{"id":"https://openalex.org/W1836105801","doi":"https://doi.org/10.1007/s10485-011-9255-2","title":"The groupoidal analogue Theta~ to Joyal's category Theta is a test category","display_name":"The groupoidal analogue Theta~ to Joyal's category Theta is a test category","publication_year":2010,"publication_date":"2010-12-20","ids":{"openalex":"https://openalex.org/W1836105801","doi":"https://doi.org/10.1007/s10485-011-9255-2","mag":"1836105801"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1012.4319","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1012.4319","pdf_url":"https://arxiv.org/pdf/1012.4319","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"},"type":"preprint","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1012.4319","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014734680","display_name":"Dimitri Ara","orcid":"https://orcid.org/0000-0002-8025-9236"},"institutions":[{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ara, Dimitri","raw_affiliation_strings":["Institut de Math\u00e9matiques de Marseille"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Marseille","institution_ids":["https://openalex.org/I4210138206"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014734680"],"corresponding_institution_ids":["https://openalex.org/I4210138206"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.06743158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9973999857902527,"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":0.9652000069618225,"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/test","display_name":"Test (biology)","score":0.6293618083000183},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4533237814903259},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36449718475341797},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3589758574962616},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.12614646553993225},{"id":"https://openalex.org/keywords/paleontology","display_name":"Paleontology","score":0.06844624876976013}],"concepts":[{"id":"https://openalex.org/C2777267654","wikidata":"https://www.wikidata.org/wiki/Q3519023","display_name":"Test (biology)","level":2,"score":0.6293618083000183},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4533237814903259},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36449718475341797},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3589758574962616},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.12614646553993225},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.06844624876976013}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:arXiv.org:1012.4319","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1012.4319","pdf_url":"https://arxiv.org/pdf/1012.4319","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1012.4319","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1012.4319","pdf_url":"https://arxiv.org/pdf/1012.4319","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":0.5,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W155382641","https://openalex.org/W1595870841","https://openalex.org/W1978580858","https://openalex.org/W1995696029","https://openalex.org/W2137635776"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0,39],"introduce":[1],"the":[2,22,43,54],"groupoidal":[3],"analogue":[4],"\\tilde\\Theta":[5,15,31,49,68],"to":[6,48,61,69,79,83],"Joyal's":[7],"cell":[8],"category":[9,20],"\\Theta":[10,47],"and":[11],"we":[12],"prove":[13,41],"that":[14,28,42],"is":[16,50],"a":[17,36],"strict":[18],"test":[19],"in":[21,35,53],"sense":[23,55],"of":[24,56,65,72],"Grothendieck.":[25,57],"This":[26,58],"implies":[27],"presheaves":[29,66,73],"on":[30,67,74],"model":[32],"homotopy":[33],"types":[34],"canonical":[37,44],"way.":[38],"also":[40],"functor":[45],"from":[46],"aspherical,":[51],"again":[52],"allows":[59],"us":[60],"compare":[62],"weak":[63,70],"equivalences":[64,71],"\\Theta.":[75,84],"Our":[76],"proofs":[77],"apply":[78],"other":[80],"categories":[81],"analogous":[82]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}
