Pub Date : 2023-09-20DOI: 10.1007/s00233-023-10380-z
Tim Stokes
Abstract We obtain an ESN theorem for a very general class of biunary semigroups with idempotent-valued domain and range operations, representing them in terms of small categories equipped with a suitable biaction of the identities on the category. Our results generalise the recent work of Fitzgerald and Kinyon connecting localisable semigroups to transcription categories, as well as that of Lawson linking Ehresmann semigroups to categories with Ehresmann biaction. In contrast to most approaches to ESN theorems, we do not require the categories to be ordered or for their sets of identities to possess any particular structure. Throughout, the biunary semigroups are represented using categories rather than generalised categories of any kind, and we obtain category isomorphisms between the clesses of semigroups and their associated enriched categories, rather than category equivalences. Our results cover the class of DRC-semigroups considered by Jones and Shoufeng Wang, but they also cover cases where not both congruence conditions hold, including examples such as the semigroup of binary relations on a set under demonic composition equipped with domain and range operations.
{"title":"Ehresmann–Schein–Nambooripad theorems for classes of biunary semigroups","authors":"Tim Stokes","doi":"10.1007/s00233-023-10380-z","DOIUrl":"https://doi.org/10.1007/s00233-023-10380-z","url":null,"abstract":"Abstract We obtain an ESN theorem for a very general class of biunary semigroups with idempotent-valued domain and range operations, representing them in terms of small categories equipped with a suitable biaction of the identities on the category. Our results generalise the recent work of Fitzgerald and Kinyon connecting localisable semigroups to transcription categories, as well as that of Lawson linking Ehresmann semigroups to categories with Ehresmann biaction. In contrast to most approaches to ESN theorems, we do not require the categories to be ordered or for their sets of identities to possess any particular structure. Throughout, the biunary semigroups are represented using categories rather than generalised categories of any kind, and we obtain category isomorphisms between the clesses of semigroups and their associated enriched categories, rather than category equivalences. Our results cover the class of DRC-semigroups considered by Jones and Shoufeng Wang, but they also cover cases where not both congruence conditions hold, including examples such as the semigroup of binary relations on a set under demonic composition equipped with domain and range operations.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-13DOI: 10.1007/s00233-023-10381-y
Bruce Ebanks
{"title":"Levi-Civita functional equations on commutative monoids with tractable prime ideals","authors":"Bruce Ebanks","doi":"10.1007/s00233-023-10381-y","DOIUrl":"https://doi.org/10.1007/s00233-023-10381-y","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135733977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-22DOI: 10.1007/s00233-023-10375-w
Jukkrit Daengsaen, S. Leeratanavalee
{"title":"Semilattices of simple and regular n-ary semigroups","authors":"Jukkrit Daengsaen, S. Leeratanavalee","doi":"10.1007/s00233-023-10375-w","DOIUrl":"https://doi.org/10.1007/s00233-023-10375-w","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42258148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-18DOI: 10.1007/s00233-023-10376-9
B. M. Vernikov
{"title":"Book review of “Advances in the theory of varieties of semigroups” by Edmond W. H. Lee","authors":"B. M. Vernikov","doi":"10.1007/s00233-023-10376-9","DOIUrl":"https://doi.org/10.1007/s00233-023-10376-9","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44264445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.1007/s00233-023-10368-9
Fardin Amini, S. Saeidi
{"title":"Pettis-integration approach for characterizing almost periodic functions and flows","authors":"Fardin Amini, S. Saeidi","doi":"10.1007/s00233-023-10368-9","DOIUrl":"https://doi.org/10.1007/s00233-023-10368-9","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"107 1","pages":"1 - 16"},"PeriodicalIF":0.7,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46386598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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