{"id":"https://openalex.org/W7204925789","doi":"https://doi.org/10.48550/arxiv.2608.31020","title":"Semiorthogonal decompositions of stable $\\infty$-categories","display_name":"Semiorthogonal decompositions of stable $\\infty$-categories","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204925789","doi":"https://doi.org/10.48550/arxiv.2608.31020"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.31020","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31020","pdf_url":"https://arxiv.org/pdf/2608.31020","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/2608.31020","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148841853","display_name":"Rio Haeussler Albi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Albi, Rio Haeussler","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5148841853"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.7515000104904175,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.7515000104904175,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.22849999368190765,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.014100000262260437,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semiorthogonal-decompositions","display_name":"semiorthogonal decompositions","score":0.9980000257492065},{"id":"https://openalex.org/keywords/stable-infinity-categories","display_name":"stable infinity-categories","score":0.8769999742507935},{"id":"https://openalex.org/keywords/reconstruction-theorem","display_name":"reconstruction theorem","score":0.9419999718666077},{"id":"https://openalex.org/keywords/projective-space","display_name":"projective space","score":0.8230000138282776},{"id":"https://openalex.org/keywords/derived-categories","display_name":"derived categories","score":0.40700000524520874}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7103000283241272},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6758000254631042},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.48559999465942383},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.3901999890804291},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.382099986076355},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3643999993801117},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3573000133037567},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34310001134872437},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25760000944137573},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2542000114917755},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.31020","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31020","pdf_url":"https://arxiv.org/pdf/2608.31020","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.2608.31020","doi":"https://doi.org/10.48550/arxiv.2608.31020","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.31020","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:2608.31020","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31020","pdf_url":"https://arxiv.org/pdf/2608.31020","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/W7204925789.pdf","grobid_xml":"https://content.openalex.org/works/W7204925789.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W8598270","https://openalex.org/W1680171265","https://openalex.org/W2144392866","https://openalex.org/W2218836616","https://openalex.org/W2900255252","https://openalex.org/W2982444608","https://openalex.org/W4400539933","https://openalex.org/W4414828909"],"related_works":["https://openalex.org/W4221159340","https://openalex.org/W4390529179","https://openalex.org/W3197454857","https://openalex.org/W2144392866","https://openalex.org/W2888575907","https://openalex.org/W4416541317","https://openalex.org/W4281388924","https://openalex.org/W7098939868","https://openalex.org/W2045214724","https://openalex.org/W7215947953"],"abstract_inverted_index":{"We":[0,87],"define":[1],"semiorthogonal":[2,14,43,67],"decompositions":[3,15,44],"of":[4,7,13,27,50,77,94,102],"stable":[5,36,71],"$\\infty$-categories":[6,28],"length":[8],"$n$,":[9],"extending":[10],"the":[11,74,82,92],"theory":[12],"presented":[16],"in":[17,35,91],"arXiv:2106.02873.":[18],"Prior":[19],"to":[20,32,41,98],"this,":[21],"we":[22,61],"explicitly":[23],"construct":[24],"an":[25],"equivalence":[26],"relating":[29],"Waldhausen":[30],"diagrams":[31],"coherent":[33],"complexes":[34],"$\\infty$-categories.":[37],"This":[38],"allows":[39],"us":[40],"view":[42],"from":[45],"two":[46],"different":[47],"perspectives,":[48],"each":[49],"which":[51],"has":[52],"its":[53,85],"unique":[54],"advantages":[55],"and":[56],"disadvantages.":[57],"Under":[58],"mild":[59],"conditions,":[60],"prove":[62],"a":[63,70,78,100],"reconstruction":[64,90,101],"theorem":[65],"for":[66],"decompositions,":[68],"recovering":[69],"$\\infty$-category":[72],"as":[73],"(op)lax":[75],"limit":[76],"diagram":[79],"formed":[80],"by":[81],"subcategories":[83],"constituting":[84],"decomposition.":[86],"apply":[88],"this":[89],"case":[93],"Beilinson's":[95],"exceptional":[96],"collection,":[97],"obtain":[99],"$D^b(\\text{Coh}(\\mathbb{P}^n))$.":[103]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
