Free bounded archimedean ℓ-algebras

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

Saved in:
Bibliographic Details
Published inApplied categorical structures Vol. 29; no. 5; pp. 879 - 888
Main Authors Bezhanishvili, G., Carai, L., Morandi, P. J.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2021
Springer Nature B.V
Subjects
Convex and Discrete Geometry
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Theory of Computation
06F20
Gelfand duality
13J25
54C30
08B20
Bounded archimedean
algebra
Free objects
06F25
46A40
Online AccessGet full text

Cover

More Information
Summary:We show that free objects on sets do not exist in the category ba ℓ of bounded archimedean ℓ -algebras. On the other hand, we introduce the category of weighted sets and prove that free objects on weighted sets do exist in ba ℓ . We conclude by discussing several consequences of this result.
ISSN:0927-2852
1572-9095
DOI:10.1007/s10485-021-09637-x