{"id":"https://openalex.org/W4388020755","doi":"https://doi.org/10.32408/compositionality-5-10","title":"Traced Monads and Hopf Monads","display_name":"Traced Monads and Hopf Monads","publication_year":2023,"publication_date":"2023-10-30","ids":{"openalex":"https://openalex.org/W4388020755","doi":"https://doi.org/10.32408/compositionality-5-10"},"language":"en","primary_location":{"id":"doi:10.32408/compositionality-5-10","is_oa":true,"landing_page_url":"http://dx.doi.org/10.32408/compositionality-5-10","pdf_url":"https://compositionality.episciences.org/13529/pdf","source":{"id":"https://openalex.org/S4210182901","display_name":"Compositionality","issn_l":"2631-4444","issn":["2631-4444"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Compositionality","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://compositionality.episciences.org/13529/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022707936","display_name":"Masahito Hasegawa","orcid":"https://orcid.org/0000-0003-3460-8615"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masahito Hasegawa","raw_affiliation_strings":["Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan"],"raw_orcid":"https://orcid.org/0000-0003-3460-8615","affiliations":[{"raw_affiliation_string":"Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064711276","display_name":"Jean-Simon Pacaud Lemay","orcid":"https://orcid.org/0000-0003-4124-3722"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Jean-Simon Pacaud Lemay","raw_affiliation_strings":["School of Mathematical and Physical Sciences, Macquarie University, Sydney, New South Wales, Australia"],"raw_orcid":"https://orcid.org/0000-0003-4124-3722","affiliations":[{"raw_affiliation_string":"School of Mathematical and Physical Sciences, Macquarie University, Sydney, New South Wales, Australia","institution_ids":["https://openalex.org/I99043593"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022707936"],"corresponding_institution_ids":["https://openalex.org/I22299242"],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":1.0648,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.76275992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"5","issue":null,"first_page":"10","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9980999827384949,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/monad","display_name":"Monad (category theory)","score":0.8664759397506714},{"id":"https://openalex.org/keywords/symmetric-monoidal-category","display_name":"Symmetric monoidal category","score":0.7201457619667053},{"id":"https://openalex.org/keywords/hopf-algebra","display_name":"Hopf algebra","score":0.6494922041893005},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6302372217178345},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6117122769355774},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.5619379878044128},{"id":"https://openalex.org/keywords/monoidal-category","display_name":"Monoidal category","score":0.5567677021026611},{"id":"https://openalex.org/keywords/quasitriangular-hopf-algebra","display_name":"Quasitriangular Hopf algebra","score":0.45541810989379883},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4314183294773102},{"id":"https://openalex.org/keywords/enriched-category","display_name":"Enriched category","score":0.4257679581642151},{"id":"https://openalex.org/keywords/cartesian-closed-category","display_name":"Cartesian closed category","score":0.42071717977523804},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.2423572540283203},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.07559165358543396},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.07513090968132019}],"concepts":[{"id":"https://openalex.org/C33959348","wikidata":"https://www.wikidata.org/wiki/Q1630568","display_name":"Monad (category theory)","level":3,"score":0.8664759397506714},{"id":"https://openalex.org/C98912367","wikidata":"https://www.wikidata.org/wiki/Q17103860","display_name":"Symmetric monoidal category","level":3,"score":0.7201457619667053},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.6494922041893005},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6302372217178345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6117122769355774},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.5619379878044128},{"id":"https://openalex.org/C2779904274","wikidata":"https://www.wikidata.org/wiki/Q1945014","display_name":"Monoidal category","level":2,"score":0.5567677021026611},{"id":"https://openalex.org/C130856480","wikidata":"https://www.wikidata.org/wiki/Q7269541","display_name":"Quasitriangular Hopf algebra","level":5,"score":0.45541810989379883},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4314183294773102},{"id":"https://openalex.org/C156163052","wikidata":"https://www.wikidata.org/wiki/Q5379515","display_name":"Enriched category","level":3,"score":0.4257679581642151},{"id":"https://openalex.org/C171032842","wikidata":"https://www.wikidata.org/wiki/Q1725874","display_name":"Cartesian