{"id":"https://openalex.org/W1983546908","doi":"https://doi.org/10.2168/lmcs-9(3:22)2013","title":"Exploring the Boundaries of Monad Tensorability on Set","display_name":"Exploring the Boundaries of Monad Tensorability on Set","publication_year":2013,"publication_date":"2013-09-18","ids":{"openalex":"https://openalex.org/W1983546908","doi":"https://doi.org/10.2168/lmcs-9(3:22)2013","mag":"1983546908"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-9(3:22)2013","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-9(3:22)2013","pdf_url":"https://lmcs.episciences.org/740/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/740/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112266022","display_name":"Nathan Bowler","orcid":null},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Nathan Bowler","raw_affiliation_strings":["Department of Mathematics, Universitt Hamburg","Department of Mathematics, Universit\u00e4t Hamburg"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universitt Hamburg","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"Department of Mathematics, Universit\u00e4t Hamburg","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005129928","display_name":"\u0421. \u0421. \u0413\u043e\u043d\u0447\u0430\u0440\u043e\u0432","orcid":"https://orcid.org/0000-0001-7465-1189"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sergey Goncharov","raw_affiliation_strings":["Department of Computer Science Friedrich-Alexander-Universit\u00e4t Erlangen-NUrnberg"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science Friedrich-Alexander-Universit\u00e4t Erlangen-NUrnberg","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053041930","display_name":"Paul Blain Levy","orcid":"https://orcid.org/0000-0003-0864-1876"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Paul Blain Levy","raw_affiliation_strings":["School of Computer Science, University of Birmingham"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Birmingham","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073765060","display_name":"Lutz Schr\u00f6der","orcid":"https://orcid.org/0000-0002-3146-5906"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lutz Schr\u00f6der","raw_affiliation_strings":["Department of Computer Science Friedrich-Alexander-Universit\u00e4t Erlangen-NUrnberg"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science Friedrich-Alexander-Universit\u00e4t Erlangen-NUrnberg","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5112266022"],"corresponding_institution_ids":["https://openalex.org/I159176309"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.06659845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"Volume 9, Issue 3","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T10142","display_name":"Formal Methods in Verification","score":0.9987999796867371,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9961000084877014,"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/monad","display_name":"Monad (category theory)","score":0.9111613631248474},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6364277005195618},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.5969836711883545},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.5872405767440796},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5338510274887085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5279896259307861},{"id":"https://openalex.org/keywords/principle-of-compositionality","display_name":"Principle of compositionality","score":0.5217229127883911},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.4907015562057495},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.4792385399341583},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4205189645290375},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3941640853881836},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3308665454387665},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3244556784629822},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.3031732439994812},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1983165144920349},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07821711897850037}],"concepts":[{"id":"https://openalex.org/C33959348","wikidata":"https://www.wikidata.org/wiki/Q1630568","display_name":"Monad (category theory)","level":3,"score":0.9111613631248474},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6364277005195618},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5969836711883545},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.5872405767440796},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5338510274887085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5279896259307861},{"id":"https://openalex.org/C121375916","wikidata":"https://www.wikidata.org/wiki/Q936559","display_name":"Principle of compositionality","level":2,"score":0.5217229127883911},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.4907015562057495},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.4792385399341583},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4205189645290375},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3941640853881836},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3308665454387665},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3244556784629822},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.3031732439994812},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1983165144920349},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07821711897850037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.2168/lmcs-9(3:22)2013","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-9(3:22)2013","pdf_url":"https://lmcs.episciences.org/740/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1309.2128","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1309.2128","pdf_url":"https://arxiv.org/pdf/1309.2128","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.755.1906","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.755.1906","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1309.2128.