{"id":"https://openalex.org/W3164799725","doi":"https://doi.org/10.1109/lics52264.2021.9470541","title":"Types Are Internal \u221e-Groupoids","display_name":"Types Are Internal \u221e-Groupoids","publication_year":2021,"publication_date":"2021-06-29","ids":{"openalex":"https://openalex.org/W3164799725","doi":"https://doi.org/10.1109/lics52264.2021.9470541","mag":"3164799725"},"language":"en","primary_location":{"id":"doi:10.1109/lics52264.2021.9470541","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics52264.2021.9470541","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.birmingham.ac.uk/en/publications/7d45301f-cf55-4451-b47a-727968158b79","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001438390","display_name":"Eric Finster","orcid":"https://orcid.org/0000-0002-6027-7488"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Eric Finster","raw_affiliation_strings":["Department of Computer Science, Cambridge University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Cambridge University","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016840314","display_name":"Antoine Allioux","orcid":null},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Antoine Allioux","raw_affiliation_strings":["Inria & IRIF, Universit\u00e9 de Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria & IRIF, Universit\u00e9 de Paris, France","institution_ids":["https://openalex.org/I204730241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065124885","display_name":"Matthieu Sozeau","orcid":"https://orcid.org/0000-0001-6452-8806"},"institutions":[{"id":"https://openalex.org/I4210117005","display_name":"Laboratoire des Sciences du Num\u00e9rique de Nantes","ror":"https://ror.org/02snf8m58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I4210117005","https://openalex.org/I4210124215","https://openalex.org/I4210127572","https://openalex.org/I4210139971","https://openalex.org/I97188460","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Matthieu Sozeau","raw_affiliation_strings":["Inria & LS2N, Universit\u00e9 de Nantes, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria & LS2N, Universit\u00e9 de Nantes, France","institution_ids":["https://openalex.org/I4210117005","https://openalex.org/I97188460"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05327443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"abs 1705 3307","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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":0.9995999932289124,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9789999723434448,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.679009735584259},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.640789270401001},{"id":"https://openalex.org/keywords/unital","display_name":"Unital","score":0.6390337347984314},{"id":"https://openalex.org/keywords/universe","display_name":"Universe","score":0.5812002420425415},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.5779964923858643},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5452594757080078},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5192713737487793},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.51473069190979},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5079413056373596},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.49987220764160156},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45088279247283936},{"id":"https://openalex.org/keywords/double-groupoid","display_name":"Double groupoid","score":0.4305843114852905},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3955089747905731},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3218616247177124},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0755757987499237},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.060191720724105835}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.679009735584259},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.640789270401001},{"id":"https://openalex.org/C160873635","wikidata":"https://www.wikidata.org/wiki/Q17148807","display_name":"Unital","level":3,"score":0.6390337347984314},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.5812002420425415},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.5779964923858643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5452594757080078},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5192713737487793},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.51473069190979},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5079413056373596},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.49987220764160156},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45088279247283936},{"id":"https://openalex.org/C75328951","wikidata":"https://www.wikidata.org/wiki/Q17008126","display_name":"Double groupoid","level":2,"score":0.4305843114852905},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3955089747905731},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3218616247177124},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0755757987499237},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.060191720724105835},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/lics52264.2021.9470541","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics52264.2021.9470541","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/7d45301f-cf55-4451-b47a-727968158b79","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/7d45301f-cf55-4451-b47a-727968158b79","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Finster, E, Sozeau, M & Allioux, A 2021, Types are internal \u221e-groupoids. in 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)., 9470541, Proceedings - Symposium on Logic in Computer Science, Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/LICS52264.2021.9470541","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:pure.atira.dk:publications/7d45301f-cf55-4451-b47a-727968158b79","is_oa":false,"landing_page_url":"https://birmingham.elsevierpure.com/en/publications/7d45301f-cf55-4451-b47a-727968158b79","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/328879","is_oa":false,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/328879","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"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":"Conference Object"},{"id":"doi:10.17863/cam.76325","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.76325","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Other"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/7d45301f-cf55-4451-b47a-727968158b79","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/7d45301f-cf55-4451-b47a-727968158b79","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Finster, E, Sozeau, M & Allioux, A 2021, Types are internal \u221e-groupoids. in 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)., 9470541, Proceedings - Symposium on Logic in Computer Science, Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/LICS52264.2021.9470541","raw_type":"contributionToPeriodical"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1677393765","https://openalex.org/W1979101142","https://openalex.org/W2018415539","https://openalex.org/W2022608773","https://openalex.org/W2054195362","https://openalex.org/W2098691999","https://openalex.org/W2129064963","https://openalex.org/W2151404275","https://openalex.org/W2151520617","https://openalex.org/W2612506836","https://openalex.org/W2883252932","https://openalex.org/W2915711730","https://openalex.org/W2951532718","https://openalex.org/W2995356144","https://openalex.org/W3044307770","https://openalex.org/W3100912421","https://openalex.org/W3178701861","https://openalex.org/W4240072532","https://openalex.org/W4322716113","https://openalex.org/W6737194455","https://openalex.org/W6752720638","https://openalex.org/W6759394446","https://openalex.org/W6780745407","https://openalex.org/W6797661991"],"related_works":["https://openalex.org/W1937042829","https://openalex.org/W3212738197","https://openalex.org/W4387561090","https://openalex.org/W2951530300","https://openalex.org/W4224218583","https://openalex.org/W3021517041","https://openalex.org/W73679669","https://openalex.org/W3107907878","https://openalex.org/W3011899323","https://openalex.org/W3134004195"],"abstract_inverted_index":{"By":[0],"extending":[1],"type":[2,24,49,56,70],"theory":[3,50],"with":[4],"a":[5,20,30,43],"universe":[6,64],"of":[7,22,32,45,57,65,74],"definitionally":[8],"associative":[9],"and":[10,51,78],"unital":[11],"polynomial":[12],"monads,":[13],"we":[14,52],"show":[15],"how":[16],"to":[17,28,42,48,62],"arrive":[18],"at":[19],"definition":[21,44],"opetopic":[23],"which":[25],"is":[26,60,81],"able":[27],"encode":[29],"number":[31],"fully":[33],"coherent":[34],"algebraic":[35],"structures.":[36],"In":[37],"particular,":[38],"our":[39],"approach":[40],"leads":[41],"\u221e-groupoid":[46,76],"internal":[47],"prove":[53],"that":[54],"the":[55,63,72],"such":[58],"\u221e-groupoids":[59],"equivalent":[61],"types.":[66],"That":[67],"is,":[68],"every":[69],"admits":[71],"structure":[73,80],"an":[75],"internally,":[77],"this":[79],"unique.":[82]},"counts_by_year":[],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}