{"id":"https://openalex.org/W4411716326","doi":"https://doi.org/10.1007/s10485-025-09817-z","title":"Higher Catoids, Higher Quantales and their Correspondences","display_name":"Higher Catoids, Higher Quantales and their Correspondences","publication_year":2025,"publication_date":"2025-06-27","ids":{"openalex":"https://openalex.org/W4411716326","doi":"https://doi.org/10.1007/s10485-025-09817-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10485-025-09817-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-025-09817-z","pdf_url":null,"source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10485-025-09817-z","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059622355","display_name":"Cameron Calk","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Cameron Calk","raw_affiliation_strings":["LIX, CNRS, \u00c9cole polytechnique, Institut Polytechnique de Paris, Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIX, CNRS, \u00c9cole polytechnique, Institut Polytechnique de Paris, Palaiseau, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I142476485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063718422","display_name":"Philippe Malbos","orcid":"https://orcid.org/0000-0003-4449-0091"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Philippe Malbos","raw_affiliation_strings":["Institut Camille Jordan, UMR5208, CNRS, Universit\u00e9 Claude Bernard Lyon 1, Villeurbanne, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Camille Jordan, UMR5208, CNRS, Universit\u00e9 Claude Bernard Lyon 1, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210104796"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084356882","display_name":"Damien Pous","orcid":"https://orcid.org/0000-0002-1220-4399"},"institutions":[{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Damien Pous","raw_affiliation_strings":["LIP, CNRS, ENS de Lyon, Lyon, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP, CNRS, ENS de Lyon, Lyon, France","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004734550","display_name":"Georg Struth","orcid":"https://orcid.org/0000-0001-9466-7815"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["FR","GB"],"is_corresponding":true,"raw_author_name":"Georg Struth","raw_affiliation_strings":["Collegium de Lyon, Universit\u00e9 de Lyon, Lyon, France","Department of Computer Science, University of Sheffield, Sheffield, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Collegium de Lyon, Universit\u00e9 de Lyon, Lyon, France","institution_ids":["https://openalex.org/I100532134"]},{"raw_affiliation_string":"Department of Computer Science, University of Sheffield, Sheffield, UK","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5004734550","https://openalex.org/A5059622355","https://openalex.org/A5063718422","https://openalex.org/A5084356882"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I4210104796","https://openalex.org/I91136226"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":{"value":3290,"currency":"USD","value_usd":3290},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07792732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12748","display_name":"Molecular spectroscopy and chirality","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12748","display_name":"Molecular spectroscopy and chirality","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9811000227928162,"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":0.9671000242233276,"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":0.3989963233470917}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3989963233470917}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10485-025-09817-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-025-09817-z","pdf_url":null,"source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05409389v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05409389","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Applied Categorical Structures, 2025, 33 (4), pp.25. ⟨10.1007/s10485-025-09817-z⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10485-025-09817-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-025-09817-z","pdf_url":null,"source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3584739849","display_name":"Community of mathematics and fundamental computer science in Lyon","funder_award_id":"ANR-10-LABX-0070","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W578948905","https://openalex.org/W951121043","https://openalex.org/W1580101121","https://openalex.org/W1643571618","https://openalex.org/W1741900621","https://openalex.org/W1974090329","https://openalex.org/W1975977228","https://openalex.org/W1981049756","https://openalex.org/W1981404622","https://openalex.org/W1991748341","https://openalex.org/W1992205482","https://openalex.org/W1995530003","https://openalex.org/W2001616837","https://openalex.org/W2006006495","https://openalex.org/W2029200235","https://openalex.org/W2030227845","https://openalex.org/W2030797349","https://openalex.org/W2040661328","https://openalex.org/W2045528636","https://openalex.org/W2049894505","https://openalex.org/W2076580453","https://openalex.org/W2077270594","https://openalex.org/W2088405398","https://openalex.org/W2092347581","https://openalex.org/W2096490078","https://openalex.org/W2099163661","https://openalex.org/W2154941532","https://openalex.org/W2315064349","https://openalex.org/W2574983198","https://openalex.org/W2595681828","https://openalex.org/W2777301030","https://openalex.org/W2963586432","https://openalex.org/W3004605428","https://openalex.org/W3004734796","https://openalex.org/W3038132642","https://openalex.org/W3099575900","https://openalex.org/W3099900407","https://openalex.org/W3103638436","https://openalex.org/W3116169907","https://openalex.org/W3144697355","https://openalex.org/W3200330456","https://openalex.org/W3205026340","https://openalex.org/W3209423998","https://openalex.org/W4206519031","https://openalex.org/W4240175364","https://openalex.org/W4241603199","https://openalex.org/W4313258554","https://openalex.org/W4322007845","https://openalex.org/W4399711528","https://openalex.org/W4402489425","https://openalex.org/W4408515792","https://openalex.org/W7071626199"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"We":[1,28,50,76,110],"introduce":[2,30],"$$\\omega":[3,10,31,37,55,60,142,147,160],"$$":[4,11,32,38,56,61,143,148,161],"-catoids":[5,57],"as":[6],"generalisations":[7],"of":[8,141],"(strict)":[9],"-categories":[12],"and":[13,58,72,91,105,128,139,146],"in":[14,25,47,107,167],"particular":[15],"the":[16,36,136,153],"higher":[17],"path":[18],"categories":[19],"generated":[20],"by":[21],"computads":[22],"or":[23],"polygraphs":[24],"higher-dimensional":[26,48,108],"rewriting.":[27,49,109],"also":[29,111],"-quantales":[33],"that":[34],"generalise":[35],"-Kleene":[39,131,144,162],"algebras":[40,163],"recently":[41],"proposed":[42],"for":[43,123,159],"algebraic":[44],"coherence":[45],"proofs":[46,106],"then":[51],"establish":[52],"correspondences":[53,79],"between":[54,69],"convolution":[59,92],"-quantales.":[62],"These":[63,133],"are":[64],"related":[65],"to":[66,80,101,114],"J\u00f3nsson-Tarski-style":[67],"dualisms":[68],"relational":[70],"structures":[71],"lattices":[73],"with":[74,84],"operators.":[75],"extend":[77],"these":[78],"$$(\\omega,p)$$":[81,93],"-catoids,":[82,119],"catoids":[83],"a":[85],"groupoid":[86],"structure":[87],"above":[88,98],"some":[89,99],"dimension,":[90],"-quantales,":[94],"using":[95],"Dedekind":[96],"quantales":[97],"dimension":[100],"capture":[102],"homotopic":[103],"constructions":[104,134],"specialise":[112],"them":[113],"finitely":[115],"decomposable":[116],"$$(\\omega,":[117,125,129],"p)$$":[118,126,130],"an":[120,168],"appropriate":[121],"setting":[122],"defining":[124],"-semirings":[127],"algebras.":[132],"support":[135],"systematic":[137],"development":[138],"justification":[140],"algebra":[145],"-quantale":[149],"axioms,":[150],"improving":[151],"on":[152],"recent":[154],"approach":[155],"mentioned,":[156],"where":[157],"axioms":[158],"have":[164],"been":[165],"introduced":[166],"ad":[169],"hoc":[170],"fashion.":[171]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}