249326","wikidata":"https://www.wikidata.org/wiki/Q1777803","display_name":"Coalgebra","level":3,"score":0.8941490054130554},{"id":"https://openalex.org/C40220748","wikidata":"https://www.wikidata.org/wiki/Q4227156","display_name":"Coinduction","level":3,"score":0.870659351348877},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.724992573261261},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6179468035697937},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6091627478599548},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.5804010629653931},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4816388189792633},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.463897705078125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45490771532058716},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4455212950706482},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37523284554481506},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32387882471084595},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.23638/lmcs-15(3:14)2019","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-15(3:14)2019","pdf_url":"https://lmcs.episciences.org/5680/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1712.08526","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.08526","pdf_url":"https://arxiv.org/pdf/1712.08526","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1712.08526","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1712.08526","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.23638/lmcs-15(3:14)2019","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-15(3:14)2019","pdf_url":"https://lmcs.episciences.org/5680/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6600000262260437,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G177484282","display_name":null,"funder_award_id":"FP7/2007-2013","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G2726473892","display_name":null,"funder_award_id":"ANR-11-IDEX-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3584739849","display_name":null,"funder_award_id":"ANR-10-LABX-0070","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3602240456","display_name":null,"funder_award_id":"678157","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4031590434","display_name":null,"funder_award_id":"320571","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4866930200","display_name":null,"funder_award_id":"ANR-11-IDEX","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5549440890","display_name":null,"funder_award_id":"ANR-10-LAB","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5701317573","display_name":null,"funder_award_id":"11-IDEX-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7240651115","display_name":null,"funder_award_id":"ANR-10","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7823808512","display_name":null,"funder_award_id":"ANR-11-IDEX-000","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8917127843","display_name":null,"funder_award_id":"LABEX","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2779132223.pdf","grobid_xml":"https://content.openalex.org/works/W2779132223.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W71537616","https://openalex.org/W165755327","https://openalex.org/W172004165","https://openalex.org/W1485825789","https://openalex.org/W1503973138","https://openalex.org/W1509918383","https://openalex.org/W1526289988","https://openalex.org/W1527403862","https://openalex.org/W1533548386","https://openalex.org/W1539196615","https://openalex.org/W1577383226","https://openalex.org/W1583463787","https://openalex.org/W1969279113","https://openalex.org/W1985557227","https://openalex.org/W1987150452","https://openalex.org/W2005133733","https://openalex.org/W2006433153","https://openalex.org/W2008838944","https://openalex.org/W2014364142","https://openalex.org/W2023035194","https://openalex.org/W2026552167","https://openalex.org/W2046213250","https://openalex.org/W2057843304","https://openalex.org/W2064390891","https://openalex.org/W2077019667","https://openalex.org/W2085552917","https://openalex.org/W2089549471","https://openalex.org/W2101032471","https://openalex.org/W2115290331","https://openalex.org/W2117627793","https://openalex.org/W2119231401","https://openalex.org/W2120713972","https://openalex.org/W2128995870","https://openalex.org/W2129064963","https://openalex.org/W2139427429","https://openalex.org/W2184297521","https://openalex.org/W2245651640","https://openalex.org/W2341511048","https://openalex.org/W2468444917","https://openalex.org/W2530227870","https://openalex.org/W2582036626","https://openalex.org/W2613375231","https://openalex.org/W2964176916","https://openalex.org/W3102633916","https://openalex.org/W3143135297"],"related_works":["https://openalex.org/W2138773009","https://openalex.org/W2046125821","https://openalex.org/W2058610334","https://openalex.org/W2904778759","https://openalex.org/W4287705132","https://openalex.org/W1695839598","https://openalex.org/W2071463650","https://openalex.org/W2779132223","https://openalex.org/W2613375231","https://openalex.org/W2968061697"],"abstract_inverted_index":{"In":[0,105],"the":[1,9,21,30,51,67,79,83,87,109,114,126,134],"context":[2],"of":[3,11,20,56,82,86,103,133],"abstract":[4,101],"coinduction":[5,22],"in":[6],"complete":[7],"lattices,":[8],"notion":[10,53,102],"compatible":[12,27],"function":[13,144],"makes":[14],"it":[15,65,76],"possible":[16],"to":[17,39,47,131,147],"introduce":[18],"enhancements":[19,34,132],"proof":[23,136],"principle.":[24],"The":[25],"largest":[26],"function,":[28],"called":[29],"companion,":[31],"subsumes":[32],"most":[33],"and":[35,74],"has":[36],"been":[37],"proved":[38],"enjoy":[40],"many":[41],"good":[42],"properties.":[43],"Here":[44],"we":[45,92,107,138],"move":[46],"universal":[48],"coalgebra,":[49],"where":[50],"corresponding":[52],"is":[54,71],"that":[55,63,75,111,141],"a":[57,72,99,118,148],"final":[58,68,84],"distributive":[59,69,119],"law.":[60],"We":[61],"show":[62],"when":[64],"exists,":[66],"law":[70,120],"monad,":[73],"coincides":[77],"with":[78],"codensity":[80,96],"monad":[81,97],"sequence":[85],"given":[88],"functor.":[89],"On":[90],"sets,":[91],"moreover":[93],"characterise":[94],"this":[95],"using":[98],"new":[100],"causality.":[104],"particular,":[106],"recover":[108],"fact":[110],"on":[112],"streams,":[113],"functions":[115],"definable":[116],"by":[117],"or":[121],"GSOS":[122],"specification":[123],"are":[124],"precisely":[125],"causal":[127,143],"functions.":[128],"Going":[129],"back":[130],"coinductive":[135],"principle,":[137],"finally":[139],"obtain":[140],"any":[142],"gives":[145],"rise":[146],"valid":[149],"up-to-context":[150],"technique.":[151]},"counts_by_year":[],"updated_date":"2026-04-20T07:46:08.049788","created_date":"2025-10-10T00:00:00"}