Fraïssé theory for Cuntz semigroups
Journal article, 2024

We develop a theory of Cauchy sequences and intertwinings for morphisms of Cuntz semigroups, which generalizes all past approaches to study metric-like properties of the invariant. Further, the techniques presented here can be applied to all known refinements of the Cuntz semigroup, including those that may be used in new classification results. As a particular application, we introduce a Fraïssé theory for abstract Cuntz semigroups akin to the theory of Fraïssé categories developed by Kubiś. We also show that any (Cuntz) Fraïssé category has a unique Fraïssé limit which is both universal and homogeneous. Several examples of such categories and their Fraïssé limits are given throughout the paper.

Cuntz semigroup

Fraïssé theory

Cauchy sequences

Cu-distance

Author

Laurent Cantier

Universitat Autonoma de Barcelona (UAB)

Czech Academy of Sciences

Eduard Vilalta Vila

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of Algebra

0021-8693 (ISSN) 1090-266X (eISSN)

Vol. 658 319-364

Subject Categories

Algebra and Logic

DOI

10.1016/j.jalgebra.2024.05.052

More information

Latest update

7/16/2024