{"id":"https://openalex.org/W3039106737","doi":"https://doi.org/10.1017/s0960129521000098","title":"An interpretation of dependent type theory in a model category of locally cartesian closed categories","display_name":"An interpretation of dependent type theory in a model category of locally cartesian closed categories","publication_year":2021,"publication_date":"2021-05-01","ids":{"openalex":"https://openalex.org/W3039106737","doi":"https://doi.org/10.1017/s0960129521000098","mag":"3039106737"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129521000098","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129521000098","pdf_url":null,"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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2007.02900","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103081105","display_name":"Martin E. Bidlingmaier","orcid":"https://orcid.org/0000-0003-2238-8731"},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Martin E. Bidlingmaier","raw_affiliation_strings":["Department of Computer Science, Aarhus University, Aarhus, Denmark"],"raw_orcid":"https://orcid.org/0000-0003-2238-8731","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aarhus University, Aarhus, Denmark","institution_ids":["https://openalex.org/I204337017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103081105"],"corresponding_institution_ids":["https://openalex.org/I204337017"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06213663,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"5","first_page":"469","last_page":"494"},"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":0.9991000294685364,"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":0.9991000294685364,"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":0.9811000227928162,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.953499972820282,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.8907685279846191},{"id":"https://openalex.org/keywords/closed-category","display_name":"Closed category","score":0.6961542367935181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.665907621383667},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.6492100954055786},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.6477862596511841},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.5746376514434814},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.5715746283531189},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.5688866972923279},{"id":"https://openalex.org/keywords/concrete-category","display_name":"Concrete category","score":0.5077656507492065},{"id":"https://openalex.org/keywords/equivalence-of-categories","display_name":"Equivalence of categories","score":0.4980909824371338},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.49109888076782227},{"id":"https://openalex.org/keywords/derived-category","display_name":"Derived category","score":0.4816388189792633},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.4713950455188751},{"id":"https://openalex.org/keywords/category-of-sets","display_name":"Category of sets","score":0.4541468322277069},{"id":"https://openalex.org/keywords/natural-transformation","display_name":"Natural transformation","score":0.43928876519203186},{"id":"https://openalex.org/keywords/model-category","display_name":"Model category","score":0.4275874197483063},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.4216792583465576},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40944769978523254},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3923211395740509},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2812952995300293},{"id":"https://openalex.org/keywords/homotopy-category","display_name":"Homotopy category","score":0.1992088258266449}],"concepts":[{"id":"https://openalex.org/C171032842","wikidata":"https://www.wikidata.org/wiki/Q1725874","display_name":"Cartesian closed category","level":2,"score":0.8907685279846191},{"id":"https://openalex.org/C7879355","wikidata":"https://www.wikidata.org/wiki/Q5135329","display_name":"Closed category","level":3,"score":0.6961542367935181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.665907621383667},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.6492100954055786},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.6477862596511841},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.5746376514434814},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.5715746283531189},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.5688866972923279},{"id":"https://openalex.org/C128520899","wikidata":"https://www.wikidata.org/wiki/Q1575634","display_name":"Concrete category","level":3,"score":0.5077656507492065},{"id":"https://openalex.org/C11846945","wikidata":"https://www.wikidata.org/wiki/Q1082992","display_name":"Equivalence of categories","level":3,"score":0.4980909824371338},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.49109888076782227},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.4816388189792633},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.4713950455188751},{"id":"https://openalex.org/C72727785","wikidata":"https://www.wikidata.org/wiki/Q2518298","display_name":"Category of sets","level":3,"score":0.4541468322277069},{"id":"https://openalex.org/C99633028","wikidata":"https://www.wikidata.org/wiki/Q1442189","display_name":"Natural transformation","level":3,"score":0.43928876519203186},{"id":"https://openalex.org/C131359564","wikidata":"https://www.wikidata.org/wiki/Q1941896","display_name":"Model