closed category","level":2,"score":0.42071717977523804},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.2423572540283203},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.07559165358543396},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.07513090968132019},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.32408/compositionality-5-10","is_oa":true,"landing_page_url":"http://dx.doi.org/10.32408/compositionality-5-10","pdf_url":"https://compositionality.episciences.org/13529/pdf","source":{"id":"https://openalex.org/S4210182901","display_name":"Compositionality","issn_l":"2631-4444","issn":["2631-4444"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Compositionality","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.32408/compositionality-5-10","is_oa":true,"landing_page_url":"http://dx.doi.org/10.32408/compositionality-5-10","pdf_url":"https://compositionality.episciences.org/13529/pdf","source":{"id":"https://openalex.org/S4210182901","display_name":"Compositionality","issn_l":"2631-4444","issn":["2631-4444"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Compositionality","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5913768863","display_name":null,"funder_award_id":"JPMJER1603","funder_id":"https://openalex.org/F4320338112","funder_display_name":"Exploratory Research for Advanced Technology"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320338112","display_name":"Exploratory Research for Advanced Technology","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388020755.pdf","grobid_xml":"https://content.openalex.org/works/W4388020755.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W158035142","https://openalex.org/W195403090","https://openalex.org/W1578654632","https://openalex.org/W1605626978","https://openalex.org/W1644475622","https://openalex.org/W1975166962","https://openalex.org/W2095747698","https://openalex.org/W2096885339","https://openalex.org/W2099628768","https://openalex.org/W2099741610","https://openalex.org/W2099951171","https://openalex.org/W2102357532","https://openalex.org/W2111008373","https://openalex.org/W2151856726","https://openalex.org/W2157114307","https://openalex.org/W2165527471","https://openalex.org/W2167575691","https://openalex.org/W2728096305","https://openalex.org/W2946034447","https://openalex.org/W2950993906","https://openalex.org/W4210278276","https://openalex.org/W4236073713"],"related_works":["https://openalex.org/W2316040467","https://openalex.org/W4244360710","https://openalex.org/W1986885420","https://openalex.org/W2167575691","https://openalex.org/W4221164648","https://openalex.org/W2415965387","https://openalex.org/W3131286612","https://openalex.org/W3176696360","https://openalex.org/W2010611147","https://openalex.org/W4312122767"],"abstract_inverted_index":{"A":[0,23],"traced":[1,8,15,33,86,108,119,145,188,204,222],"monad":[2,5,48,142,146,177,211],"is":[3,49,94,101,137,143,152,212],"a":[4,7,30,45,50,95,139,144,153,179],"on":[6,118,178],"symmetric":[9,16,46,51,62,87,140,175,232],"monoidal":[10,17,88,120,190,206],"category":[11],"that":[12,71,138,224,235],"lifts":[13],"the":[14,38,42,67,73,102,128,199],"structure":[18,76],"to":[19,28,77,98],"its":[20],"Eilenberg-Moore":[21,39,79,129],"category.":[22,40,130,182],"long-standing":[24],"question":[25,97],"has":[26],"been":[27],"provide":[29,158,218],"characterization":[31],"of":[32,69,134,161,221],"monads":[34,64,70,106,117,194,223,234],"without":[35,126],"explicitly":[36],"mentioning":[37,127],"On":[41],"other":[43],"hand,":[44],"Hopf":[47,63,105,116,141,155,163,171,176,193,210,227,233],"bimonad":[52],"whose":[53],"fusion":[54],"operators":[55],"are":[56,65,90,225,236],"invertible.":[57],"For":[58],"compact":[59,74,82,180],"closed":[60,75,83,181],"categories,":[61,121,191,207],"precisely":[66],"kind":[68],"lift":[72],"their":[78],"categories.":[80],"Since":[81],"categories":[84,89],"and":[85,107,148],"closely":[91],"related,":[92],"it":[93,151],"natural":[96],"ask":[99],"what":[100],"relationship":[103],"between":[104],"monads.":[109],"In":[110],"this":[111,135],"paper,":[112],"we":[113],"introduce":[114],"trace-coherent":[115,154,162,192,209],"which":[122],"can":[123,195],"be":[124,196],"characterized":[125],"The":[131],"main":[132],"theorem":[133],"paper":[136],"if":[147,150],"only":[149],"monad.":[156,215],"We":[157,183,216],"many":[159],"examples":[160,220],"monads,":[164,228],"such":[165],"as":[166,229,231],"those":[167],"induced":[168],"by":[169],"cocommutative":[170],"algebras":[172],"or":[173],"any":[174,208],"also":[184,217],"explain":[185],"how":[186],"for":[187,203],"Cartesian":[189],"expressed":[197],"using":[198],"Conway":[200],"operator,":[201],"while":[202],"coCartesian":[205],"an":[213],"idempotent":[214],"separating":[219],"not":[226,237],"well":[230],"trace-coherent.":[238]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
