{"id":"https://openalex.org/W2019966914","doi":"https://doi.org/10.1016/s1571-0661(04)00107-0","title":"Tripos Theory in Retrospect","display_name":"Tripos Theory in Retrospect","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2019966914","doi":"https://doi.org/10.1016/s1571-0661(04)00107-0","mag":"2019966914"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)00107-0","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)00107-0","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(04)00107-0","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035484728","display_name":"Andrew M. Pitts","orcid":"https://orcid.org/0000-0001-7775-3471"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Andrew M. Pitts","raw_affiliation_strings":["Computer Laboratory, Cambridge University, Cambridge, UK","Computer Laboratory, Cambridge University Cambridge UK"],"affiliations":[{"raw_affiliation_string":"Computer Laboratory, Cambridge University, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Computer Laboratory, Cambridge University Cambridge UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035484728"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":1.9539,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.85370606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"23","issue":"1","first_page":"111","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9927999973297119,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9927999973297119,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9872000217437744,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9757000207901001,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.9373207092285156},{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.7060061693191528},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5722141861915588},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5347819328308105},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4931003749370575},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.47410115599632263},{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.42327550053596497},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40010368824005127},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.16690906882286072},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10017678141593933},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.07921537756919861}],"concepts":[{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.9373207092285156},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.7060061693191528},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5722141861915588},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5347819328308105},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4931003749370575},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.47410115599632263},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.42327550053596497},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40010368824005127},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.16690906882286072},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10017678141593933},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07921537756919861},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/s1571-0661(04)00107-0","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)00107-0","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.32.2696","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.2696","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cl.cam.ac.uk/papers/amp12/tritr.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.4.6027","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.6027","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cl.cam.ac.uk/~amp12/papers/tritr/tritr.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.45.4600","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.4600","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cl.cam.ac.uk/papers/ap/tritr.ps.gz","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)00107-0","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)00107-0","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1557351111","https://openalex.org/W1605765292","https://openalex.org/W1608610169","https://openalex.org/W2002346383","https://openalex.org/W2043566933","https://openalex.org/W2068932960","https://openalex.org/W2086061699","https://openalex.org/W2099684400","https://openalex.org/W2107093915","https://openalex.org/W2127394739","https://openalex.org/W2137850935","https://openalex.org/W2161023112","https://openalex.org/W2802435120","https://openalex.org/W4240266424","https://openalex.org/W4243933121","https://openalex.org/W6758947918"],"related_works":["https://openalex.org/W2952078890","https://openalex.org/W4300880366","https://openalex.org/W2291208220","https://openalex.org/W2951427440","https://openalex.org/W4301022236","https://openalex.org/W2887094389","https://openalex.org/W1987689608","https://openalex.org/W2042945291","https://openalex.org/W2100490097","https://openalex.org/W2289603781"],"abstract_inverted_index":{"The":[0,32],"notion":[1],"of":[2,16,28,45,49,63,100,105],"\u2018tripos\u2019":[3],"was":[4],"motivated":[5],"by":[6],"the":[7,29,39,43,47,73,84],"desire":[8],"to":[9,42],"explain":[10],"in":[11,56],"what":[12],"sense":[13],"Higgs'":[14],"description":[15],"sheaf":[17],"toposes":[18,25],"as":[19,38,54],"H-valued":[20],"sets":[21],"and":[22,81],"Hyland's":[23],"realizability":[24],"are":[26,98],"instances":[27],"same":[30],"construction.":[31],"construction":[33],"itself":[34],"can":[35],"be":[36],"seen":[37],"universal":[40],"solution":[41],"problem":[44],"realizing":[46],"predicates":[48],"a":[50,57,78,88],"first":[51],"order":[52],"hyperdoctrine":[53,86],"subobjects":[55],"logos":[58,75],"that":[59,72],"has":[60],"all":[61],"quotients":[62],"equivalence":[64],"relations.":[65],"In":[66],"this":[67,94,103],"note":[68],"it":[69],"is":[70,76],"shown":[71],"resulting":[74],"actually":[77],"topos":[79],"if":[80,83],"only":[82],"original":[85],"satisfies":[87],"certain":[89],"comprehension":[90],"property.":[91],"Triposes":[92],"satisfy":[93],"property,":[95],"but":[96],"there":[97],"examples":[99],"non-triposes":[101],"satisfying":[102],"form":[104],"comprehension.":[106]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}