{"id":"https://openalex.org/W2150369467","doi":"https://doi.org/10.1305/ndjfl/1099238447","title":"Ultrasheaves and Double Negation","display_name":"Ultrasheaves and Double Negation","publication_year":2004,"publication_date":"2004-10-01","ids":{"openalex":"https://openalex.org/W2150369467","doi":"https://doi.org/10.1305/ndjfl/1099238447","mag":"2150369467"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1099238447","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1099238447","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-4/Ultrasheaves-and-Double-Negation/10.1305/ndjfl/1099238447.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-4/Ultrasheaves-and-Double-Negation/10.1305/ndjfl/1099238447.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048294977","display_name":"Steve Awodey","orcid":"https://orcid.org/0000-0001-9005-179X"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]},{"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":false,"raw_author_name":"Steve Awodey","raw_affiliation_strings":["Department of Mathematics University of Uppsala PO Box 480 S-751 06 Uppsala SWEDEN","Department of Philosophy Carnegie Mellon University 5000 Forbes Avenue Pittsburgh PA 15213","University of Notre Dame"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Uppsala PO Box 480 S-751 06 Uppsala SWEDEN","institution_ids":[]},{"raw_affiliation_string":"Department of Philosophy Carnegie Mellon University 5000 Forbes Avenue Pittsburgh PA 15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067216808","display_name":"Jonas Eliasson","orcid":"https://orcid.org/0000-0003-1789-9238"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]},{"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":false,"raw_author_name":"Jonas Eliasson","raw_affiliation_strings":["University of Notre Dame","Department of Mathematics University of Uppsala PO Box 480 S-751 06 Uppsala SWEDEN","Department of Philosophy Carnegie Mellon University 5000 Forbes Avenue Pittsburgh PA 15213"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Mathematics University of Uppsala PO Box 480 S-751 06 Uppsala SWEDEN","institution_ids":[]},{"raw_affiliation_string":"Department of Philosophy Carnegie Mellon University 5000 Forbes Avenue Pittsburgh PA 15213","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3932,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62398509,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"45","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9937999844551086,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9937999844551086,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9886000156402588,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/topos-theory","display_name":"Topos theory","score":0.9773600101470947},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.894334077835083},{"id":"https://openalex.org/keywords/subcategory","display_name":"Subcategory","score":0.8216190338134766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6777989864349365},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4863210618495941},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.3094291090965271},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.12871608138084412},{"id":"https://openalex.org/keywords/literature","display_name":"Literature","score":0.0455511212348938},{"id":"https://openalex.org/keywords/art","display_name":"Art","score":0.0362110435962677}],"concepts":[{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.9773600101470947},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.894334077835083},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.8216190338134766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6777989864349365},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4863210618495941},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.3094291090965271},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.12871608138084412},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0455511212348938},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0362110435962677}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1305/ndjfl/1099238447","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1099238447","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-4/Ultrasheaves-and-Double-Negation/10.1305/ndjfl/1099238447.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/6493022","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Ultrasheaves_and_Double_Negation/6493022","pdf_url":"https://figshare.com/articles/journal_contribution/Ultrasheaves_and_Double_Negation/6493022","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:figshare.com:article/6493025","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Ultrasheaves_and_Double-Negation/6493025","pdf_url":"https://figshare.com/articles/Ultrasheaves_and_Double-Negation/6493025","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:repository.cmu.edu:philosophy-1072","is_oa":false,"landing_page_url":"http://repository.cmu.edu/cgi/viewcontent.cgi?article=1072&context=philosophy","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Philosophy","raw_type":"text"},{"id":"pmh:oai:repository.cmu.edu:philosophy-1145","is_oa":false,"landing_page_url":"http://repository.cmu.edu/philosophy/153","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Philosophy","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6493022","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Journal contribution"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1099238447","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1099238447","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"doi:10.1184/r1/6493022.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6493022.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"JournalArticle"},{"id":"doi:10.1184/r1/6493025.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6493025.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"JournalArticle"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1099238447","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1099238447","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-4/Ultrasheaves-and-Double-Negation/10.1305/ndjfl/1099238447.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310207","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2150369467.pdf","grobid_xml":"https://content.openalex.org/works/W2150369467.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W36355091","https://openalex.org/W131047781","https://openalex.org/W232986403","https://openalex.org/W950096932","https://openalex.org/W1499154644","https://openalex.org/W1971195030","https://openalex.org/W1988155600","https://openalex.org/W1996830918","https://openalex.org/W1997558102","https://openalex.org/W1997968929","https://openalex.org/W2001916998","https://openalex.org/W2015875856","https://openalex.org/W2023562444","https://openalex.org/W2068932960","https://openalex.org/W2069787050","https://openalex.org/W2075382666","https://openalex.org/W2078108932","https://openalex.org/W2106472259","https://openalex.org/W2619559139"],"related_works":["https://openalex.org/W3110986101","https://openalex.org/W4246327958","https://openalex.org/W2579704584","https://openalex.org/W4319982912","https://openalex.org/W2803072931","https://openalex.org/W3125091610","https://openalex.org/W376795554","https://openalex.org/W4226068787","https://openalex.org/W1949059319","https://openalex.org/W955009269"],"abstract_inverted_index":{"Moerdijk":[0],"has":[1],"introduced":[2],"a":[3,8,40],"topos":[4,24,48,53],"of":[5,10,25,30,44,49],"sheaves":[6,26],"on":[7,27,54],"category":[9],"filters.":[11,55],"Following":[12],"his":[13],"suggestion,":[14],"we":[15],"prove":[16],"that":[17],"its":[18],"double":[19,41],"negation":[20,42],"subtopos":[21],"is":[22],"the":[23,28,47,52],"subcategory":[29],"ultrafilters\u2014the":[31],"ultrasheaves.":[32],"We":[33],"then":[34],"use":[35],"this":[36],"result":[37],"to":[38],"establish":[39],"translation":[43],"results":[45],"between":[46],"ultrasheaves":[50],"and":[51]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
