{"id":"https://openalex.org/W1517326308","doi":"https://doi.org/10.1007/978-0-387-34735-6_20","title":"Completing Categorical Algebras","display_name":"Completing Categorical Algebras","publication_year":2006,"publication_date":"2006-12-14","ids":{"openalex":"https://openalex.org/W1517326308","doi":"https://doi.org/10.1007/978-0-387-34735-6_20","mag":"1517326308"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-34735-6_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-34735-6_20","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-34735-6_20.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-34735-6_20.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050710436","display_name":"Stephen L. Bloom","orcid":null},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stephen L. Bloom","raw_affiliation_strings":["Department of Computer Science, Stevens Institute of Technology, Hoboken"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Stevens Institute of Technology, Hoboken","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017293831","display_name":"Zolt\u00e1n \u00c9sik","orcid":null},"institutions":[{"id":"https://openalex.org/I227486990","display_name":"University of Szeged","ror":"https://ror.org/01pnej532","country_code":"HU","type":"education","lineage":["https://openalex.org/I227486990"]},{"id":"https://openalex.org/I55952717","display_name":"Universidad Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES","HU"],"is_corresponding":false,"raw_author_name":"Zolt\u00e1n \u00c9sik","raw_affiliation_strings":["GRLMC, Rovira i Virgili University, Tarragona, Spain","Institute for Informatics, University of Szeged, Szeged, Hungary"],"affiliations":[{"raw_affiliation_string":"GRLMC, Rovira i Virgili University, Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]},{"raw_affiliation_string":"Institute for Informatics, University of Szeged, Szeged, Hungary","institution_ids":["https://openalex.org/I227486990"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050710436"],"corresponding_institution_ids":["https://openalex.org/I108468826"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.09875483,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"231","last_page":"249"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9987000226974487,"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":0.9987000226974487,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9983999729156494,"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/T10142","display_name":"Formal Methods in Verification","score":0.9983999729156494,"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/categorical-variable","display_name":"Categorical variable","score":0.6814995408058167},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.3609832525253296},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34244826436042786},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15552347898483276}],"concepts":[{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.6814995408058167},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.3609832525253296},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34244826436042786},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15552347898483276}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-0-387-34735-6_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-34735-6_20","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-34735-6_20.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-0-387-34735-6_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-34735-6_20","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-34735-6_20.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1517326308.pdf"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W258022877","https://openalex.org/W1503973138","https://openalex.org/W1582269801","https://openalex.org/W1594900487","https://openalex.org/W1608752509","https://openalex.org/W1967390724","https://openalex.org/W1972289972","https://openalex.org/W1987134164","https://openalex.org/W1991735660","https://openalex.org/W2023022663","https://openalex.org/W2045594629","https://openalex.org/W2061786858","https://openalex.org/W2150320481","https://openalex.org/W2173961470","https://openalex.org/W2610899059","https://openalex.org/W4210249530","https://openalex.org/W4210478186","https://openalex.org/W4212873186","https://openalex.org/W4251097190","https://openalex.org/W4388310185","https://openalex.org/W6630104300"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4386799044","https://openalex.org/W2773208253","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2560646951"],"abstract_inverted_index":{"Let":[0],"\u03a3":[1,145],"be":[2],"a":[3,13,19,38,72,95,135,150,159],"ranked":[4],"set.":[5],"A":[6,33],"categorical":[7,35],"\u03a3-algebra,":[8],"c\u03a3a":[9,39,80,86,136,151,160],"for":[10,25,78],"short,":[11],"is":[12,37,61,83,134,142,149,158],"small":[14],"category":[15,73],"C":[16,22,81,87,118,122,133,141,148,157],"equipped":[17],"with":[18],"functor":[20,54],"\u03c3C:":[21],"n":[23,30],"\u2192C,":[24],"each":[26,53],"\u03c3":[27],"\u2208":[28],"\u03a3n,":[29],"\u2265":[31],"0.":[32],"continuous":[34,97],"\u03a3-algebra":[36],"which":[40,93],"has":[41],"an":[42,84,143],"initial":[43],"object":[44],"and":[45,109],"all":[46],"colimits":[47,57],"of":[48,58,66,99,105,128,137,152,161],"\u03c9-chains,":[49],"i.e.,":[50],"functors":[51],"\u2115\u2265C;":[52],"\u03c3c":[55],"preserves":[56],"\u03c9-chains.":[59],"(\u2115":[60],"the":[62,67,103,111],"linearly":[63],"ordered":[64,144],"set":[65],"nonnegative":[68],"integers":[69],"considered":[70],"as":[71,74],"usual.)We":[75],"prove":[76],"that":[77,115],"any":[79],"there":[82],"\u03c9-continuous":[85],"\u03c9,":[88],"unique":[89],"up":[90],"to":[91],"equivalence,":[92],"forms":[94],"\u201cfree":[96],"completion\u201d":[98],"C.":[100],"We":[101,124],"generalize":[102],"notion":[104],"inequation":[106],"(and":[107],"equation)":[108],"show":[110],"inequations":[112],"or":[113],"equations":[114],"hold":[116,120],"in":[117,121],"also":[119],"\u03c9.":[123],"then":[125],"find":[126],"examples":[127],"this":[129],"completion":[130],"when":[131],"-":[132,140,147,156],"finite":[138,153,162],"\u03a3-trees":[139],"algebra":[146],"A-sychronization":[154],"trees":[155],"words":[163],"on":[164],"A.":[165]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-01-15T23:16:33.117629","created_date":"2025-10-10T00:00:00"}
