{"title":"逆半群正交作用的极大序Groupoid和Galois对应","authors":"Wesley G. Lautenschlaeger, Thaísa Tamusiunas","doi":"10.1007/s10485-023-09742-z","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce maximal ordered groupoids and study some of their properties. Also, we use the Ehresmann–Schein–Nambooripad Theorem, which establishes a one-to-one correspondence between inverse semigroups and a class of ordered groupoids, to prove a Galois correspondence for the case of inverse semigroups acting orthogonally on commutative rings.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maximal Ordered Groupoids and a Galois Correspondence for Inverse Semigroup Orthogonal Actions\",\"authors\":\"Wesley G. Lautenschlaeger, Thaísa Tamusiunas\",\"doi\":\"10.1007/s10485-023-09742-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce maximal ordered groupoids and study some of their properties. Also, we use the Ehresmann–Schein–Nambooripad Theorem, which establishes a one-to-one correspondence between inverse semigroups and a class of ordered groupoids, to prove a Galois correspondence for the case of inverse semigroups acting orthogonally on commutative rings.</p></div>\",\"PeriodicalId\":7952,\"journal\":{\"name\":\"Applied Categorical Structures\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Categorical Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10485-023-09742-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Categorical Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10485-023-09742-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Maximal Ordered Groupoids and a Galois Correspondence for Inverse Semigroup Orthogonal Actions
We introduce maximal ordered groupoids and study some of their properties. Also, we use the Ehresmann–Schein–Nambooripad Theorem, which establishes a one-to-one correspondence between inverse semigroups and a class of ordered groupoids, to prove a Galois correspondence for the case of inverse semigroups acting orthogonally on commutative rings.
期刊介绍：
Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant.
Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.
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