{"id":"https://openalex.org/W3205541275","doi":"https://doi.org/10.1017/s0960129521000281","title":"Coherence for bicategorical cartesian closed structure","display_name":"Coherence for bicategorical cartesian closed structure","publication_year":2021,"publication_date":"2021-08-01","ids":{"openalex":"https://openalex.org/W3205541275","doi":"https://doi.org/10.1017/s0960129521000281","mag":"3205541275"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129521000281","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129521000281","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ora.ox.ac.uk/objects/uuid:59a34434-d860-4934-856a-29886110ce8b","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080675787","display_name":"Marcelo Fiore","orcid":"https://orcid.org/0000-0001-8558-3492"},"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":false,"raw_author_name":"Marcelo Fiore","raw_affiliation_strings":["Department of Computer Science and Technology, University of Cambridge, Cambridge, UK"],"raw_orcid":"https://orcid.org/0000-0001-8558-3492","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, University of Cambridge, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038782398","display_name":"Philip Saville","orcid":"https://orcid.org/0000-0002-8320-0280"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Philip Saville","raw_affiliation_strings":["Department of Computer Science, University of Oxford, Oxford, UK","School of Informatics, University of Edinburgh, Edinburgh, UK"],"raw_orcid":"https://orcid.org/0000-0002-8320-0280","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"School of Informatics, University of Edinburgh, Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038782398"],"corresponding_institution_ids":["https://openalex.org/I40120149","https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":1.3362,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7919482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":"7","first_page":"822","last_page":"849"},"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":0.9962000250816345,"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":0.9962000250816345,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9922999739646912,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9790999889373779,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cartesian-closed-category","display_name":"Cartesian closed category","score":0.9149075150489807},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.8110811114311218},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.6226363778114319},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.6202512383460999},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4265408515930176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4093093276023865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.382357656955719},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3771545886993408},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3506760597229004},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3410494923591614},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12254515290260315}],"concepts":[{"id":"https://openalex.org/C171032842","wikidata":"https://www.wikidata.org/wiki/Q1725874","display_name":"Cartesian closed category","level":2,"score":0.9149075150489807},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.8110811114311218},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.6226363778114319},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.6202512383460999},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4265408515930176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4093093276023865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.382357656955719},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3771545886993408},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3506760597229004},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3410494923591614},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12254515290260315},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0960129521000281","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129521000281","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:59a34434-d860-4934-856a-29886110ce8b","is_oa":true,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:59a34434-d860-4934-856a-29886110ce8b","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/328882","is_oa":false,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/328882","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"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":"Article"},{"id":"doi:10.17863/cam.76328","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.76328","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","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":"pmh:oai:ora.ox.ac.uk:uuid:59a34434-d860-4934-856a-29886110ce8b","is_oa":true,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:59a34434-d860-4934-856a-29886110ce8b","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2723597063","display_name":null,"funder_award_id":"EP/V002309/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5071449251","display_name":"Monoidal bicategories, linear logic and operads","funder_award_id":"EP/V002309/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W158035142","https://openalex.org/W578297193","https://openalex.org/W823132808","https://openalex.org/W1507692549","https://openalex.org/W1508490157","https://openalex.org/W1520174560","https://openalex.org/W1555673433","https://openalex.org/W1649578155","https://openalex.org/W1677393765","https://openalex.org/W1754209139","https://openalex.org/W1859542606","https://openalex.org/W1908473049","https://openalex.org/W1958250673","https://openalex.org/W1979791105","https://openalex.org/W1990916178","https://openalex.org/W2000806582","https://openalex.org/W2001462012","https://openalex.org/W2021757832","https://openalex.org/W2022595765","https://openalex.org/W2038364868","https://openalex.org/W2045868464","https://openalex.org/W2047862786","https://openalex.org/W2049362364","https://openalex.org/W2077270594","https://openalex.org/W2081723613","https://openalex.org/W2088862781","https://openalex.org/W2089773888","https://openalex.org/W2094580575","https://openalex.org/W2126306617","https://openalex.org/W2127791900","https://openalex.org/W2134485769","https://openalex.org/W2136376264","https://openalex.org/W2324455841","https://openalex.org/W2503188811","https://openalex.org/W2734361589","https://openalex.org/W2887090517","https://openalex.org/W2964091627","https://openalex.org/W3029012198","https://openalex.org/W3039816335","https://openalex.org/W3080239152","https://openalex.org/W3099664084","https://openalex.org/W3102303293","https://openalex.org/W4205374018","https://openalex.org/W4210699837","https://openalex.org/W4213084408","https://openalex.org/W4247343810","https://openalex.org/W4255149864","https://openalex.org/W6623327223","https://openalex.org/W6630384586","https://openalex.org/W6637929743","https://openalex.org/W6640697532","https://openalex.org/W6661619876","https://openalex.org/W6679982171","https://openalex.org/W6753978648","https://openalex.org/W6779706976","https://openalex.org/W6781913068"],"related_works":["https://openalex.org/W2372920785","https://openalex.org/W3030274415","https://openalex.org/W68628300","https://openalex.org/W1693746038","https://openalex.org/W2394316068","https://openalex.org/W2990703796","https://openalex.org/W3187469014","https://openalex.org/W190761777","https://openalex.org/W402981012","https://openalex.org/W2127138362"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"prove":[2],"a":[3,35,51,71,117],"strictification":[4],"theorem":[5],"for":[6,17,102,125],"cartesian":[7,29,39,67],"closed":[8,30,40,68],"bicategories.":[9],"First,":[10],"we":[11,43,61,87,135],"adapt":[12],"Power\u2019s":[13],"proof":[14],"of":[15,83,91,127],"coherence":[16,58],"bicategories":[18],"with":[19,27,37],"finite":[20],"bilimits":[21],"to":[22,34,46,50,99],"show":[23,44,62,100],"that":[24,63,92],"every":[25],"bicategory":[26,69],"bicategorical":[28],"structure":[31],"is":[32,74,89],"biequivalent":[33],"2-category":[36],"2-categorical":[38],"structure.":[41],"Then":[42],"how":[45],"extend":[47],"this":[48],"result":[49],"Mac":[52],"Lane-style":[53],"\u201call":[54],"pasting":[55],"diagrams":[56],"commute\u201d":[57],"theorem:":[59],"precisely,":[60],"in":[64,116],"the":[65,103,137],"free":[66],"on":[70],"graph,":[72],"there":[73],"at":[75],"most":[76],"one":[77],"2-cell":[78],"between":[79],"any":[80],"parallel":[81],"pair":[82],"1-cells.":[84],"The":[85,111],"argument":[86],"employ":[88],"reminiscent":[90],"used":[93],"by":[94],"\u010cubri\u0107,":[95],"Dybjer,":[96],"and":[97,121],"Scott":[98],"normalisation":[101],"simply-typed":[104],"lambda":[105],"calculus":[106],"(\u010cubri\u0107":[107],"et":[108],"al.,":[109],"1998).":[110],"main":[112],"results":[113],"first":[114],"appeared":[115],"conference":[118],"paper":[119],"(Fiore":[120],"Saville,":[122],"2020)":[123],"but":[124],"reasons":[126],"space":[128],"many":[129],"details":[130],"are":[131],"omitted":[132],"there;":[133],"here":[134],"provide":[136],"full":[138],"development.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
