{"id":"https://openalex.org/W4385342924","doi":"https://doi.org/10.4204/eptcs.380.1","title":"Canonical Gradings of Monads","display_name":"Canonical Gradings of Monads","publication_year":2023,"publication_date":"2023-07-28","ids":{"openalex":"https://openalex.org/W4385342924","doi":"https://doi.org/10.4204/eptcs.380.1"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.380.1","pdf_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?ACT2022.1.pdf","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":false,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"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},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?ACT2022.1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004140160","display_name":"Flavien Breuvart","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I4210156583","display_name":"Laboratoire d'Informatique de Paris-Nord","ror":"https://ror.org/05g1zjw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210156583","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Flavien Breuvart","raw_affiliation_strings":["LIPN - Laboratoire d'Informatique de Paris-Nord (Institut Galil\u00e9e, Universit\u00e9 Paris 13, 99 avenue Jean-Baptiste Cl\u00e9ment, F-93430, Villetaneuse - France)"],"affiliations":[{"raw_affiliation_string":"LIPN - Laboratoire d'Informatique de Paris-Nord (Institut Galil\u00e9e, Universit\u00e9 Paris 13, 99 avenue Jean-Baptiste Cl\u00e9ment, F-93430, Villetaneuse - France)","institution_ids":["https://openalex.org/I4210091279","https://openalex.org/I4210156583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047709110","display_name":"Dylan McDermott","orcid":"https://orcid.org/0000-0002-6705-1449"},"institutions":[{"id":"https://openalex.org/I123185442","display_name":"Reykjav\u00edk University","ror":"https://ror.org/05d2kyx68","country_code":"IS","type":"education","lineage":["https://openalex.org/I123185442"]}],"countries":["IS"],"is_corresponding":false,"raw_author_name":"Dylan McDermott","raw_affiliation_strings":["Reykjav\u00edk University (Iceland)"],"affiliations":[{"raw_affiliation_string":"Reykjav\u00edk University (Iceland)","institution_ids":["https://openalex.org/I123185442"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074922343","display_name":"Tarmo Uustalu","orcid":"https://orcid.org/0000-0002-1297-0579"},"institutions":[{"id":"https://openalex.org/I123185442","display_name":"Reykjav\u00edk University","ror":"https://ror.org/05d2kyx68","country_code":"IS","type":"education","lineage":["https://openalex.org/I123185442"]},{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]}],"countries":["EE","IS"],"is_corresponding":false,"raw_author_name":"Tarmo Uustalu","raw_affiliation_strings":["Reykjav\u00edk University (Iceland)","TalTech - Tallinn University of Technology (Ehitajate tee 5, 19086 Tallinn - Estonia)"],"affiliations":[{"raw_affiliation_string":"Reykjav\u00edk University (Iceland)","institution_ids":["https://openalex.org/I123185442"]},{"raw_affiliation_string":"TalTech - Tallinn University of Technology (Ehitajate tee 5, 19086 Tallinn - Estonia)","institution_ids":["https://openalex.org/I111112146"]}]}],"institution_assertions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0,"provenance":"doaj"},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":67},"biblio":{"volume":"380","issue":null,"first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9942,"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":0.9942,"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":0.9931,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.61409277},{"id":"https://openalex.org/keywords/monoidal-category","display_name":"Monoidal category","score":0.43594304},{"id":"https://openalex.org/keywords/canonical-form","display_name":"Canonical form","score":0.42882404},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.42635378}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7158205},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.61409277},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.58232915},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.51347023},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5116392},{"id":"https://openalex.org/C2779904274","wikidata":"https://www.wikidata.org/wiki/Q1945014","display_name":"Monoidal category","level":2,"score":0.43594304},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.42882404},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.42635378},{"id":"https://openalex.org/C156163052","wikidata":"https://www.wikidata.org/wiki/Q5379515","display_name":"Enriched category","level":3,"score":0.42091572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39714655},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.16729355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13315511},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.380.1","pdf_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?ACT2022.1.pdf","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":false,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"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},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.16558","pdf_url":"http://arxiv.org/pdf/2307.16558","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://hal.science/hal-04676021","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.2307.16558","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.380.1","pdf_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?ACT2022.1.pdf","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":false,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"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},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":["https://openalex.org/W4385342924"],"referenced_works_count":13,"referenced_works":["https://openalex.org/W156546173","https://openalex.org/W1606211906","https://openalex.org/W2002967907","https://openalex.org/W2007738069","https://openalex.org/W2016389769","https://openalex.org/W2046137117","https://openalex.org/W2046449629","https://openalex.org/W2156876717","https://openalex.org/W2339107952","https://openalex.org/W2893246288","https://openalex.org/W2963951024","https://openalex.org/W3136039576","https://openalex.org/W4293813127"],"related_works":["https://openalex.org/W4387799810","https://openalex.org/W3103633364","https://openalex.org/W2726771738","https://openalex.org/W2488035445","https://openalex.org/W2156541639","https://openalex.org/W2150762370","https://openalex.org/W2101433240","https://openalex.org/W205933276","https://openalex.org/W2051110641","https://openalex.org/W1551462233"],"abstract_inverted_index":{"We":[0,28,59,80],"define":[1],"a":[2,7,11,17,24,38,43,69],"notion":[3,25],"of":[4,6,19,26,46,56,68,71],"grading":[5,45],"monoid":[8],"T":[9],"in":[10],"monoidal":[12],"category":[13],"C,":[14],"relative":[15],"to":[16,51],"class":[18],"morphisms":[20],"M":[21,36],"(which":[22],"provide":[23],"M-subobject).":[27],"show":[29,82],"that,":[30],"under":[31],"reasonable":[32],"conditions":[33],"(including":[34],"that":[35,83],"forms":[37],"factorization":[39],"system),":[40],"there":[41],"is":[42,50,76],"canonical":[44,66,87],"T.":[47],"Our":[48],"application":[49],"graded":[52],"monads":[53],"and":[54],"models":[55],"computational":[57],"effects.":[58],"demonstrate":[60],"our":[61],"results":[62],"by":[63],"characterizing":[64],"the":[65],"gradings":[67],"number":[70],"monads,":[72],"for":[73,89],"which":[74],"C":[75],"endofunctors":[77],"with":[78],"composition.":[79],"also":[81],"we":[84],"can":[85],"obtain":[86],"grades":[88],"algebraic":[90],"operations.":[91]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4385342924","counts_by_year":[],"updated_date":"2025-01-18T11:42:05.479531","created_date":"2023-07-29"}