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Free bounded archimedean \(\ell \)-algebras

Abstract

We show that free objects on sets do not exist in the category \({\varvec{ba}}\varvec{\ell }\) of bounded archimedean \(\ell \)-algebras. On the other hand, we introduce the category of weighted sets and prove that free objects on weighted sets do exist in \({\varvec{ba}}\varvec{\ell }\). We conclude by discussing several consequences of this result.

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Correspondence to L. Carai.

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Communicated by Jorge Picado.

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Bezhanishvili, G., Carai, L. & Morandi, P.J. Free bounded archimedean \(\ell \)-algebras. Appl Categor Struct 29, 879–888 (2021). https://doi.org/10.1007/s10485-021-09637-x

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Keywords

  • Bounded archimedean \(\ell \)-algebra
  • Gelfand duality
  • Free objects

Mathematics Subject Classification

  • 06F25
  • 13J25
  • 06F20
  • 46A40
  • 08B20
  • 54C30