Induced and higher-dimensional stable independence

TL;DR

This paper extends the theory of stable independence in accessible categories, showing how it can be transferred and applied to categories of groups and modules, and linking it to higher-dimensional independence.

Contribution

It provides new technical conditions for transferring stable independence notions and connects these to higher-dimensional independence in accessible categories.

Findings

Stable independence can be transferred from subcategories to entire categories.

Applications to categories of groups and modules extend previous results.

Stable independence implies higher-dimensional independence under certain hypotheses.

Abstract

We provide several crucial technical extensions of the theory of stable independence notions in accessible categories. In particular, we describe circumstances under which a stable independence notion can be transferred from a subcategory to a category as a whole, and examine a number of applications to categories of groups and modules, extending results of [MAa]. We prove, too, that under the hypotheses of [LRV], a stable independence notion immediately yields higher-dimensional independence as in [SV].