Fra\"iss\'e Theory for Cuntz semigroups

TL;DR

This paper develops a Fra"issé theory for Cuntz semigroups, establishing the existence and uniqueness of universal, homogeneous limits within this category, and provides concrete examples and computations.

Contribution

It introduces a Fra"issé framework for Cuntz semigroups, extending the theory to this algebraic setting and analyzing their limits and properties.

Findings

Existence and uniqueness of Fra"isse9 limits for Cuntz semigroups

Construction of examples and explicit computation of limits

Development of a general theory of Cauchy sequences in Cu category

Abstract

We introduce a Fra\"iss\'e theory for abstract Cuntz semigroups akin to the theory of Fra\"iss\'e categories developed by Kubi\'s. In particular, we show that any (Cuntz) Fra\"iss\'e category has a unique Fra\"iss\'e limit which is both universal and homogeneous. We also give several examples of such categories and compute their Fra\"iss\'e limits. During our investigations, we develop a general theory of Cauchy sequences and intertwinings in the category Cu.