{"title":"Tensor product in the category of effect algebras","authors":"Dominik Lachman","doi":"10.1007/s00012-026-00938-7","DOIUrl":null,"url":null,"abstract":"<div><p>We study a tensor product in the category of effect algebras and in the category of partially ordered Abelian groups with order unit. We show that the tensor product preserves all the constructions that are essentially colimits over a connected diagram. Further, we prove the construction of a universal group for an effect algebra preserves all tensor products. We establish the corresponding functor from the category of effect algebras to the category of unital Abelian po-groups as a strong monoidal functor. We note that the technique we use in establishing the result could be used in various similar situations. Finally, we show that the tensor product of effect algebras does not preserve the Riesz decomposition property, which was an open question for a while.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 3","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2026-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00938-7.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Universalis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00012-026-00938-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We study a tensor product in the category of effect algebras and in the category of partially ordered Abelian groups with order unit. We show that the tensor product preserves all the constructions that are essentially colimits over a connected diagram. Further, we prove the construction of a universal group for an effect algebra preserves all tensor products. We establish the corresponding functor from the category of effect algebras to the category of unital Abelian po-groups as a strong monoidal functor. We note that the technique we use in establishing the result could be used in various similar situations. Finally, we show that the tensor product of effect algebras does not preserve the Riesz decomposition property, which was an open question for a while.
期刊介绍：
Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.
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