{"id":"https://openalex.org/W200058515","doi":"https://doi.org/10.1016/j.jal.2013.04.001","title":"A model of type theory in simplicial sets","display_name":"A model of type theory in simplicial sets","publication_year":2013,"publication_date":"2013-04-25","ids":{"openalex":"https://openalex.org/W200058515","doi":"https://doi.org/10.1016/j.jal.2013.04.001","mag":"200058515"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jal.2013.04.001","pdf_url":null,"source":{"id":"https://openalex.org/S164898596","display_name":"Journal of Applied Logic","issn_l":"1570-8683","issn":["1570-8683","1570-8691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.jal.2013.04.001","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022583176","display_name":"Thomas Streicher","orcid":"https://orcid.org/0000-0001-6725-0168"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technical University of Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"T. Streicher","raw_affiliation_strings":["Fachbereich 4 Mathematik, TU Darmstadt, Schlo\u00dfgartenstr. 7, D-64289 Darmstadt, Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich 4 Mathematik, TU Darmstadt, Schlo\u00dfgartenstr. 7, D-64289 Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022583176"],"corresponding_institution_ids":["https://openalex.org/I31512782"],"apc_list":null,"apc_paid":null,"fwci":2.917,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":24,"citation_normalized_percentile":{"value":0.877416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":92},"biblio":{"volume":"12","issue":"1","first_page":"45","last_page":"49"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9986,"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":0.9986,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.959,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9507,"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/model-category","display_name":"Model category","score":0.799147},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.7260094},{"id":"https://openalex.org/keywords/constructive-set-theory","display_name":"Constructive set theory","score":0.53572756},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.51520044},{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.4966324},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.43550783},{"id":"https://openalex.org/keywords/cofibration","display_name":"Cofibration","score":0.4189966},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.41352203}],"concepts":[{"id":"https://openalex.org/C131359564","wikidata":"https://www.wikidata.org/wiki/Q1941896","display_name":"Model category","level":4,"score":0.799147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.77679217},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.7682892},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.7260094},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.66568565},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6632624},{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.53572756},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5297091},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.51520044},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.51492536},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.4966324},{"id":"https://openalex.org/C155366967","wikidata":"https://www.wikidata.org/wiki/Q1467124","display_name":"Simplicial set","level":4,"score":0.4926327},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.43892047},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.43550783},{"id":"https://openalex.org/C150275644","wikidata":"https://www.wikidata.org/wiki/Q1048949","display_name":"Cofibration","level":5,"score":0.4189966},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.41352203},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.30988678},{"id":"https://openalex.org/C191752858","wikidata":"https://www.wikidata.org/wiki/Q6358325","display_name":"n-connected","level":3,"score":0.2593945},{"id":"https://openalex.org/C168334404","wikidata":"https://www.wikidata.org/wiki/Q7309601","display_name":"Regular homotopy","level":4,"score":0.22862273},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.13230082},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11829114},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jal.2013.04.001","pdf_url":null,"source":{"id":"https://openalex.org/S164898596","display_name":"Journal of Applied Logic","issn_l":"1570-8683","issn":["1570-8683","1570-8691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jal.2013.04.001","pdf_url":null,"source":{"id":"https://openalex.org/S164898596","display_name":"Journal of Applied Logic","issn_l":"1570-8683","issn":["1570-8683","1570-8691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":11,"referenced_works":["https://openalex.org/W1512931629","https://openalex.org/W1530632394","https://openalex.org/W1533094521","https://openalex.org/W1553511155","https://openalex.org/W1683762557","https://openalex.org/W2130779085","https://openalex.org/W2148713425","https://openalex.org/W2475129850","https://openalex.org/W2476069610","https://openalex.org/W3102482356","https://openalex.org/W4246016820"],"related_works":["https://openalex.org/W4310560426","https://openalex.org/W4254408107","https://openalex.org/W4253188024","https://openalex.org/W37325539","https://openalex.org/W2949663047","https://openalex.org/W2527406090","https://openalex.org/W2133717328","https://openalex.org/W2064817625","https://openalex.org/W200058515","https://openalex.org/W1990738469"],"abstract_inverted_index":{"We":[0],"describe":[1],"how":[2],"to":[3,69,107,109],"interpret":[4],"constructive":[5],"type":[6,84],"theory":[7],"in":[8,71],"the":[9,42,53],"topos":[10],"of":[11,22,87,97],"simplicial":[12],"sets":[13],"where":[14],"types":[15,23,80],"appear":[16],"as":[17,24,33,111],"Kan":[18,25,28,98],"complexes":[19,29],"and":[20,40,52],"families":[21],"fibrations.":[26],"Since":[27],"may":[30],"be":[31],"understood":[32],"weak":[34],"higher-dimensional":[35],"groupoids":[36],"this":[37,72,91,101],"model":[38,45,92],"generalizes":[39],"extends":[41],"(ordinary)":[43],"groupoid":[44],"which":[46,65],"was":[47],"introduced":[48],"by":[49,90],"M.":[50],"Hofmann":[51],"author":[54],"about":[55],"20":[56],"years":[57],"ago.":[58],"Finally,":[59],"we":[60],"discuss":[61],"Voevodsky's":[62],"Univalence":[63],"Axiom":[64],"has":[66,104],"been":[67],"shown":[68],"hold":[70],"model.":[73],"This":[74],"axiom":[75],"roughly":[76],"states":[77],"that":[78],"isomorphic":[79],"are":[81],"equal.":[82],"The":[83],"theoretic":[85],"notion":[86],"isomorphism":[88],"provided":[89],"coincides":[93],"with":[94],"homotopy":[95],"equivalence":[96],"complexes.":[99],"For":[100],"reason":[102],"it":[103,110],"become":[105],"common":[106],"refer":[108],"Homotopy":[112],"Type":[113],"Theory.":[114]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W200058515","counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2025-01-16T22:32:04.816362","created_date":"2016-06-24"}