{"id":"https://openalex.org/W2965079939","doi":"https://doi.org/10.1109/lics.2019.8785687","title":"Describing free $\\omega$ -categories","display_name":"Describing free $\\omega$ -categories","publication_year":2019,"publication_date":"2019-06-01","ids":{"openalex":"https://openalex.org/W2965079939","doi":"https://doi.org/10.1109/lics.2019.8785687","mag":"2965079939"},"language":"en","primary_location":{"id":"doi:10.1109/lics.2019.8785687","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2019.8785687","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056266268","display_name":"Simon Forest","orcid":"https://orcid.org/0000-0003-4311-1678"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"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"]},{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Simon Forest","raw_affiliation_strings":["Ecole Polytechnique and Univcrsit\u00e9 Paris Diderot"],"affiliations":[{"raw_affiliation_string":"Ecole Polytechnique and Univcrsit\u00e9 Paris Diderot","institution_ids":["https://openalex.org/I169173203","https://openalex.org/I142476485","https://openalex.org/I204730241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071277319","display_name":"Samuel Mimram","orcid":"https://orcid.org/0000-0002-0767-2569"},"institutions":[{"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":false,"raw_author_name":"Samuel Mimram","raw_affiliation_strings":["Ecole Polytechnique"],"affiliations":[{"raw_affiliation_string":"Ecole Polytechnique","institution_ids":["https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056266268"],"corresponding_institution_ids":["https://openalex.org/I142476485","https://openalex.org/I169173203","https://openalex.org/I204730241"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19342962,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9993000030517578,"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":0.9993000030517578,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.988099992275238,"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"}},{"id":"https://openalex.org/T10420","display_name":"Intracranial Aneurysms: Treatment and Complications","score":0.9754999876022339,"subfield":{"id":"https://openalex.org/subfields/2728","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generality","display_name":"Generality","score":0.8043456077575684},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.6789606809616089},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.6224308609962463},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6208427548408508},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5765224099159241},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5728732943534851},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.4890347421169281},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4870160222053528},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4672059416770935},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40283939242362976},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3466981053352356}],"concepts":[{"id":"https://openalex.org/C2780767217","wikidata":"https://www.wikidata.org/wiki/Q5532421","display_name":"Generality","level":2,"score":0.8043456077575684},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.6789606809616089},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.6224308609962463},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6208427548408508},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5765224099159241},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5728732943534851},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.4890347421169281},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4870160222053528},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4672059416770935},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40283939242362976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3466981053352356},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lics.2019.8785687","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2019.8785687","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1538154182","https://openalex.org/W1568306369","https://openalex.org/W1983574799","https://openalex.org/W2076580453","https://openalex.org/W2118288032","https://openalex.org/W2137843891","https://openalex.org/W2154941532","https://openalex.org/W2211918953","https://openalex.org/W3002563859","https://openalex.org/W4234758456","https://openalex.org/W4288558681","https://openalex.org/W4293389194","https://openalex.org/W4294334811","https://openalex.org/W6631982137","https://openalex.org/W6634130761","https://openalex.org/W6677818150","https://openalex.org/W6688889868"],"related_works":["https://openalex.org/W2045049461","https://openalex.org/W1978893398","https://openalex.org/W2201908702","https://openalex.org/W4381094582","https://openalex.org/W2369625323","https://openalex.org/W2364579609","https://openalex.org/W1977906818","https://openalex.org/W1522139108","https://openalex.org/W2951667359","https://openalex.org/W2010795980"],"abstract_inverted_index":{"The":[0],"notion":[1,57],"of":[2,10,18,70,86,98,106,152],"pasting":[3,33],"diagram":[4,34],"is":[5,24,40,92],"central":[6],"in":[7,58,100,130],"the":[8,22,44,68,87,104,121,140],"study":[9],"strict":[11],"\u03c9":[12],"-categories:":[13],"it":[14,50],"encodes":[15],"a":[16,32,107,127,135,149],"collection":[17],"morphisms":[19],"for":[20],"which":[21,39,95,144],"composition":[23],"defined":[25],"unambiguously.":[26],"As":[27],"such,":[28],"we":[29,112,133],"expect":[30],"that":[31,115,138],"itself":[35],"describes":[36],"an":[37],"\u03c9-category":[38],"freely":[41],"generated":[42],"by":[43,125],"cells":[45,99],"constituting":[46],"it.":[47],"In":[48,109],"practice,":[49],"seems":[51],"very":[52],"difficult":[53],"to":[54,74,102],"characterize":[55],"this":[56,110],"full":[59],"generality":[60],"and":[61,77,143],"various":[62],"definitions":[63],"have":[64],"been":[65],"proposed":[66],"with":[67],"aim":[69],"being":[71],"reasonably":[72],"easy":[73],"compute":[75],"with,":[76],"including":[78],"common":[79],"examples":[80],"(e.g.":[81],"cubes":[82],"or":[83],"orientals).":[84],"One":[85],"most":[88],"tractable":[89],"such":[90],"structure":[91],"parity":[93,116,153],"complexes,":[94],"uses":[96],"sets":[97],"order":[101],"represent":[103],"boundaries":[105],"cell.":[108],"work,":[111],"first":[113],"show":[114],"complexes":[117],"do":[118],"not":[119],"satisfy":[120],"aforementioned":[122],"freeness":[123,141],"property":[124,142],"providing":[126],"mechanized":[128],"proof":[129],"Agda.":[131],"Then,":[132],"propose":[134],"new":[136],"formalism":[137],"satisfies":[139],"can":[145],"be":[146],"seen":[147],"as":[148],"corrected":[150],"version":[151],"complexes.":[154]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
