{"id":"https://openalex.org/W2054195362","doi":"https://doi.org/10.1017/s0960129514000486","title":"Univalent categories and the Rezk completion","display_name":"Univalent categories and the Rezk completion","publication_year":2015,"publication_date":"2015-01-19","ids":{"openalex":"https://openalex.org/W2054195362","doi":"https://doi.org/10.1017/s0960129514000486","mag":"2054195362"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129514000486","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129514000486","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2CF86322C8415DE832BE304B4DC04D09/S0960129514000486a.pdf/div-class-title-univalent-categories-and-the-rezk-completion-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2CF86322C8415DE832BE304B4DC04D09/S0960129514000486a.pdf/div-class-title-univalent-categories-and-the-rezk-completion-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005424215","display_name":"Benedikt Ahrens","orcid":"https://orcid.org/0000-0002-6786-4538"},"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/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"BENEDIKT AHRENS","raw_affiliation_strings":["Institut de Recherche en Informatique de Toulouse, Universit\u00e9 Paul Sabatier, France E-mail:","Institut de Recherche en Informatique de Toulouse"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Informatique de Toulouse, Universit\u00e9 Paul Sabatier, France E-mail:","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I4210119061"]},{"raw_affiliation_string":"Institut de Recherche en Informatique de Toulouse","institution_ids":["https://openalex.org/I4210119061"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037922223","display_name":"Krzysztof Kapulkin","orcid":"https://orcid.org/0000-0002-8141-2554"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"KRZYSZTOF KAPULKIN","raw_affiliation_strings":["University of Pittsburgh, Pittsburgh, PA, U.S.A. E-mail:","University of Pittsburgh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pittsburgh, Pittsburgh, PA, U.S.A. E-mail:","institution_ids":["https://openalex.org/I170201317"]},{"raw_affiliation_string":"University of Pittsburgh","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065839536","display_name":"Michael Shulman","orcid":"https://orcid.org/0000-0002-9948-6682"},"institutions":[{"id":"https://openalex.org/I160856358","display_name":"University of San Diego","ror":"https://ror.org/03jbbze48","country_code":"US","type":"education","lineage":["https://openalex.org/I160856358"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"MICHAEL SHULMAN","raw_affiliation_strings":["University of San Diego, San Diego, CA, U.S.A. E-mail:","University Of San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of San Diego, San Diego, CA, U.S.A. E-mail:","institution_ids":["https://openalex.org/I160856358"]},{"raw_affiliation_string":"University Of San Diego","institution_ids":["https://openalex.org/I160856358"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.9239,"has_fulltext":true,"cited_by_count":75,"citation_normalized_percentile":{"value":0.99558318,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"25","issue":"5","first_page":"1010","last_page":"1039"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9986000061035156,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9883999824523926,"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/axiom","display_name":"Axiom","score":0.7018780708312988},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6951749324798584},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6115559935569763},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.606330931186676},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.576193630695343},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.5648328065872192},{"id":"https://openalex.org/keywords/extensionality","display_name":"Extensionality","score":0.5520376563072205},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.544159471988678},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.5396137237548828},{"id":"https://openalex.org/keywords/stack","display_name":"Stack (abstract data type)","score":0.5188859105110168},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4947473406791687},{"id":"https://openalex.org/keywords/2-category","display_name":"2-category","score":0.48929068446159363},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42443251609802246},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.41948166489601135},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3245782256126404},{"id":"https://openalex.org/keywords/closed-category","display_name":"Closed category","score":0.30719664692878723},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.21056097745895386},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20962688326835632},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09665486216545105},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08833983540534973}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7018780708312988},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6951749324798584},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6115559935569763},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.606330931186676},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.576193630695343},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.5648328065872192},{"id":"https://openalex.org/C150355047","wikidata":"https://www.wikidata.org/wiki/Q965432","display_name":"Extensionality","level":2,"score":0.5520376563072205},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.544159471988678},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.5396137237548828},{"id":"https://openalex.org/C9395851","wikidata":"https://www.wikidata.org/wiki/Q177929","display_name":"Stack (abstract data type)","level":2,"score":0.5188859105110168},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4947473406791687},{"id":"https://openalex.org/C46263353","wikidata":"https://www.wikidata.org/wiki/Q4596935","display_name":"2-category","level":4,"score":0.48929068446159363},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42443251609802246},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.41948166489601135},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3245782256126404},{"id":"https://openalex.org/C7879355","wikidata":"https://www.wikidata.org/wiki/Q5135329","display_name":"Closed category","level":3,"score":0.30719664692878723},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.21056097745895386},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20962688326835632},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09665486216545105},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08833983540534973},{"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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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":7,"locations":[{"id":"doi:10.1017/s0960129514000486","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129514000486","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2CF86322C8415DE832BE304B4DC04D09/S0960129514000486a.pdf/div-class-title-univalent-categories-and-the-rezk-completion-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1303.0584","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.0584","pdf_url":"https://arxiv.org/pdf/1303.0584","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:CiteSeerX.psu:10.1.1.721.173","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.721.173","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://benedikt-ahrens.org/talks/types2013_ahrens.