{"id":"https://openalex.org/W1975997375","doi":"https://doi.org/10.2307/2586659","title":"The shuffle Hopf algebra and noncommutative full completeness","display_name":"The shuffle Hopf algebra and noncommutative full completeness","publication_year":1998,"publication_date":"1998-12-01","ids":{"openalex":"https://openalex.org/W1975997375","doi":"https://doi.org/10.2307/2586659","mag":"1975997375"},"language":"en","primary_location":{"id":"doi:10.2307/2586659","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586659","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087503903","display_name":"Richard Blute","orcid":null},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"R. F. Blute","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario Kin 6N5, Canada. E-mail:","Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario Kin 6N5, Canada. E-mail: rblute@mathstat.uottawa.ca"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario Kin 6N5, Canada. E-mail:","institution_ids":["https://openalex.org/I153718931"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario Kin 6N5, Canada. E-mail: rblute@mathstat.uottawa.ca","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061486314","display_name":"Philip Scott","orcid":"https://orcid.org/0000-0002-6289-4260"},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"P. J. Scott","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario Kin 6N5, Canada. E-mail:","Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario Kin 6N5, Canada. E-mail: phil@dinats.mathstat.uottawa.ca"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario Kin 6N5, Canada. E-mail:","institution_ids":["https://openalex.org/I153718931"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario Kin 6N5, Canada. E-mail: phil@dinats.mathstat.uottawa.ca","institution_ids":["https://openalex.org/I153718931"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087503903"],"corresponding_institution_ids":["https://openalex.org/I153718931"],"apc_list":null,"apc_paid":null,"fwci":3.2966,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.92394315,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"63","issue":"4","first_page":"1413","last_page":"1436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.993399977684021,"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/T11567","display_name":"semigroups and automata theory","score":0.9901999831199646,"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/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.7986711859703064},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7713991403579712},{"id":"https://openalex.org/keywords/hopf-algebra","display_name":"Hopf algebra","score":0.6948709487915039},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5808016061782837},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5401067137718201},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5276663899421692},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5212265253067017},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.5143567323684692},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.4660215377807617},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4259818196296692},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.42305946350097656},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41749969124794006},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41239243745803833}],"concepts":[{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.7986711859703064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7713991403579712},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.6948709487915039},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5808016061782837},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5401067137718201},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5276663899421692},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5212265253067017},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.5143567323684692},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.4660215377807617},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4259818196296692},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42305946350097656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41749969124794006},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41239243745803833},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2307/2586659","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586659","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745640","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745640","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":"pmh:oai:CiteSeerX.psu:10.1.1.131.6634","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.131.6634","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://aix1.uottawa.ca/~rblute/shuf.