{"id":"https://openalex.org/W2195145082","doi":"https://doi.org/10.1007/s10485-017-9490-2","title":"The Category of Matroids","display_name":"The Category of Matroids","publication_year":2017,"publication_date":"2017-04-20","ids":{"openalex":"https://openalex.org/W2195145082","doi":"https://doi.org/10.1007/s10485-017-9490-2","mag":"2195145082"},"language":"en","primary_location":{"id":"doi:10.1007/s10485-017-9490-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-017-9490-2","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10485-017-9490-2.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"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":"Applied Categorical Structures","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs10485-017-9490-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Chris Heunen","orcid":"https://orcid.org/0000-0001-7393-2640"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Chris Heunen","raw_affiliation_strings":["University of Edinburgh, Edinburgh, UK"],"affiliations":[{"raw_affiliation_string":"University of Edinburgh, Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":null,"display_name":"Vaia Patta","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Vaia Patta","raw_affiliation_strings":["University of Oxford, Oxford, UK"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.474,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.63502966,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"2","first_page":"205","last_page":"237"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.7164999842643738,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.7164999842643738,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.07670000195503235,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.04699999839067459,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.9192000031471252},{"id":"https://openalex.org/keywords/coproduct","display_name":"Coproduct","score":0.8392000198364258},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.6700000166893005},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5770999789237976},{"id":"https://openalex.org/keywords/adjoint-functors","display_name":"Adjoint functors","score":0.4611999988555908},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.4147000014781952},{"id":"https://openalex.org/keywords/concrete-category","display_name":"Concrete category","score":0.3395000100135803},{"id":"https://openalex.org/keywords/functor-category","display_name":"Functor category","score":0.33899998664855957}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9192000031471252},{"id":"https://openalex.org/C36259021","wikidata":"https://www.wikidata.org/wiki/Q692689","display_name":"Coproduct","level":2,"score":0.8392000198364258},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7897999882698059},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.6700000166893005},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5849000215530396},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5770999789237976},{"id":"https://openalex.org/C153778094","wikidata":"https://www.wikidata.org/wiki/Q357858","display_name":"Adjoint functors","level":3,"score":0.4611999988555908},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.4147000014781952},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3691999912261963},{"id":"https://openalex.org/C128520899","wikidata":"https://www.wikidata.org/wiki/Q1575634","display_name":"Concrete category","level":3,"score":0.3395000100135803},{"id":"https://openalex.org/C48808802","wikidata":"https://www.wikidata.org/wiki/Q2007878","display_name":"Functor category","level":3,"score":0.33899998664855957},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.3292999863624573},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.290800005197525},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C99633028","wikidata":"https://www.wikidata.org/wiki/Q1442189","display_name":"Natural transformation","level":3,"score":0.27070000767707825},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.26600000262260437},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26460000872612},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.25859999656677246}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10485-017-9490-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-017-9490-2","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10485-017-9490-2.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"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":"Applied Categorical Structures","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/40fbf317-de57-4cf0-8a26-917eed053e88","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/40fbf317-de57-4cf0-8a26-917eed053e88","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Heunen, C & Patta, V 2017, 'The Category of Matroids', Applied Categorical Structures, pp. 1-33. https://doi.org/10.1007/s10485-017-9490-2","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1512.01390","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.01390","pdf_url":"https://arxiv.org/pdf/1512.01390","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:pure.ed.ac.uk:publications/40fbf317-de57-4cf0-8a26-917eed053e88","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11820/40fbf317-de57-4cf0-8a26-917eed053e88","pdf_url":"https://www.research.ed.ac.uk/en/publications/40fbf317-de57-4cf0-8a26-917eed053e88","source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"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":"Heunen, C & Patta, V 2017, 'The Category of Matroids', Applied Categorical Structures, pp. 1-33. https://doi.org/10.1007/s10485-017-9490-2","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s10485-017-9490-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-017-9490-2","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10485-017-9490-2.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"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":"Applied Categorical Structures","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1361938442","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1933864196","display_name":"DTA - University of Oxford","funder_award_id":"EP/K503113/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2417737897","display_name":null,"funder_award_id":"EP/L002388/2","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3843893429","display_name":null,"funder_award_id":"L002388","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6722386679","display_name":"Combining Viewpoints in Quantum Theory","funder_award_id":"EP/L002388/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7687705331","display_name":null,"funder_award_id":"EP/L002388/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8886761049","display_name":null,"funder_award_id":"EPSRC Fellowship","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2195145082.pdf","grobid_xml":"https://content.openalex.org/works/W2195145082.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W159585222","https://openalex.org/W1483018308","https://openalex.org/W1978376980","https://openalex.org/W2048616864","https://openalex.org/W2051751378","https://openalex.org/W2054769043","https://openalex.org/W2065504016","https://openalex.org/W2090277543","https://openalex.org/W2099599882","https://openalex.org/W2120713972","https://openalex.org/W2142015299","https://openalex.org/W2151856726","https://openalex.org/W2156361463","https://openalex.org/W2315912899","https://openalex.org/W2324284068","https://openalex.org/W2912108921","https://openalex.org/W4210276494","https://openalex.org/W4231868828","https://openalex.org/W4243479980","https://openalex.org/W4252750270","https://openalex.org/W4255288880"],"related_works":[],"abstract_inverted_index":{"The":[0],"structure":[1],"of":[2,5,28,51,91,95,97,106],"the":[3,26,33,49,98],"category":[4,50],"matroids":[6,92],"and":[7,15,30,37,62],"strong":[8],"maps":[9],"is":[10,45,55],"investigated:":[11],"it":[12],"has":[13],"coproducts":[14],"equalizers,":[16],"but":[17,78],"not":[18,79],"products":[19],"or":[20],"coequalizers;":[21],"there":[22,44,58,71],"are":[23,59,72,86],"functors":[24],"from":[25,83],"categories":[27],"graphs":[29],"vector":[31],"spaces,":[32],"latter":[34],"being":[35],"faithful":[36],"having":[38],"a":[39,46,68,89],"nearly":[40,56],"full":[41],"Kan":[42],"extension;":[43],"functor":[47],"to":[48],"geometric":[52],"lattices,":[53],"that":[54],"full;":[57],"various":[60],"adjunctions":[61],"free":[63],"constructions":[64,82],"on":[65],"subcategories,":[66],"inducing":[67],"simplification":[69],"monad;":[70],"two":[73],"orthogonal":[74],"factorization":[75],"systems;":[76],"some,":[77],"many,":[80],"combinatorial":[81],"matroid":[84],"theory":[85],"functorial.":[87],"Finally,":[88],"characterization":[90],"in":[93,104],"terms":[94,105],"optimality":[96],"greedy":[99],"algorithm":[100],"can":[101],"be":[102],"rephrased":[103],"limits.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}
