{"id":"https://openalex.org/W4415134457","doi":"https://doi.org/10.48550/arxiv.2506.02759","title":"The algebraic small object argument as a saturation","display_name":"The algebraic small object argument as a saturation","publication_year":2025,"publication_date":"2025-06-03","ids":{"openalex":"https://openalex.org/W4415134457","doi":"https://doi.org/10.48550/arxiv.2506.02759"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2506.02759","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.02759","pdf_url":"https://arxiv.org/pdf/2506.02759","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.02759","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011551684","display_name":"Evan Cavallo","orcid":"https://orcid.org/0000-0001-8174-7496","observed_orcids":["https://orcid.org/0000-0001-8174-7496"]},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Cavallo, Evan","raw_affiliation_strings":["University of Gothenburg and Chalmers University of Technology , Gothenburg , Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Gothenburg and Chalmers University of Technology , Gothenburg , Sweden","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103055014","display_name":"Christian Sattler","orcid":"https://orcid.org/0000-0001-6374-4427","observed_orcids":["https://orcid.org/0000-0001-6374-4427"]},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Sattler, Christian","raw_affiliation_strings":["University of Gothenburg and Chalmers University of Technology , Gothenburg , Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Gothenburg and Chalmers University of Technology , Gothenburg , Sweden","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"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":0.9613999724388123,"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":0.9613999724388123,"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":0.024800000712275505,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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":0.003700000001117587,"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/double-categories","display_name":"double categories","score":0.7710000276565552},{"id":"https://openalex.org/keywords/cellular-complexes","display_name":"cell complexes","score":0.6909999847412109},{"id":"https://openalex.org/keywords/free-monads","display_name":"free monads","score":0.8059999942779541},{"id":"https://openalex.org/keywords/electric-generators","display_name":"generators","score":0.38999998569488525}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7581999897956848},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5658000111579895},{"id":"https://openalex.org/C33959348","wikidata":"https://www.wikidata.org/wiki/Q1630568","display_name":"Monad (category theory)","level":3,"score":0.5529999732971191},{"id":"https://openalex.org/C182327082","wikidata":"https://www.wikidata.org/wiki/Q428290","display_name":"Algebraic closure","level":5,"score":0.5408999919891357},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.5116000175476074},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4756999909877777},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.43970000743865967},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39399999380111694},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38929998874664307},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.3221000134944916},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.2671000063419342},{"id":"https://openalex.org/C74497983","wikidata":"https://www.wikidata.org/wiki/Q1330788","display_name":"Weierstrass factorization theorem","level":3,"score":0.2572000026702881},{"id":"https://openalex.org/C89290136","wikidata":"https://www.wikidata.org/wiki/Q550791","display_name":"Algebraic extension","level":5,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2506.02759","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.02759","pdf_url":"https://arxiv.org/pdf/2506.02759","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2506.02759","doi":"https://doi.org/10.48550/arxiv.2506.02759","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.02759","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.02759","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.02759","pdf_url":"https://arxiv.org/pdf/2506.02759","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415134457.pdf","grobid_xml":"https://content.openalex.org/works/W4415134457.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1481180394","https://openalex.org/W1486673991","https://openalex.org/W1487093245","https://openalex.org/W1498879885","https://openalex.org/W1511011089","https://openalex.org/W1514512265","https://openalex.org/W1583122470","https://openalex.org/W1595870841","https://openalex.org/W1715524359","https://openalex.org/W2033824108","https://openalex.org/W2054776476","https://openalex.org/W2079655821","https://openalex.org/W2100355522","https://openalex.org/W2103976662","https://openalex.org/W2106528441","https://openalex.org/W2170071327","https://openalex.org/W2172068359","https://openalex.org/W2550513301","https://openalex.org/W2584882036","https://openalex.org/W2609662765","https://openalex.org/W2946009963","https://openalex.org/W2959217929","https://openalex.org/W2964301279","https://openalex.org/W3003698201","https://openalex.org/W3088239002","https://openalex.org/W4230387122","https://openalex.org/W4244873611","https://openalex.org/W4311759913","https://openalex.org/W4324301561","https://openalex.org/W4400105132","https://openalex.org/W4413440400","https://openalex.org/W6947580019","https://openalex.org/W7117996197"],"related_works":["https://openalex.org/W2172068359","https://openalex.org/W3014898078","https://openalex.org/W7115598006","https://openalex.org/W7095545365","https://openalex.org/W6947580019","https://openalex.org/W2357937838","https://openalex.org/W2029919605","https://openalex.org/W4413966021","https://openalex.org/W2486197487","https://openalex.org/W2502796705"],"abstract_inverted_index":{"We":[0,19],"analyze":[1],"the":[2,43,69,90,96,99],"structure":[3,78],"of":[4,36,47,89,95,98],"left":[5,23,37,85],"maps":[6,38],"in":[7,30],"algebraic":[8,15],"weak":[9],"factorization":[10],"systems":[11],"constructed":[12,27],"using":[13],"Garner's":[14,33],"small":[16,49],"object":[17,50],"argument.":[18],"find":[20],"that":[21,41],"any":[22],"map":[24],"can":[25],"be":[26],"from":[28,81],"generators":[29,82],"Bourke":[31],"and":[32,57],"double":[34],"category":[35],"by":[39],"operations":[40,46],"parallel":[42],"classical":[44],"cell-complex-forming":[45],"Quillen's":[48],"argument":[51,91],"(coproducts,":[52],"cobase":[53],"changes,":[54],"transfinite":[55],"composites,":[56],"retracts).":[58],"Our":[59],"main":[60],"theorems":[61],"are":[62],"phrased":[63],"as":[64],"\"saturation\"":[65],"principles,":[66],"which":[67],"express":[68],"closure":[70],"conditions":[71],"necessary":[72],"for":[73],"a":[74,103],"given":[75],"property":[76],"or":[77],"to":[79,83],"extend":[80],"all":[84],"maps.":[86],"The":[87],"core":[88],"is":[92],"an":[93],"analysis":[94],"construction":[97],"free":[100],"monad":[101],"on":[102],"pointed":[104],"endofunctor.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-14T00:00:00"}
