{"id":"https://openalex.org/W7223813593","doi":"https://doi.org/10.48550/arxiv.2610.33183","title":"Elmendorf's Theorem for $\\infty$-categories","display_name":"Elmendorf's Theorem for $\\infty$-categories","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223813593","doi":"https://doi.org/10.48550/arxiv.2610.33183"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.33183","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33183","pdf_url":"https://arxiv.org/pdf/2610.33183","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.33183","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012682097","display_name":"Peter J. Rowley","orcid":"https://orcid.org/0000-0002-3044-7271","observed_orcids":["https://orcid.org/0000-0002-3044-7271"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rowley, Peter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5012682097"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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":1.0,"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":1.0,"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":0.0,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/simplicial-groups","display_name":"simplicial groups","score":0.8360000252723694},{"id":"https://openalex.org/keywords/infinity-categories","display_name":"infinity-categories","score":0.8700000047683716},{"id":"https://openalex.org/keywords/quillen-equivalence","display_name":"Quillen equivalence","score":0.875},{"id":"https://openalex.org/keywords/homotopy-category","display_name":"homotopy category","score":0.7440000176429749},{"id":"https://openalex.org/keywords/orbit-category","display_name":"orbit category","score":0.878000020980835},{"id":"https://openalex.org/keywords/presheaves","display_name":"presheaves","score":0.8220000267028809}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8574000000953674},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.6028000116348267},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.5723999738693237},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.512499988079071},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5070000290870667},{"id":"https://openalex.org/C147688034","wikidata":"https://www.wikidata.org/wiki/Q1626416","display_name":"Homotopy group","level":3,"score":0.446399986743927},{"id":"https://openalex.org/C119720664","wikidata":"https://www.wikidata.org/wiki/Q3527185","display_name":"Whitehead theorem","level":4,"score":0.4429999887943268},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42559999227523804},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C2776863286","wikidata":"https://www.wikidata.org/wiki/Q17104639","display_name":"Weak equivalence","level":3,"score":0.3336000144481659},{"id":"https://openalex.org/C64245159","wikidata":"https://www.wikidata.org/wiki/Q3983972","display_name":"Simplicial approximation theorem","level":5,"score":0.33079999685287476},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C191752858","wikidata":"https://www.wikidata.org/wiki/Q6358325","display_name":"n-connected","level":3,"score":0.2930000126361847},{"id":"https://openalex.org/C35234519","wikidata":"https://www.wikidata.org/wiki/Q3983973","display_name":"Homotopy lifting property","level":4,"score":0.2734000086784363},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C131359564","wikidata":"https://www.wikidata.org/wiki/Q1941896","display_name":"Model category","level":4,"score":0.26899999380111694}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.33183","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33183","pdf_url":"https://arxiv.org/pdf/2610.33183","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,"listed_in":[],"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":"doi:10.48550/arxiv.2610.33183","doi":"https://doi.org/10.48550/arxiv.2610.33183","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.33183","pdf_url":null,"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,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.33183","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33183","pdf_url":"https://arxiv.org/pdf/2610.33183","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,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223813593.pdf","grobid_xml":"https://content.openalex.org/works/W7223813593.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2227238850","https://openalex.org/W1583479134","https://openalex.org/W2410829626","https://openalex.org/W3150516425","https://openalex.org/W2795810649","https://openalex.org/W3034351801","https://openalex.org/W1662723472","https://openalex.org/W2985974228","https://openalex.org/W1563989028","https://openalex.org/W2166138121"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"Teleman's":[2],"study":[3],"of":[4,16,22,48,56,63,70],"gauged":[5],"topological":[6],"quantum":[7],"field":[8],"theories,":[9],"our":[10],"main":[11],"result":[12],"is":[13,35,40],"an":[14,68],"analog":[15,69],"Elmendorf's":[17],"theorem":[18,72],"in":[19,73],"the":[20,45,53,60],"setting":[21],"simplicial":[23,37],"group":[24],"actions":[25],"on":[26,59],"$\\infty$-categories.":[27],"In":[28],"particular,":[29],"we":[30],"prove":[31],"that":[32],"if":[33],"$G$":[34],"a":[36,41],"group,":[38],"there":[39],"Quillen":[42],"equivalence":[43],"between":[44],"homotopy":[46,54],"category":[47,55,62],"$\\infty$-categories":[49],"with":[50],"$G$-action":[51],"and":[52],"$\\infty$-category-valued":[57],"presheaves":[58],"orbit":[61],"$G$.":[64],"We":[65],"also":[66],"show":[67],"Whitehead's":[71],"this":[74],"setting.":[75]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-28T00:00:00"}