{"id":"https://openalex.org/W2054110340","doi":"https://doi.org/10.1016/s1571-0661(05)80303-2","title":"Equational Lifting Monads","display_name":"Equational Lifting Monads","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2054110340","doi":"https://doi.org/10.1016/s1571-0661(05)80303-2","mag":"2054110340"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(05)80303-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80303-2","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(05)80303-2","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036951085","display_name":"Anna Bucalo","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anna Bucalo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082534690","display_name":"Carsten F\u00fchrmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carsten F\u00fchrmann","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110256373","display_name":"Alex Simpson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alex Simpson","raw_affiliation_strings":["School of Informatics"],"affiliations":[{"raw_affiliation_string":"School of Informatics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036951085"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0778,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.88502651,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"29","issue":null,"first_page":"22","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9972000122070312,"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":0.9972000122070312,"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":0.9563999772071838,"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":0.9180999994277954,"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/monad","display_name":"Monad (category theory)","score":0.9379554986953735},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5980644226074219},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5395097136497498},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.470355749130249},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4472905397415161},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3818460702896118},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.23172372579574585},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.049519240856170654}],"concepts":[{"id":"https://openalex.org/C33959348","wikidata":"https://www.wikidata.org/wiki/Q1630568","display_name":"Monad (category theory)","level":3,"score":0.9379554986953735},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5980644226074219},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5395097136497498},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.470355749130249},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4472905397415161},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3818460702896118},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.23172372579574585},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.049519240856170654},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/s1571-0661(05)80303-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80303-2","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:10.1.1.100.7278","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.7278","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.bath.ac.uk/~cf/lifting.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.48.3299","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.3299","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dcs.ed.ac.uk/home/als/Research/lifting.ps.gz","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(05)80303-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80303-2","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W16477519","https://openalex.org/W583126019","https://openalex.org/W1511232673","https://openalex.org/W1566009901","https://openalex.org/W1633776801","https://openalex.org/W1997143185","https://openalex.org/W2005230371","https://openalex.org/W2017778827","https://openalex.org/W2023861274","https://openalex.org/W2065261632","https://openalex.org/W2079028772","https://openalex.org/W2142922307","https://openalex.org/W2156876717"],"related_works":["https://openalex.org/W4226430568","https://openalex.org/W2115785609","https://openalex.org/W2770491433","https://openalex.org/W4296959858","https://openalex.org/W2754254730","https://openalex.org/W3136039576","https://openalex.org/W99544092","https://openalex.org/W4313533159","https://openalex.org/W1985548572","https://openalex.org/W2133665531"],"abstract_inverted_index":{"We":[0,25],"introduce":[1],"the":[2,42,46,51,55,63,98],"notion":[3],"of":[4,45,54,67,82,97,101,115],"an":[5],"equational":[6,29,58,65,87,102],"lifting":[7,30,59,88,103],"monad:":[8],"a":[9,33,36,76,94],"commutative":[10],"strong":[11],"monad":[12,31],"satisfying":[13],"one":[14],"additional":[15],"equation":[16],"(valid":[17],"for":[18,78],"monads":[19,60,104],"arising":[20],"from":[21],"partial":[22,37,52,68,83],"map":[23,38,69,84],"classifiers).":[24],"prove":[26],"that":[27,41],"any":[28],"has":[32],"representation":[34,72],"by":[35],"classifier":[39],"such":[40],"Kleisli":[43,99,107],"category":[44,53],"former":[47],"fully":[48],"embeds":[49],"in":[50,117],"latter.":[56],"Thus":[57],"precisely":[61],"capture":[62],"(partial)":[64],"properties":[66,81],"classifiers.":[70],"The":[71],"theorem":[73],"also":[74],"provides":[75],"tool":[77],"transferring":[79],"non-equational":[80],"classifiers":[85],"to":[86],"monads.":[89],"It":[90],"is":[91,114],"proved":[92],"using":[93],"direct":[95],"axiomatization":[96,113],"categories":[100,108],"as":[105],"abstract":[106],"with":[109],"extra":[110],"structure.":[111],"This":[112],"interest":[116],"its":[118],"own":[119],"right.":[120],"1":[121]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
