{"title":"Flatness properties of acts over semigroups","authors":"V. Laan, Ülo Reimaa, L. Tart, Elery Teor","doi":"10.52547/cgasa.15.1.59","DOIUrl":null,"url":null,"abstract":"In this paper we study flatness properties (pullback flatness, limit flatness, finite limit flatness) of acts over semigroups. These are defined by requiring preservation of certain limits from the functor of tensor multiplication by a given act. We give a description of firm pullback flat acts using Conditions (P) and (E). We also study pure epimorphisms and their connections to finitely presented acts and pullback flat acts. We study these flatness properties in the category of all acts, as well as in the category of unitary acts and in the category of firm acts, which arise naturally in the Morita theory of semigroups.","PeriodicalId":41919,"journal":{"name":"Categories and General Algebraic Structures with Applications","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Categories and General Algebraic Structures with Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52547/cgasa.15.1.59","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper we study flatness properties (pullback flatness, limit flatness, finite limit flatness) of acts over semigroups. These are defined by requiring preservation of certain limits from the functor of tensor multiplication by a given act. We give a description of firm pullback flat acts using Conditions (P) and (E). We also study pure epimorphisms and their connections to finitely presented acts and pullback flat acts. We study these flatness properties in the category of all acts, as well as in the category of unitary acts and in the category of firm acts, which arise naturally in the Morita theory of semigroups.
期刊介绍：
Categories and General Algebraic Structures with Applications is an international journal published by Shahid Beheshti University, Tehran, Iran, free of page charges. It publishes original high quality research papers and invited research and survey articles mainly in two subjects: Categories (algebraic, topological, and applications in mathematics and computer sciences) and General Algebraic Structures (not necessarily classical algebraic structures, but universal algebras such as algebras in categories, semigroups, their actions, automata, ordered algebraic structures, lattices (of any kind), quasigroups, hyper universal algebras, and their applications.
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