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:1847e2030e7f45ea8c0e2fb7fff532c0","is_oa":true,"landing_page_url":"https://doaj.org/article/1847e2030e7f45ea8c0e2fb7fff532c0","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 9, Issue 3 (2013)","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/182cd675-944f-4bb0-935b-78741d50aa1d","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/182cd675-944f-4bb0-935b-78741d50aa1d","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bowler, N, Goncharov, S, Levy, P B & Schr\u00f6der, L 2013, 'Exploring the boundaries of monad tensorability on set', Logical Methods in Computer Science, vol. 9, no. 3, 22. https://doi.org/10.2168/LMCS-9(3:22)2013","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/182cd675-944f-4bb0-935b-78741d50aa1d","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=84884824708&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bowler, N, Goncharov, S, Levy, P B & Schr\u00f6der, L 2013, 'Exploring the boundaries of monad tensorability on set', Logical Methods in Computer Science, vol. 9, no. 3, 22. https://doi.org/10.2168/LMCS-9(3:22)2013","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-9(3:22)2013","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-9(3:22)2013","pdf_url":"https://lmcs.episciences.org/740/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1361938442","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5830914335","display_name":null,"funder_award_id":"EP/E056091/1","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1983546908.pdf","grobid_xml":"https://content.openalex.org/works/W1983546908.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W38906659","https://openalex.org/W69808434","https://openalex.org/W583126019","https://openalex.org/W986162294","https://openalex.org/W1498220043","https://openalex.org/W1510067240","https://openalex.org/W1521014576","https://openalex.org/W1538724214","https://openalex.org/W1549977012","https://openalex.org/W1556162816","https://openalex.org/W1585980631","https://openalex.org/W1965620900","https://openalex.org/W1970598198","https://openalex.org/W1980827618","https://openalex.org/W1997143185","https://openalex.org/W2072351525","https://openalex.org/W2087404516","https://openalex.org/W2091590322","https://openalex.org/W2102459565","https://openalex.org/W2164262222"],"related_works":["https://openalex.org/W2138773009","https://openalex.org/W2904778759","https://openalex.org/W4287705132","https://openalex.org/W2078516608","https://openalex.org/W2127005761","https://openalex.org/W3214473273","https://openalex.org/W3043991061","https://openalex.org/W3099810744","https://openalex.org/W4302612925","https://openalex.org/W2950890655"],"abstract_inverted_index":{"We":[0,77],"study":[1],"a":[2,75,113],"composition":[3],"operation":[4],"on":[5],"monads,":[6],"equivalently":[7],"presented":[8],"as":[9],"large":[10],"equational":[11],"theories.":[12,35],"Specifically,":[13],"we":[14,82,134],"discuss":[15],"the":[16,30,33,40,61,66,85,106,131],"existence":[17],"of":[18,23,29,42,52,63,87,100,108],"tensors,":[19],"which":[20,45],"are":[21],"combinations":[22],"theories":[24,53],"that":[25,84,123,136],"impose":[26],"mutual":[27],"commutation":[28],"operations":[31],"from":[32,144],"component":[34],"As":[36],"such,":[37],"they":[38],"extend":[39],"sum":[41],"two":[43,79,88,97],"theories,":[44],"is":[46,72],"just":[47],"their":[48],"unrestrained":[49],"combination.":[50],"Tensors":[51],"arise":[54],"in":[55,58,60,92],"several":[56],"contexts;":[57],"particular,":[59],"semantics":[62],"programming":[64],"languages,":[65],"monad":[67],"transformer":[68],"for":[69],"global":[70],"state":[71],"given":[73],"by":[74,95],"tensor.":[76],"present":[78],"main":[80],"results:":[81],"show":[83,135],"tensor":[86],"monads":[89,141],"need":[90],"not":[91],"general":[93],"exist":[94,143],"presenting":[96],"counterexamples,":[98],"one":[99],"them":[101],"involving":[102],"finite":[103],"powerset":[104,140,146],"(i.e.":[105],"theory":[107],"join":[109],"semilattices);":[110],"this":[111],"solves":[112],"somewhat":[114],"long-standing":[115],"open":[116],"problem,":[117],"and":[118],"contrasts":[119],"with":[120,138],"recent":[121],"results":[122],"had":[124],"ruled":[125],"out":[126],"previously":[127],"expected":[128],"counterexamples.":[129],"On":[130],"other":[132],"hand,":[133],"tensors":[137],"bounded":[139],"do":[142],"countable":[145],"upwards.":[147]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