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.1503","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.1503","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sunsite.doc.ic.ac.uk/ic.doc/theory/theory/theory/guests/Scott/shuf.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.3428","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.3428","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sunsite.doc.ic.ac.uk/ic.doc/theory/theory/theory/guests/Scott/shufA4.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W4861723","https://openalex.org/W10605051","https://openalex.org/W65926239","https://openalex.org/W84695432","https://openalex.org/W132036571","https://openalex.org/W159715351","https://openalex.org/W744396148","https://openalex.org/W1480685649","https://openalex.org/W1512931629","https://openalex.org/W1526036637","https://openalex.org/W1533055209","https://openalex.org/W1566685225","https://openalex.org/W1590029082","https://openalex.org/W1870018393","https://openalex.org/W1979324214","https://openalex.org/W1981398295","https://openalex.org/W2032735854","https://openalex.org/W2041917765","https://openalex.org/W2050134666","https://openalex.org/W2050396985","https://openalex.org/W2054969282","https://openalex.org/W2074070481","https://openalex.org/W2078432227","https://openalex.org/W2079171825","https://openalex.org/W2083818592","https://openalex.org/W2086377938","https://openalex.org/W2094685149","https://openalex.org/W2099684400","https://openalex.org/W2109851385","https://openalex.org/W2120950381","https://openalex.org/W2131781021","https://openalex.org/W2169086642","https://openalex.org/W2315068134","https://openalex.org/W2479478569","https://openalex.org/W2596987805","https://openalex.org/W2618896829","https://openalex.org/W2739060726","https://openalex.org/W2911340109","https://openalex.org/W2911865844","https://openalex.org/W2914837968","https://openalex.org/W3039671159","https://openalex.org/W3161688318","https://openalex.org/W4234269419","https://openalex.org/W4234835746","https://openalex.org/W6622125799","https://openalex.org/W6684618234","https://openalex.org/W6741399932","https://openalex.org/W6758338737"],"related_works":["https://openalex.org/W3111851529","https://openalex.org/W4210820417","https://openalex.org/W1657799247","https://openalex.org/W1661873676","https://openalex.org/W2949772116","https://openalex.org/W2034563384","https://openalex.org/W4297663571","https://openalex.org/W467679","https://openalex.org/W4237345912","https://openalex.org/W1701381474"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2,154],"a":[3,12,34,48,60,74,90,95,107,119,155,168],"full":[4],"completeness":[5],"theorem":[6,121],"for":[7,124],"the":[8,53,76,111,125,146,163,184,200],"multiplicative":[9],"fragment":[10],"of":[11,14,36,47,63,78,94,110,145,149,157,170],"variant":[13],"noncommutative":[15,189,194],"linear":[16,20],"logic,":[17],"Yetter's":[18],"cyclic":[19],"logic":[21,127],"(CyLL).":[22],"The":[23,172],"semantics":[24],"is":[25,106,122,166],"obtained":[26,123],"by":[27,160],"interpreting":[28],"proofs":[29,80,136],"as":[30,73,89,137],"dinatural":[31],"transformations":[32,41],"on":[33,203],"category":[35],"topological":[37],"vector":[38,61,102],"spaces,":[39],"these":[40],"being":[42],"equivariant":[43],"under":[44,142],"certain":[45,143],"actions":[46,144],"noncocommutative":[49],"Hopf":[50,177],"algebra":[51,55],"called":[52],"shuffle":[54],"Multiplicative":[56],"sequents":[57],"are":[58,140],"assigned":[59],"space":[62,71],"such":[64],"dinaturals,":[65],"and":[66],"we":[67,134,152],"show":[68],"that":[69,132,158,162],"this":[70,180],"has":[72],"basis":[75],"denotations":[77],"cut-free":[79],"in":[81,179,192],"CyLL":[82],"+":[83,129],"MIX.":[84,130],"This":[85,104],"can":[86],"be":[87],"viewed":[88],"fully":[91],"faithful":[92],"representation":[93],"free":[96],"*-autonomous":[97],"category,":[98],"canonically":[99],"enriched":[100],"over":[101],"spaces.":[103],"paper":[105,181],"natural":[108],"extension":[109],"authors'":[112],"previous":[113],"work,":[114],"\u201cLinear":[115],"L\u00e4uchli":[116],"Semantics\u201d,":[117],"where":[118],"similar":[120],"commutative":[126,187],"MLL":[128],"In":[131],"paper,":[133],"interpret":[135],"dinaturals":[138],"which":[139],"invariant":[141],"additive":[147],"group":[148],"integers.":[150],"Here":[151],"also":[153],"simplification":[156],"work":[159],"showing":[161],"invariance":[164,201],"criterion":[165],"actually":[167],"consequence":[169],"dinaturality.":[171],"passage":[173,185],"from":[174,186],"groups":[175],"to":[176,183,188],"algebras":[178],"corresponds":[182],"logic.":[190],"However,":[191],"our":[193],"setting,":[195],"one":[196],"must":[197],"still":[198],"keep":[199],"condition":[202],"dinaturals.":[204]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":30},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
