{"id":"https://openalex.org/W4416240788","doi":"https://doi.org/10.1007/s10485-025-09836-w","title":"An Overview of Colax and Virtual Double Categories","display_name":"An Overview of Colax and Virtual Double Categories","publication_year":2025,"publication_date":"2025-11-15","ids":{"openalex":"https://openalex.org/W4416240788","doi":"https://doi.org/10.1007/s10485-025-09836-w"},"language":"en","primary_location":{"id":"doi:10.1007/s10485-025-09836-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10485-025-09836-w","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008811217","display_name":"Marco Grandis","orcid":null},"institutions":[{"id":"https://openalex.org/I83816512","display_name":"University of Genoa","ror":"https://ror.org/0107c5v14","country_code":"IT","type":"education","lineage":["https://openalex.org/I83816512"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Marco Grandis","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Genova, 16146, Genova, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Genova, 16146, Genova, Italy","institution_ids":["https://openalex.org/I83816512"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008811217"],"corresponding_institution_ids":["https://openalex.org/I83816512"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.41642478,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"6","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":0.9746000170707703,"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":0.9746000170707703,"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":0.009499999694526196,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.004000000189989805,"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/homotopy","display_name":"Homotopy","score":0.5569000244140625},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.5558000206947327},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.5259000062942505},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4943999946117401},{"id":"https://openalex.org/keywords/adjoint-functors","display_name":"Adjoint functors","score":0.4867999851703644},{"id":"https://openalex.org/keywords/finitary","display_name":"Finitary","score":0.4169999957084656},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.40939998626708984},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.3970000147819519}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7803999781608582},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5735999941825867},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.5569000244140625},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.5558000206947327},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.5259000062942505},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4943999946117401},{"id":"https://openalex.org/C153778094","wikidata":"https://www.wikidata.org/wiki/Q357858","display_name":"Adjoint functors","level":3,"score":0.4867999851703644},{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.4169999957084656},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.40939998626708984},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.3970000147819519},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3955000042915344},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.38089999556541443},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C2780580338","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Adjunction","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C48808802","wikidata":"https://www.wikidata.org/wiki/Q2007878","display_name":"Functor category","level":3,"score":0.319599986076355},{"id":"https://openalex.org/C99633028","wikidata":"https://www.wikidata.org/wiki/Q1442189","display_name":"Natural transformation","level":3,"score":0.30309998989105225},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C75328951","wikidata":"https://www.wikidata.org/wiki/Q17008126","display_name":"Double groupoid","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C36259021","wikidata":"https://www.wikidata.org/wiki/Q692689","display_name":"Coproduct","level":2,"score":0.27059999108314514}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10485-025-09836-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10485-025-09836-w","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W136934826","https://openalex.org/W158035142","https://openalex.org/W1677393765","https://openalex.org/W2103988001","https://openalex.org/W2962766827","https://openalex.org/W4210927122","https://openalex.org/W4212902885","https://openalex.org/W4239283511","https://openalex.org/W4243241156","https://openalex.org/W4393965016","https://openalex.org/W4403557103","https://openalex.org/W4403886602"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-28T09:03:24.017778","created_date":"2025-11-15T00:00:00"}