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.721.7285","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.721.7285","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://benedikt-ahrens.org/publications/TYPES2013_Ahrens_Kapulkin_Shulman.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.759.3095","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.759.3095","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1303.0584.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/c8e947cc-7369-4433-ac99-c00ffb35a2af","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/c8e947cc-7369-4433-ac99-c00ffb35a2af","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":"Ahrens, B, Kapulkin, K & Shulman, M 2015, 'Univalent categories and the Rezk completion', Mathematical Structures in Computer Science, vol. 25, no. 5, pp. 1010-1039. https://doi.org/10.1017/S0960129514000486","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/c8e947cc-7369-4433-ac99-c00ffb35a2af","is_oa":false,"landing_page_url":"http://www.journals.cambridge.org/abstract_S0960129514000486","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":"Ahrens , B , Kapulkin , K & Shulman , M 2015 , ' Univalent categories and the Rezk completion ' , Mathematical Structures in Computer Science , vol. 25 , no. 5 , pp. 1010-1039 . https://doi.org/10.1017/S0960129514000486","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1017/s0960129514000486","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129514000486","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2CF86322C8415DE832BE304B4DC04D09/S0960129514000486a.pdf/div-class-title-univalent-categories-and-the-rezk-completion-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4062780233","display_name":"Research in Mathematics","funder_award_id":"1128155","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G434351297","display_name":"Homotopy and Type Theory","funder_award_id":"1001191","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4414853111","display_name":null,"funder_award_id":"ANR 11-LABX- 0040","funder_id":"https://openalex.org/F4320335230","funder_display_name":"Centre International de Math\u00e9matiques et Informatique de Toulouse"},{"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/G52474758","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse","funder_award_id":"ANR-11-IDEX-0002","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5261993341","display_name":null,"funder_award_id":"ANR-11IDEX-0002-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6942917955","display_name":null,"funder_award_id":"ANR-11-LABX-0040-CIMI","funder_id":"https://openalex.org/F4320335230","funder_display_name":"Centre International de Math\u00e9matiques et Informatique de Toulouse"},{"id":"https://openalex.org/G7786692064","display_name":"Centre International de Math\u00e9matiques et d'Informatique (de Toulouse)","funder_award_id":"ANR-11-LABX-0040","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8732291166","display_name":null,"funder_award_id":"DMS-1128155","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8938184468","display_name":null,"funder_award_id":"ANR-11-IDEX-0002-02","funder_id":"https://openalex.org/F4320335230","funder_display_name":"Centre International de Math\u00e9matiques et Informatique de Toulouse"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320335230","display_name":"Centre International de Math\u00e9matiques et Informatique de Toulouse","ror":"https://ror.org/017tgbk05"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054195362.pdf","grobid_xml":"https://content.openalex.org/works/W2054195362.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W51202918","https://openalex.org/W574120026","https://openalex.org/W1560091341","https://openalex.org/W1569447798","https://openalex.org/W1768814311","https://openalex.org/W1895711163","https://openalex.org/W1936971149","https://openalex.org/W1997582403","https://openalex.org/W2039140273","https://openalex.org/W2054195362","https://openalex.org/W2102538436","https://openalex.org/W2120323684","https://openalex.org/W2130779085","https://openalex.org/W2150941507","https://openalex.org/W2475129850","https://openalex.org/W2734631935","https://openalex.org/W2962780223","https://openalex.org/W3102482356","https://openalex.org/W6741111802"],"related_works":["https://openalex.org/W2613438777","https://openalex.org/W2119472394","https://openalex.org/W3082642538","https://openalex.org/W4297816910","https://openalex.org/W4297727768","https://openalex.org/W2810660572","https://openalex.org/W1974294638","https://openalex.org/W2083682852","https://openalex.org/W4293377261","https://openalex.org/W3005980421"],"abstract_inverted_index":{"We":[0],"develop":[1],"category":[2,80],"theory":[3],"within":[4],"Univalent":[5],"Foundations,":[6],"which":[7,33],"is":[8,59,81],"a":[9,16,28,43,85,89,101,118],"foundational":[10],"system":[11],"for":[12,32,108],"mathematics":[13],"based":[14],"on":[15],"homotopical":[17,93],"interpretation":[18],"of":[19,30,37,45,53,104,117],"dependent":[20],"type":[21,52,64],"theory.":[22],"In":[23,92],"this":[24,97],"system,":[25],"we":[26,68,76],"propose":[27],"definition":[29],"\u2018category\u2019":[31],"equality":[34],"and":[35,94,111],"equivalence":[36],"categories":[38,41],"agree.":[39],"Such":[40],"satisfy":[42],"version":[44,103],"the":[46,51,62,105,114],"univalence":[47],"axiom,":[48],"saying":[49],"that":[50,78],"isomorphisms":[54],"between":[55,65],"any":[56,79],"two":[57],"objects":[58],"equivalent":[60,83],"to":[61,84,100,113],"identity":[63],"these":[66],"objects;":[67],"call":[69],"them":[70],"\u2018saturated\u2019":[71],"or":[72],"\u2018univalent\u2019":[73],"categories.":[74],"Moreover,":[75],"show":[77],"weakly":[82],"univalent":[86],"one":[87],"in":[88],"universal":[90],"way.":[91],"higher-categorical":[95],"semantics,":[96],"construction":[98],"corresponds":[99],"truncated":[102],"Rezk":[106],"completion":[107,116],"Segal":[109],"spaces,":[110],"also":[112],"stack":[115],"prestack.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2020-11-23T00:00:00"}