{"id":"https://openalex.org/W2951884685","doi":"https://doi.org/10.2168/lmcs-6(3:24)2010","title":"Weak omega-categories from intensional type theory","display_name":"Weak omega-categories from intensional type theory","publication_year":2010,"publication_date":"2010-09-17","ids":{"openalex":"https://openalex.org/W2951884685","doi":"https://doi.org/10.2168/lmcs-6(3:24)2010","mag":"2951884685"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-6(3:24)2010","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-6(3:24)2010","pdf_url":"https://lmcs.episciences.org/1062/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":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/1062/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021916916","display_name":"Peter LeFanu Lumsdaine","orcid":"https://orcid.org/0000-0003-1390-2970"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peter LeFanu Lumsdaine","raw_affiliation_strings":["Department of Mathematics, Carnegie Mellon Univerisity, Pittsburgh, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Carnegie Mellon Univerisity, Pittsburgh, U.S.A","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5021916916"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":1.2232,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.78207817,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"Volume 6, 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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9959999918937683,"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/T10832","display_name":"Pituitary Gland Disorders and Treatments","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2712","display_name":"Endocrinology, Diabetes and Metabolism"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/contractible-space","display_name":"Contractible space","score":0.7704229354858398},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.7427059412002563},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6296632289886475},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.6162233948707581},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5824005603790283},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5460179448127747},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.5031225085258484},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.4481675326824188},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41453588008880615},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3538844585418701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2552584707736969},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.20860621333122253},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15931954979896545},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12244817614555359},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.09406530857086182}],"concepts":[{"id":"https://openalex.org/C169611556","wikidata":"https://www.wikidata.org/wiki/Q230689","display_name":"Contractible space","level":2,"score":0.7704229354858398},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.7427059412002563},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6296632289886475},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.6162233948707581},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5824005603790283},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5460179448127747},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5031225085258484},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.4481675326824188},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41453588008880615},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3538844585418701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2552584707736969},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.20860621333122253},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15931954979896545},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12244817614555359},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.09406530857086182},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2168/lmcs-6(3:24)2010","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-6(3:24)2010","pdf_url":"https://lmcs.episciences.org/1062/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:0812.0409","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0812.0409","pdf_url":"https://arxiv.org/pdf/0812.0409","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":"pmh:oai:doaj.org/article:df51e39ea482472dbf69a3861894c7a5","is_oa":true,"landing_page_url":"https://doaj.org/article/df51e39ea482472dbf69a3861894c7a5","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 6, Issue 3 (2010)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-6(3:24)2010","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-6(3:24)2010","pdf_url":"https://lmcs.episciences.org/1062/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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2951884685.pdf","grobid_xml":"https://content.openalex.org/works/W2951884685.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1520893111","https://openalex.org/W1556689307","https://openalex.org/W1677393765","https://openalex.org/W1975282362","https://openalex.org/W2006941708","https://openalex.org/W2022585163","https://openalex.org/W2035244622","https://openalex.org/W2102538436","https://openalex.org/W2136213479","https://openalex.org/W2148713425","https://openalex.org/W2158324835","https://openalex.org/W2170599098","https://openalex.org/W3100912421","https://openalex.org/W3102482356","https://openalex.org/W4214621180","https://openalex.org/W4295120359"],"related_works":["https://openalex.org/W3083301185","https://openalex.org/W4306816010","https://openalex.org/W2170599098","https://openalex.org/W2787703111","https://openalex.org/W2163980057","https://openalex.org/W4225424606","https://openalex.org/W4306353309","https://openalex.org/W4386614239","https://openalex.org/W4283575722","https://openalex.org/W3120415410"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,14],"for":[3],"any":[4,52],"type":[5,15,53],"in":[6,25],"Martin-L\\\"of":[7],"Intensional":[8],"Type":[9],"Theory,":[10],"the":[11,26,49],"terms":[12,50],"of":[13,28,37,45,51],"and":[16,41,54],"its":[17,55],"higher":[18],"identity":[19,56],"types":[20],"form":[21],"a":[22,33],"weak":[23],"omega-category":[24],"sense":[27],"Leinster.":[29],"Precisely,":[30],"we":[31],"construct":[32],"contractible":[34],"globular":[35],"operad":[36,47],"definable":[38],"composition":[39],"laws,":[40],"give":[42],"an":[43],"action":[44],"this":[46],"on":[48],"types.":[57]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
