{"id":"https://openalex.org/W4399766563","doi":"https://doi.org/10.1007/s10208-024-09660-z","title":"Koszul Complexes and Relative Homological Algebra of Functors Over Posets","display_name":"Koszul Complexes and Relative Homological Algebra of Functors Over Posets","publication_year":2024,"publication_date":"2024-06-18","ids":{"openalex":"https://openalex.org/W4399766563","doi":"https://doi.org/10.1007/s10208-024-09660-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-024-09660-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09660-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09660-z.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09660-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102765156","display_name":"Wojciech Chach\u00f3lski","orcid":"https://orcid.org/0000-0001-5459-3161"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Wojciech Chach\u00f3lski","raw_affiliation_strings":["Mathematics, KTH, S-10044, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics, KTH, S-10044, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000234111","display_name":"Andrea Guidolin","orcid":"https://orcid.org/0000-0002-7397-475X"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Andrea Guidolin","raw_affiliation_strings":["Mathematics, KTH, S-10044, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics, KTH, S-10044, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075516604","display_name":"Isaac Ren","orcid":"https://orcid.org/0000-0002-3898-7758"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Isaac Ren","raw_affiliation_strings":["Mathematics, KTH, S-10044, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics, KTH, S-10044, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049927421","display_name":"Martina Scolamiero","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Martina Scolamiero","raw_affiliation_strings":["Mathematics, KTH, S-10044, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics, KTH, S-10044, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046727410","display_name":"Francesca Tombari","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Francesca Tombari","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, 04103, Leipzig, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, 04103, Leipzig, Germany","institution_ids":["https://openalex.org/I4210119712","https://openalex.org/I4210091327"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102765156"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.7543,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85733786,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"25","issue":"4","first_page":"1121","last_page":"1165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"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":0.9994999766349792,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.8681398630142212},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.7998104095458984},{"id":"https://openalex.org/keywords/homological-algebra","display_name":"Homological algebra","score":0.6993488669395447},{"id":"https://openalex.org/keywords/star-product","display_name":"Star product","score":0.6592048406600952},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47786420583724976},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42758089303970337}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8681398630142212},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.7998104095458984},{"id":"https://openalex.org/C18364862","wikidata":"https://www.wikidata.org/wiki/Q579978","display_name":"Homological algebra","level":3,"score":0.6993488669395447},{"id":"https://openalex.org/C195800304","wikidata":"https://www.wikidata.org/wiki/Q7601281","display_name":"Star product","level":2,"score":0.6592048406600952},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47786420583724976},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42758089303970337}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10208-024-09660-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09660-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09660-z.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:500904","is_oa":true,"landing_page_url":"http://doi.org/10.1007/s10208-024-09660-z>).","pdf_url":"https://eprints.soton.ac.uk/500904/1/s10208-024-09660-z.pdf","source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"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":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10208-024-09660-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09660-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09660-z.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4099999964237213,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G2677657595","display_name":"Multiple manifestations of genetic and non-genetic factors in Multiple Sclerosis disentangled with a multi-omics approach to accelerate personalised medicine","funder_award_id":"733161","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"},{"id":"https://openalex.org/F4320322509","display_name":"Kungliga Tekniska H\u00f6gskolan","ror":"https://ror.org/026vcq606"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4399766563.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W2028714634","https://openalex.org/W2044762734","https://openalex.org/W2093890854","https://openalex.org/W2167309931","https://openalex.org/W2912734548","https://openalex.org/W2942078528","https://openalex.org/W2946406480","https://openalex.org/W3118771332","https://openalex.org/W3196000381","https://openalex.org/W4300662053","https://openalex.org/W4312125038","https://openalex.org/W4362635828","https://openalex.org/W4379925081","https://openalex.org/W4391141186"],"related_works":["https://openalex.org/W2142802962","https://openalex.org/W237654051","https://openalex.org/W4288266587","https://openalex.org/W4285708448","https://openalex.org/W3027723005","https://openalex.org/W4299915272","https://openalex.org/W3151921236","https://openalex.org/W246737983","https://openalex.org/W4205352103","https://openalex.org/W3213901698"],"abstract_inverted_index":{"Abstract":[0],"Under":[1],"certain":[2],"conditions,":[3],"Koszul":[4,78],"complexes":[5,79],"can":[6],"be":[7],"used":[8],"to":[9,76],"calculate":[10],"relative":[11,29,32,59,85],"Betti":[12,49,86],"diagrams":[13,50],"of":[14,26,35,46,54,73,95],"vector":[15],"space-valued":[16],"functors":[17,39,56,74],"indexed":[18],"by":[19,42],"a":[20,90],"poset,":[21],"without":[22],"the":[23,52,70,84,93],"explicit":[24,77],"computation":[25,94],"global":[27],"minimal":[28,58],"resolutions.":[30,60],"In":[31,61],"homological":[33],"algebra":[34],"such":[36],"functors,":[37],"free":[38],"are":[40,83],"replaced":[41],"an":[43],"arbitrary":[44],"family":[45,72],"functors.":[47],"Relative":[48],"encode":[51],"multiplicities":[53],"these":[55,96],"in":[57],"this":[62],"article":[63],"we":[64],"provide":[65],"conditions":[66],"under":[67],"which":[68],"grading":[69],"chosen":[71],"leads":[75],"whose":[80],"homology":[81],"dimensions":[82],"diagrams,":[87],"thus":[88],"giving":[89],"scheme":[91],"for":[92],"numerical":[97],"descriptors.":[98]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}