category","level":4,"score":0.4275874197483063},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.4216792583465576},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40944769978523254},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3923211395740509},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2812952995300293},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.1992088258266449},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"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/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"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/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","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},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s0960129521000098","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129521000098","pdf_url":null,"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:pure.atira.dk:publications/c3281e1e-8dd5-4863-90c9-917d494bc279","is_oa":false,"landing_page_url":"https://pure.au.dk/portal/en/publications/c3281e1e-8dd5-4863-90c9-917d494bc279","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bidlingmaier, M E 2021, 'An interpretation of dependent type theory in a model category of locally cartesian closed categories', Mathematical Structures in Computer Science, vol. 31, no. 5, pp. 469-494. https://doi.org/10.1017/S0960129521000098","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2007.02900","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.02900","pdf_url":"https://arxiv.org/pdf/2007.02900","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":"mag:3039106737","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2007.02900","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2007.02900","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.02900","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2007.02900","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.02900","pdf_url":"https://arxiv.org/pdf/2007.02900","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"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4099999964237213,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1494555245","https://openalex.org/W1507692549","https://openalex.org/W1510067240","https://openalex.org/W1583122470","https://openalex.org/W1680171265","https://openalex.org/W1828583149","https://openalex.org/W1892525621","https://openalex.org/W1997146553","https://openalex.org/W2022837260","https://openalex.org/W2027614742","https://openalex.org/W2081723613","https://openalex.org/W2103181565","https://openalex.org/W2119472394","https://openalex.org/W2128849971","https://openalex.org/W2148366303","https://openalex.org/W2182184486","https://openalex.org/W2494316805","https://openalex.org/W2539626161","https://openalex.org/W2733079097","https://openalex.org/W2963083424","https://openalex.org/W2963181390","https://openalex.org/W2963214243","https://openalex.org/W3104964042","https://openalex.org/W4293252599","https://openalex.org/W6638838395","https://openalex.org/W6677634866","https://openalex.org/W6685731356"],"related_works":["https://openalex.org/W2995772018","https://openalex.org/W2160144389","https://openalex.org/W429752307","https://openalex.org/W2963249536","https://openalex.org/W2797609579","https://openalex.org/W2963131328","https://openalex.org/W2050478998","https://openalex.org/W1983244685","https://openalex.org/W2980088699","https://openalex.org/W835831504","https://openalex.org/W1568497082","https://openalex.org/W2806710741","https://openalex.org/W1533461724","https://openalex.org/W2183864785","https://openalex.org/W37362631","https://openalex.org/W3029955053","https://openalex.org/W3196246661","https://openalex.org/W2766683736","https://openalex.org/W3094567953","https://openalex.org/W2064792687"],"abstract_inverted_index":{"Abstract":[0],"Locally":[1],"cartesian":[2],"closed":[3],"(lcc)":[4],"categories":[5,47,118,145,149],"are":[6],"natural":[7],"categorical":[8],"models":[9],"of":[10,24,28,44,54,57,84,112,116,130,140,146,162],"extensional":[11],"dependent":[12,58,163],"type":[13,59,164],"theory.":[14,60,165],"This":[15],"paper":[16],"introduces":[17],"the":[18,22,42,52,77,82,113,138],"\u201cgros\u201d":[19],"semantics":[20],"in":[21,32,64,76],"category":[23,43,68,115,129],"lcc":[25,36,46,67,117,131,148,155],"categories:":[26],"Instead":[27],"constructing":[29],"an":[30,65],"interpretation":[31,63],"a":[33,55,109,127],"given":[34],"individual":[35,66],"category,":[37],"we":[38,80,125,135],"show":[39],"that":[40,123],"also":[41],"all":[45,103],"can":[48,69],"be":[49,71],"endowed":[50],"with":[51,102],"structure":[53,87],"model":[56,120,128,144,161],"The":[61,157],"original":[62,78],"then":[70,151],"recovered":[72],"by":[73,91,137],"slicing.":[74],"As":[75],"interpretation,":[79],"face":[81],"issue":[83],"coherence:":[85],"Categorical":[86],"is":[88,159],"usually":[89],"preserved":[90],"functors":[92],"only":[93],"up":[94],"to":[95],"isomorphism,":[96],"whereas":[97],"syntactic":[98],"substitution":[99],"commutes":[100],"strictly":[101],"type-theoretic":[104],"structures.":[105],"Our":[106],"solution":[107],"involves":[108],"suitable":[110],"presentation":[111],"higher":[114],"as":[119],"category.":[121],"To":[122],"end,":[124],"construct":[126],"sketches,":[132],"from":[133],"which":[134],"obtain":[136],"formalism":[139],"algebraically":[141,152],"(co)fibrant":[142],"objects":[143],"strict":[147,154],"and":[150],"cofibrant":[153],"categories.":[156],"latter":[158],"our":[160]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
