Free bounded archimedean ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-algebras

被引：0
作者：
G. Bezhanishvili
L. Carai
P. J. Morandi
机构：
[1] New Mexico State University,Department of Mathematical Sciences
来源：
Applied Categorical Structures | 2021年 / 29卷 / 5期
关键词：
Bounded archimedean ; -algebra; Gelfand duality; Free objects; 06F25; 13J25; 06F20; 46A40; 08B20; 54C30;
D O I：
10.1007/s10485-021-09637-x
中图分类号：
学科分类号：
摘要：
We show that free objects on sets do not exist in the category baℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{ba}}\varvec{\ell }$$\end{document} of bounded archimedean ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-algebras. On the other hand, we introduce the category of weighted sets and prove that free objects on weighted sets do exist in baℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{ba}}\varvec{\ell }$$\end{document}. We conclude by discussing several consequences of this result.
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页码：879 / 888
页数：9
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