{"id":"https://openalex.org/W2576157276","doi":"https://doi.org/10.1017/s0960129520000018","title":"A cubical Squier\u2019s theorem","display_name":"A cubical Squier\u2019s theorem","publication_year":2020,"publication_date":"2020-02-01","ids":{"openalex":"https://openalex.org/W2576157276","doi":"https://doi.org/10.1017/s0960129520000018","mag":"2576157276"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129520000018","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129520000018","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1612.06541","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073585078","display_name":"Maxime Lucas","orcid":"https://orcid.org/0000-0002-9680-7129"},"institutions":[{"id":"https://openalex.org/I4210130134","display_name":"Prevention of Organ Failure","ror":"https://ror.org/039j5vj89","country_code":"CA","type":"nonprofit","lineage":["https://openalex.org/I4210130134"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]},{"id":"https://openalex.org/I4210117005","display_name":"Laboratoire des Sciences du Num\u00e9rique de Nantes","ror":"https://ror.org/02snf8m58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I4210117005","https://openalex.org/I4210124215","https://openalex.org/I4210127572","https://openalex.org/I4210139971","https://openalex.org/I97188460","https://openalex.org/I97188460"]}],"countries":["CA","FR"],"is_corresponding":true,"raw_author_name":"Maxime Lucas","raw_affiliation_strings":["Inria, LS2N, Universit\u00e9 de Nantes, France","Design, study and implementation of languages for proofs and programs","Institut de Recherche en Informatique Fondamentale"],"affiliations":[{"raw_affiliation_string":"Inria, LS2N, Universit\u00e9 de Nantes, France","institution_ids":["https://openalex.org/I97188460","https://openalex.org/I4210117005"]},{"raw_affiliation_string":"Design, study and implementation of languages for proofs and programs","institution_ids":["https://openalex.org/I4210130134"]},{"raw_affiliation_string":"Institut de Recherche en Informatique Fondamentale","institution_ids":["https://openalex.org/I4210117673"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073585078"],"corresponding_institution_ids":["https://openalex.org/I4210117005","https://openalex.org/I4210117673","https://openalex.org/I4210130134","https://openalex.org/I97188460"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00216754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"2","first_page":"159","last_page":"172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9940000176429749,"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":0.9940000176429749,"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/T11567","display_name":"semigroups and automata theory","score":0.987500011920929,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9807000160217285,"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/mathematics","display_name":"Mathematics","score":0.5501785278320312},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40642961859703064}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5501785278320312},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40642961859703064}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s0960129520000018","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129520000018","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1612.06541","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.06541","pdf_url":"https://arxiv.org/pdf/1612.06541","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":"mag:2576157276","is_oa":true,"landing_page_url":"https://hal.science/hal-01662132","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"HAL (Le Centre pour la Communication Scientifique Directe)","raw_type":null},{"id":"pmh:oai:HAL:hal-04963096v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04963096","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science, 2020, 30 (2), pp.159-172. ⟨10.1017/S0960129520000018⟩","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1612.06541","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1612.06541","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1612.06541","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.06541","pdf_url":"https://arxiv.org/pdf/1612.06541","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1741900621","https://openalex.org/W1978362621","https://openalex.org/W1981049756","https://openalex.org/W2003559293","https://openalex.org/W2029200235","https://openalex.org/W2036265506","https://openalex.org/W2076580453","https://openalex.org/W2078826930","https://openalex.org/W2088405398","https://openalex.org/W2092347581","https://openalex.org/W2136213479","https://openalex.org/W2208565048","https://openalex.org/W2560894113","https://openalex.org/W4234910395","https://openalex.org/W6676577140"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2069964982","https://openalex.org/W2061531152","https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2976797620"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"homotopical":[2,15,80],"Squier\u2019s":[3,79],"theorem":[4,21,81],"relates":[5],"rewriting":[6,44],"properties":[7],"of":[8,11,17,35,78],"a":[9,12,31,36,40,55,71,75],"presentation":[10,41],"monoid":[13,37],"with":[14,42],"invariants":[16],"this":[18,47],"monoid.":[19],"This":[20],"has":[22],"since":[23],"been":[24],"extended":[25],"by":[26],"Guiraud":[27,66],"and":[28,63,67],"Malbos,":[29],"yielding":[30],"so-called":[32],"polygraphic":[33],"resolution":[34],"starting":[38],"from":[39],"suitable":[43],"properties.":[45],"In":[46],"article,":[48],"we":[49,73],"argue":[50],"that":[51],"cubical":[52,83],"categories":[53],"are":[54],"more":[56],"natural":[57],"setting":[58],"in":[59],"which":[60],"to":[61],"express":[62],"possibly":[64],"extend":[65],"Malbos":[68],"construction.":[69],"As":[70],"proof-of-concept,":[72],"give":[74],"new":[76],"proof":[77],"using":[82],"categories.":[84]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}