{"id":"https://openalex.org/W7106346309","doi":"https://doi.org/10.17863/cam.123304","title":"Hom \u03c9-categories of a computad are free","display_name":"Hom \u03c9-categories of a computad are free","publication_year":2025,"publication_date":"2025-11-20","ids":{"openalex":"https://openalex.org/W7106346309","doi":"https://doi.org/10.17863/cam.123304"},"language":"en","primary_location":{"id":"pmh:oai:www.repository.cam.ac.uk:1810/392657","doi":null,"is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/392657","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"volume":null,"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.repository.cam.ac.uk/handle/1810/392657","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Markakis, Ioannis","orcid":"https://orcid.org/0000-0001-7553-9009","observed_orcids":["https://orcid.org/0000-0001-7553-9009"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Markakis, Ioannis","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7553-9009","affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Benjamin, Thibaut","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benjamin, Thibaut","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.57345936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.9907000064849854,"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":0.9907000064849854,"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":0.0032999999821186066,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.0008999999845400453,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hom-functor","display_name":"Hom functor","score":0.9259999990463257},{"id":"https://openalex.org/keywords/suspension-functor","display_name":"suspension functor","score":0.9300000071525574},{"id":"https://openalex.org/keywords/left-adjoint","display_name":"left adjoint","score":0.7350000143051147},{"id":"https://openalex.org/keywords/higher-category-theory","display_name":"higher category theory","score":0.6480000019073486}],"concepts":[{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.8086000084877014},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7573000192642212},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6671000123023987},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5044999718666077},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49079999327659607},{"id":"https://openalex.org/C153778094","wikidata":"https://www.wikidata.org/wiki/Q357858","display_name":"Adjoint functors","level":3,"score":0.47679999470710754},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3407999873161316},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3393000066280365},{"id":"https://openalex.org/C2776055716","wikidata":"https://www.wikidata.org/wiki/Q7316893","display_name":"Retract","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3327000141143799},{"id":"https://openalex.org/C48808802","wikidata":"https://www.wikidata.org/wiki/Q2007878","display_name":"Functor category","level":3,"score":0.30239999294281006},{"id":"https://openalex.org/C155996607","wikidata":"https://www.wikidata.org/wiki/Q381725","display_name":"Exact functor","level":3,"score":0.2822999954223633},{"id":"https://openalex.org/C105341887","wikidata":"https://www.wikidata.org/wiki/Q1307987","display_name":"Suspension (topology)","level":3,"score":0.27959999442100525},{"id":"https://openalex.org/C6778880","wikidata":"https://www.wikidata.org/wiki/Q320245","display_name":"Derived functor","level":3,"score":0.2639999985694885},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:www.repository.cam.ac.uk:1810/392657","doi":null,"is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/392657","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.17863/cam.123304","doi":"https://doi.org/10.17863/cam.123304","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.123304","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:www.repository.cam.ac.uk:1810/392657","doi":null,"is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/392657","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.43086591362953186,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,27],"provide":[1],"a":[2,18,41,66,84],"new":[3],"description":[4],"of":[5,37,60,68,80,92],"the":[6,24,31,35,46,53,58,78,90],"hom":[7,32,47],"functor":[8,33,48],"on":[9,40,83],"weak":[10],"\u03c9-categories,":[11],"and":[12,70,94],"we":[13,22,56,71,87],"show":[14,29,72,88],"that":[15,21,30,73,89],"it":[16],"admits":[17],"left":[19],"adjoint":[20],"call":[23],"suspension":[25],"functor.":[26],"then":[28],"preserves":[34,77],"property":[36,79],"being":[38,81],"free":[39,82],"computad,":[42],"in":[43],"contrast":[44],"to":[45,65],"for":[49],"strict":[50],"\u03c9-categories.":[51],"Using":[52],"same":[54],"technique,":[55],"define":[57],"opposite":[59],"an":[61],"\u03c9-category":[62],"with":[63],"respect":[64],"set":[67],"dimensions,":[69],"this":[74],"construction":[75],"also":[76],"computad.":[85],"Finally,":[86],"constructions":[91],"opposites":[93],"homs":[95],"commute.":[96]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-11-23T00:00:00"}