{"title":"Injectivity in the category of C(X)-algebras","authors":"Massoud Amini, Farid Behrouzi","doi":"10.1007/s13226-024-00571-x","DOIUrl":null,"url":null,"abstract":"<p>Let <i>X</i> be a compact Hausdorff space. We show the existence and uniqueness of injective envelope in the category of unital <span>\\(C(X)\\)</span>-algebras. As an application, we characterize injective objects in the category of upper semi-continuous C*-bundles.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00571-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Let X be a compact Hausdorff space. We show the existence and uniqueness of injective envelope in the category of unital \(C(X)\)-algebras. As an application, we characterize injective objects in the category of upper semi-continuous C*-bundles.
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